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isl_union_set_compute_schedule: make preference for large bands configurable
[isl.git] / isl_polynomial.c
blob524aa6fe2649b388df3f82d3f490151d354028eb
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;
1025
1026 if (--qp->ref > 0)
1027 return;
1028
1029 isl_dim_free(qp->dim);
1030 isl_mat_free(qp->div);
1031 isl_upoly_free(qp->upoly);
1032
1033 free(qp);
1034 }
1035
1036 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1037 {
1038 int i;
1039 struct isl_upoly_rec *rec;
1040 struct isl_upoly_cst *cst;
1041
1042 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1043 if (!rec)
1044 return NULL;
1045 for (i = 0; i < 1 + power; ++i) {
1046 rec->p[i] = isl_upoly_zero(ctx);
1047 if (!rec->p[i])
1048 goto error;
1049 rec->n++;
1050 }
1051 cst = isl_upoly_as_cst(rec->p[power]);
1052 isl_int_set_si(cst->n, 1);
1053
1054 return &rec->up;
1055 error:
1056 isl_upoly_free(&rec->up);
1057 return NULL;
1058 }
1059
1060 /* r array maps original positions to new positions.
1061 */
1062 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1063 int *r)
1064 {
1065 int i;
1066 struct isl_upoly_rec *rec;
1067 struct isl_upoly *base;
1068 struct isl_upoly *res;
1069
1070 if (isl_upoly_is_cst(up))
1071 return up;
1072
1073 rec = isl_upoly_as_rec(up);
1074 if (!rec)
1075 goto error;
1076
1077 isl_assert(up->ctx, rec->n >= 1, goto error);
1078
1079 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1080 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1081
1082 for (i = rec->n - 2; i >= 0; --i) {
1083 res = isl_upoly_mul(res, isl_upoly_copy(base));
1084 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1085 }
1086
1087 isl_upoly_free(base);
1088 isl_upoly_free(up);
1089
1090 return res;
1091 error:
1092 isl_upoly_free(up);
1093 return NULL;
1094 }
1095
1096 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1097 {
1098 int n_row, n_col;
1099 int equal;
1100
1101 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1102 div1->n_col >= div2->n_col, return -1);
1103
1104 if (div1->n_row == div2->n_row)
1105 return isl_mat_is_equal(div1, div2);
1106
1107 n_row = div1->n_row;
1108 n_col = div1->n_col;
1109 div1->n_row = div2->n_row;
1110 div1->n_col = div2->n_col;
1111
1112 equal = isl_mat_is_equal(div1, div2);
1113
1114 div1->n_row = n_row;
1115 div1->n_col = n_col;
1116
1117 return equal;
1118 }
1119
1120 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1121 {
1122 int li, lj;
1123
1124 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1125 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1126
1127 if (li != lj)
1128 return li - lj;
1129
1130 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1131 }
1132
1133 struct isl_div_sort_info {
1134 isl_mat *div;
1135 int row;
1136 };
1137
1138 static int div_sort_cmp(const void *p1, const void *p2)
1139 {
1140 const struct isl_div_sort_info *i1, *i2;
1141 i1 = (const struct isl_div_sort_info *) p1;
1142 i2 = (const struct isl_div_sort_info *) p2;
1143
1144 return cmp_row(i1->div, i1->row, i2->row);
1145 }
1146
1147 /* Sort divs and remove duplicates.
1148 */
1149 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1150 {
1151 int i;
1152 int skip;
1153 int len;
1154 struct isl_div_sort_info *array = NULL;
1155 int *pos = NULL, *at = NULL;
1156 int *reordering = NULL;
1157 unsigned div_pos;
1158
1159 if (!qp)
1160 return NULL;
1161 if (qp->div->n_row <= 1)
1162 return qp;
1163
1164 div_pos = isl_dim_total(qp->dim);
1165
1166 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1167 qp->div->n_row);
1168 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1169 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1170 len = qp->div->n_col - 2;
1171 reordering = isl_alloc_array(qp->div->ctx, int, len);
1172 if (!array || !pos || !at || !reordering)
1173 goto error;
1174
1175 for (i = 0; i < qp->div->n_row; ++i) {
1176 array[i].div = qp->div;
1177 array[i].row = i;
1178 pos[i] = i;
1179 at[i] = i;
1180 }
1181
1182 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1183 div_sort_cmp);
1184
1185 for (i = 0; i < div_pos; ++i)
1186 reordering[i] = i;
1187
1188 for (i = 0; i < qp->div->n_row; ++i) {
1189 if (pos[array[i].row] == i)
1190 continue;
1191 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1192 pos[at[i]] = pos[array[i].row];
1193 at[pos[array[i].row]] = at[i];
1194 at[i] = array[i].row;
1195 pos[array[i].row] = i;
1196 }
1197
1198 skip = 0;
1199 for (i = 0; i < len - div_pos; ++i) {
1200 if (i > 0 &&
1201 isl_seq_eq(qp->div->row[i - skip - 1],
1202 qp->div->row[i - skip], qp->div->n_col)) {
1203 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1204 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1205 2 + div_pos + i - skip);
1206 qp->div = isl_mat_drop_cols(qp->div,
1207 2 + div_pos + i - skip, 1);
1208 skip++;
1209 }
1210 reordering[div_pos + array[i].row] = div_pos + i - skip;
1211 }
1212
1213 qp->upoly = reorder(qp->upoly, reordering);
1214
1215 if (!qp->upoly || !qp->div)
1216 goto error;
1217
1218 free(at);
1219 free(pos);
1220 free(array);
1221 free(reordering);
1222
1223 return qp;
1224 error:
1225 free(at);
1226 free(pos);
1227 free(array);
1228 free(reordering);
1229 isl_qpolynomial_free(qp);
1230 return NULL;
1231 }
1232
1233 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1234 int *exp, int first)
1235 {
1236 int i;
1237 struct isl_upoly_rec *rec;
1238
1239 if (isl_upoly_is_cst(up))
1240 return up;
1241
1242 if (up->var < first)
1243 return up;
1244
1245 if (exp[up->var - first] == up->var - first)
1246 return up;
1247
1248 up = isl_upoly_cow(up);
1249 if (!up)
1250 goto error;
1251
1252 up->var = exp[up->var - first] + first;
1253
1254 rec = isl_upoly_as_rec(up);
1255 if (!rec)
1256 goto error;
1257
1258 for (i = 0; i < rec->n; ++i) {
1259 rec->p[i] = expand(rec->p[i], exp, first);
1260 if (!rec->p[i])
1261 goto error;
1262 }
1263
1264 return up;
1265 error:
1266 isl_upoly_free(up);
1267 return NULL;
1268 }
1269
1270 static __isl_give isl_qpolynomial *with_merged_divs(
1271 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1272 __isl_take isl_qpolynomial *qp2),
1273 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1274 {
1275 int *exp1 = NULL;
1276 int *exp2 = NULL;
1277 isl_mat *div = NULL;
1278
1279 qp1 = isl_qpolynomial_cow(qp1);
1280 qp2 = isl_qpolynomial_cow(qp2);
1281
1282 if (!qp1 || !qp2)
1283 goto error;
1284
1285 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1286 qp1->div->n_col >= qp2->div->n_col, goto error);
1287
1288 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1289 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1290 if (!exp1 || !exp2)
1291 goto error;
1292
1293 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1294 if (!div)
1295 goto error;
1296
1297 isl_mat_free(qp1->div);
1298 qp1->div = isl_mat_copy(div);
1299 isl_mat_free(qp2->div);
1300 qp2->div = isl_mat_copy(div);
1301
1302 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1303 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1304
1305 if (!qp1->upoly || !qp2->upoly)
1306 goto error;
1307
1308 isl_mat_free(div);
1309 free(exp1);
1310 free(exp2);
1311
1312 return fn(qp1, qp2);
1313 error:
1314 isl_mat_free(div);
1315 free(exp1);
1316 free(exp2);
1317 isl_qpolynomial_free(qp1);
1318 isl_qpolynomial_free(qp2);
1319 return NULL;
1320 }
1321
1322 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1323 __isl_take isl_qpolynomial *qp2)
1324 {
1325 qp1 = isl_qpolynomial_cow(qp1);
1326
1327 if (!qp1 || !qp2)
1328 goto error;
1329
1330 if (qp1->div->n_row < qp2->div->n_row)
1331 return isl_qpolynomial_add(qp2, qp1);
1332
1333 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1334 if (!compatible_divs(qp1->div, qp2->div))
1335 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1336
1337 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1338 if (!qp1->upoly)
1339 goto error;
1340
1341 isl_qpolynomial_free(qp2);
1342
1343 return qp1;
1344 error:
1345 isl_qpolynomial_free(qp1);
1346 isl_qpolynomial_free(qp2);
1347 return NULL;
1348 }
1349
1350 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1351 __isl_keep isl_set *dom,
1352 __isl_take isl_qpolynomial *qp1,
1353 __isl_take isl_qpolynomial *qp2)
1354 {
1355 qp1 = isl_qpolynomial_add(qp1, qp2);
1356 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1357 return qp1;
1358 }
1359
1360 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1361 __isl_take isl_qpolynomial *qp2)
1362 {
1363 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1364 }
1365
1366 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1367 __isl_take isl_qpolynomial *qp, isl_int v)
1368 {
1369 if (isl_int_is_zero(v))
1370 return qp;
1371
1372 qp = isl_qpolynomial_cow(qp);
1373 if (!qp)
1374 return NULL;
1375
1376 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1377 if (!qp->upoly)
1378 goto error;
1379
1380 return qp;
1381 error:
1382 isl_qpolynomial_free(qp);
1383 return NULL;
1384
1385 }
1386
1387 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1388 {
1389 if (!qp)
1390 return NULL;
1391
1392 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1393 }
1394
1395 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1396 __isl_take isl_qpolynomial *qp, isl_int v)
1397 {
1398 if (isl_int_is_one(v))
1399 return qp;
1400
1401 if (qp && isl_int_is_zero(v)) {
1402 isl_qpolynomial *zero;
1403 zero = isl_qpolynomial_zero(isl_dim_copy(qp->dim));
1404 isl_qpolynomial_free(qp);
1405 return zero;
1406 }
1407
1408 qp = isl_qpolynomial_cow(qp);
1409 if (!qp)
1410 return NULL;
1411
1412 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1413 if (!qp->upoly)
1414 goto error;
1415
1416 return qp;
1417 error:
1418 isl_qpolynomial_free(qp);
1419 return NULL;
1420 }
1421
1422 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
1423 __isl_take isl_qpolynomial *qp, isl_int v)
1424 {
1425 return isl_qpolynomial_mul_isl_int(qp, v);
1426 }
1427
1428 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1429 __isl_take isl_qpolynomial *qp2)
1430 {
1431 qp1 = isl_qpolynomial_cow(qp1);
1432
1433 if (!qp1 || !qp2)
1434 goto error;
1435
1436 if (qp1->div->n_row < qp2->div->n_row)
1437 return isl_qpolynomial_mul(qp2, qp1);
1438
1439 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1440 if (!compatible_divs(qp1->div, qp2->div))
1441 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1442
1443 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1444 if (!qp1->upoly)
1445 goto error;
1446
1447 isl_qpolynomial_free(qp2);
1448
1449 return qp1;
1450 error:
1451 isl_qpolynomial_free(qp1);
1452 isl_qpolynomial_free(qp2);
1453 return NULL;
1454 }
1455
1456 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1457 unsigned power)
1458 {
1459 qp = isl_qpolynomial_cow(qp);
1460
1461 if (!qp)
1462 return NULL;
1463
1464 qp->upoly = isl_upoly_pow(qp->upoly, power);
1465 if (!qp->upoly)
1466 goto error;
1467
1468 return qp;
1469 error:
1470 isl_qpolynomial_free(qp);
1471 return NULL;
1472 }
1473
1474 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1475 {
1476 if (!dim)
1477 return NULL;
1478 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1479 }
1480
1481 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1482 {
1483 if (!dim)
1484 return NULL;
1485 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1486 }
1487
1488 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1489 {
1490 if (!dim)
1491 return NULL;
1492 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1493 }
1494
1495 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1496 {
1497 if (!dim)
1498 return NULL;
1499 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1500 }
1501
1502 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1503 {
1504 if (!dim)
1505 return NULL;
1506 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1507 }
1508
1509 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1510 isl_int v)
1511 {
1512 struct isl_qpolynomial *qp;
1513 struct isl_upoly_cst *cst;
1514
1515 if (!dim)
1516 return NULL;
1517
1518 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1519 if (!qp)
1520 return NULL;
1521
1522 cst = isl_upoly_as_cst(qp->upoly);
1523 isl_int_set(cst->n, v);
1524
1525 return qp;
1526 }
1527
1528 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1529 isl_int *n, isl_int *d)
1530 {
1531 struct isl_upoly_cst *cst;
1532
1533 if (!qp)
1534 return -1;
1535
1536 if (!isl_upoly_is_cst(qp->upoly))
1537 return 0;
1538
1539 cst = isl_upoly_as_cst(qp->upoly);
1540 if (!cst)
1541 return -1;
1542
1543 if (n)
1544 isl_int_set(*n, cst->n);
1545 if (d)
1546 isl_int_set(*d, cst->d);
1547
1548 return 1;
1549 }
1550
1551 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1552 {
1553 int is_cst;
1554 struct isl_upoly_rec *rec;
1555
1556 if (!up)
1557 return -1;
1558
1559 if (up->var < 0)
1560 return 1;
1561
1562 rec = isl_upoly_as_rec(up);
1563 if (!rec)
1564 return -1;
1565
1566 if (rec->n > 2)
1567 return 0;
1568
1569 isl_assert(up->ctx, rec->n > 1, return -1);
1570
1571 is_cst = isl_upoly_is_cst(rec->p[1]);
1572 if (is_cst < 0)
1573 return -1;
1574 if (!is_cst)
1575 return 0;
1576
1577 return isl_upoly_is_affine(rec->p[0]);
1578 }
1579
1580 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1581 {
1582 if (!qp)
1583 return -1;
1584
1585 if (qp->div->n_row > 0)
1586 return 0;
1587
1588 return isl_upoly_is_affine(qp->upoly);
1589 }
1590
1591 static void update_coeff(__isl_keep isl_vec *aff,
1592 __isl_keep struct isl_upoly_cst *cst, int pos)
1593 {
1594 isl_int gcd;
1595 isl_int f;
1596
1597 if (isl_int_is_zero(cst->n))
1598 return;
1599
1600 isl_int_init(gcd);
1601 isl_int_init(f);
1602 isl_int_gcd(gcd, cst->d, aff->el[0]);
1603 isl_int_divexact(f, cst->d, gcd);
1604 isl_int_divexact(gcd, aff->el[0], gcd);
1605 isl_seq_scale(aff->el, aff->el, f, aff->size);
1606 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1607 isl_int_clear(gcd);
1608 isl_int_clear(f);
1609 }
1610
1611 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1612 __isl_keep isl_vec *aff)
1613 {
1614 struct isl_upoly_cst *cst;
1615 struct isl_upoly_rec *rec;
1616
1617 if (!up || !aff)
1618 return -1;
1619
1620 if (up->var < 0) {
1621 struct isl_upoly_cst *cst;
1622
1623 cst = isl_upoly_as_cst(up);
1624 if (!cst)
1625 return -1;
1626 update_coeff(aff, cst, 0);
1627 return 0;
1628 }
1629
1630 rec = isl_upoly_as_rec(up);
1631 if (!rec)
1632 return -1;
1633 isl_assert(up->ctx, rec->n == 2, return -1);
1634
1635 cst = isl_upoly_as_cst(rec->p[1]);
1636 if (!cst)
1637 return -1;
1638 update_coeff(aff, cst, 1 + up->var);
1639
1640 return isl_upoly_update_affine(rec->p[0], aff);
1641 }
1642
1643 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1644 __isl_keep isl_qpolynomial *qp)
1645 {
1646 isl_vec *aff;
1647 unsigned d;
1648
1649 if (!qp)
1650 return NULL;
1651
1652 d = isl_dim_total(qp->dim);
1653 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1654 if (!aff)
1655 return NULL;
1656
1657 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1658 isl_int_set_si(aff->el[0], 1);
1659
1660 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1661 goto error;
1662
1663 return aff;
1664 error:
1665 isl_vec_free(aff);
1666 return NULL;
1667 }
1668
1669 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1670 __isl_keep isl_qpolynomial *qp2)
1671 {
1672 int equal;
1673
1674 if (!qp1 || !qp2)
1675 return -1;
1676
1677 equal = isl_dim_equal(qp1->dim, qp2->dim);
1678 if (equal < 0 || !equal)
1679 return equal;
1680
1681 equal = isl_mat_is_equal(qp1->div, qp2->div);
1682 if (equal < 0 || !equal)
1683 return equal;
1684
1685 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1686 }
1687
1688 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1689 {
1690 int i;
1691 struct isl_upoly_rec *rec;
1692
1693 if (isl_upoly_is_cst(up)) {
1694 struct isl_upoly_cst *cst;
1695 cst = isl_upoly_as_cst(up);
1696 if (!cst)
1697 return;
1698 isl_int_lcm(*d, *d, cst->d);
1699 return;
1700 }
1701
1702 rec = isl_upoly_as_rec(up);
1703 if (!rec)
1704 return;
1705
1706 for (i = 0; i < rec->n; ++i)
1707 upoly_update_den(rec->p[i], d);
1708 }
1709
1710 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1711 {
1712 isl_int_set_si(*d, 1);
1713 if (!qp)
1714 return;
1715 upoly_update_den(qp->upoly, d);
1716 }
1717
1718 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1719 int pos, int power)
1720 {
1721 struct isl_ctx *ctx;
1722
1723 if (!dim)
1724 return NULL;
1725
1726 ctx = dim->ctx;
1727
1728 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1729 }
1730
1731 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1732 enum isl_dim_type type, unsigned pos)
1733 {
1734 if (!dim)
1735 return NULL;
1736
1737 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1738 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1739
1740 if (type == isl_dim_set)
1741 pos += isl_dim_size(dim, isl_dim_param);
1742
1743 return isl_qpolynomial_var_pow(dim, pos, 1);
1744 error:
1745 isl_dim_free(dim);
1746 return NULL;
1747 }
1748
1749 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1750 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1751 {
1752 int i;
1753 struct isl_upoly_rec *rec;
1754 struct isl_upoly *base, *res;
1755
1756 if (!up)
1757 return NULL;
1758
1759 if (isl_upoly_is_cst(up))
1760 return up;
1761
1762 if (up->var < first)
1763 return up;
1764
1765 rec = isl_upoly_as_rec(up);
1766 if (!rec)
1767 goto error;
1768
1769 isl_assert(up->ctx, rec->n >= 1, goto error);
1770
1771 if (up->var >= first + n)
1772 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1773 else
1774 base = isl_upoly_copy(subs[up->var - first]);
1775
1776 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1777 for (i = rec->n - 2; i >= 0; --i) {
1778 struct isl_upoly *t;
1779 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1780 res = isl_upoly_mul(res, isl_upoly_copy(base));
1781 res = isl_upoly_sum(res, t);
1782 }
1783
1784 isl_upoly_free(base);
1785 isl_upoly_free(up);
1786
1787 return res;
1788 error:
1789 isl_upoly_free(up);
1790 return NULL;
1791 }
1792
1793 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1794 isl_int denom, unsigned len)
1795 {
1796 int i;
1797 struct isl_upoly *up;
1798
1799 isl_assert(ctx, len >= 1, return NULL);
1800
1801 up = isl_upoly_rat_cst(ctx, f[0], denom);
1802 for (i = 0; i < len - 1; ++i) {
1803 struct isl_upoly *t;
1804 struct isl_upoly *c;
1805
1806 if (isl_int_is_zero(f[1 + i]))
1807 continue;
1808
1809 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1810 t = isl_upoly_var_pow(ctx, i, 1);
1811 t = isl_upoly_mul(c, t);
1812 up = isl_upoly_sum(up, t);
1813 }
1814
1815 return up;
1816 }
1817
1818 /* Remove common factor of non-constant terms and denominator.
1819 */
1820 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1821 {
1822 isl_ctx *ctx = qp->div->ctx;
1823 unsigned total = qp->div->n_col - 2;
1824
1825 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1826 isl_int_gcd(ctx->normalize_gcd,
1827 ctx->normalize_gcd, qp->div->row[div][0]);
1828 if (isl_int_is_one(ctx->normalize_gcd))
1829 return;
1830
1831 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1832 ctx->normalize_gcd, total);
1833 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1834 ctx->normalize_gcd);
1835 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1836 ctx->normalize_gcd);
1837 }
1838
1839 /* Replace the integer division identified by "div" by the polynomial "s".
1840 * The integer division is assumed not to appear in the definition
1841 * of any other integer divisions.
1842 */
1843 static __isl_give isl_qpolynomial *substitute_div(
1844 __isl_take isl_qpolynomial *qp,
1845 int div, __isl_take struct isl_upoly *s)
1846 {
1847 int i;
1848 int total;
1849 int *reordering;
1850
1851 if (!qp || !s)
1852 goto error;
1853
1854 qp = isl_qpolynomial_cow(qp);
1855 if (!qp)
1856 goto error;
1857
1858 total = isl_dim_total(qp->dim);
1859 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1860 if (!qp->upoly)
1861 goto error;
1862
1863 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1864 if (!reordering)
1865 goto error;
1866 for (i = 0; i < total + div; ++i)
1867 reordering[i] = i;
1868 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1869 reordering[i] = i - 1;
1870 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1871 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1872 qp->upoly = reorder(qp->upoly, reordering);
1873 free(reordering);
1874
1875 if (!qp->upoly || !qp->div)
1876 goto error;
1877
1878 isl_upoly_free(s);
1879 return qp;
1880 error:
1881 isl_qpolynomial_free(qp);
1882 isl_upoly_free(s);
1883 return NULL;
1884 }
1885
1886 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1887 * divisions because d is equal to 1 by their definition, i.e., e.
1888 */
1889 static __isl_give isl_qpolynomial *substitute_non_divs(
1890 __isl_take isl_qpolynomial *qp)
1891 {
1892 int i, j;
1893 int total;
1894 struct isl_upoly *s;
1895
1896 if (!qp)
1897 return NULL;
1898
1899 total = isl_dim_total(qp->dim);
1900 for (i = 0; qp && i < qp->div->n_row; ++i) {
1901 if (!isl_int_is_one(qp->div->row[i][0]))
1902 continue;
1903 for (j = i + 1; j < qp->div->n_row; ++j) {
1904 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1905 continue;
1906 isl_seq_combine(qp->div->row[j] + 1,
1907 qp->div->ctx->one, qp->div->row[j] + 1,
1908 qp->div->row[j][2 + total + i],
1909 qp->div->row[i] + 1, 1 + total + i);
1910 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1911 normalize_div(qp, j);
1912 }
1913 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1914 qp->div->row[i][0], qp->div->n_col - 1);
1915 qp = substitute_div(qp, i, s);
1916 --i;
1917 }
1918
1919 return qp;
1920 }
1921
1922 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1923 * with d the denominator. When replacing the coefficient e of x by
1924 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1925 * inside the division, so we need to add floor(e/d) * x outside.
1926 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1927 * to adjust the coefficient of x in each later div that depends on the
1928 * current div "div" and also in the affine expression "aff"
1929 * (if it too depends on "div").
1930 */
1931 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1932 __isl_keep isl_vec *aff)
1933 {
1934 int i, j;
1935 isl_int v;
1936 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1937
1938 isl_int_init(v);
1939 for (i = 0; i < 1 + total + div; ++i) {
1940 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1941 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1942 continue;
1943 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1944 isl_int_fdiv_r(qp->div->row[div][1 + i],
1945 qp->div->row[div][1 + i], qp->div->row[div][0]);
1946 if (!isl_int_is_zero(aff->el[1 + total + div]))
1947 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1948 for (j = div + 1; j < qp->div->n_row; ++j) {
1949 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1950 continue;
1951 isl_int_addmul(qp->div->row[j][1 + i],
1952 v, qp->div->row[j][2 + total + div]);
1953 }
1954 }
1955 isl_int_clear(v);
1956 }
1957
1958 /* Check if the last non-zero coefficient is bigger that half of the
1959 * denominator. If so, we will invert the div to further reduce the number
1960 * of distinct divs that may appear.
1961 * If the last non-zero coefficient is exactly half the denominator,
1962 * then we continue looking for earlier coefficients that are bigger
1963 * than half the denominator.
1964 */
1965 static int needs_invert(__isl_keep isl_mat *div, int row)
1966 {
1967 int i;
1968 int cmp;
1969
1970 for (i = div->n_col - 1; i >= 1; --i) {
1971 if (isl_int_is_zero(div->row[row][i]))
1972 continue;
1973 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1974 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1975 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1976 if (cmp)
1977 return cmp > 0;
1978 if (i == 1)
1979 return 1;
1980 }
1981
1982 return 0;
1983 }
1984
1985 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1986 * We only invert the coefficients of e (and the coefficient of q in
1987 * later divs and in "aff"). After calling this function, the
1988 * coefficients of e should be reduced again.
1989 */
1990 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1991 __isl_keep isl_vec *aff)
1992 {
1993 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1994
1995 isl_seq_neg(qp->div->row[div] + 1,
1996 qp->div->row[div] + 1, qp->div->n_col - 1);
1997 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
1998 isl_int_add(qp->div->row[div][1],
1999 qp->div->row[div][1], qp->div->row[div][0]);
2000 if (!isl_int_is_zero(aff->el[1 + total + div]))
2001 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2002 isl_mat_col_mul(qp->div, 2 + total + div,
2003 qp->div->ctx->negone, 2 + total + div);
2004 }
2005
2006 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2007 * in the interval [0, d-1], with d the denominator and such that the
2008 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2009 *
2010 * After the reduction, some divs may have become redundant or identical,
2011 * so we call substitute_non_divs and sort_divs. If these functions
2012 * eliminate divs or merge two or more divs into one, the coefficients
2013 * of the enclosing divs may have to be reduced again, so we call
2014 * ourselves recursively if the number of divs decreases.
2015 */
2016 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2017 {
2018 int i;
2019 isl_vec *aff = NULL;
2020 struct isl_upoly *s;
2021 unsigned n_div;
2022
2023 if (!qp)
2024 return NULL;
2025
2026 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2027 aff = isl_vec_clr(aff);
2028 if (!aff)
2029 goto error;
2030
2031 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2032
2033 for (i = 0; i < qp->div->n_row; ++i) {
2034 normalize_div(qp, i);
2035 reduce_div(qp, i, aff);
2036 if (needs_invert(qp->div, i)) {
2037 invert_div(qp, i, aff);
2038 reduce_div(qp, i, aff);
2039 }
2040 }
2041
2042 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2043 qp->div->ctx->one, aff->size);
2044 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2045 isl_upoly_free(s);
2046 if (!qp->upoly)
2047 goto error;
2048
2049 isl_vec_free(aff);
2050
2051 n_div = qp->div->n_row;
2052 qp = substitute_non_divs(qp);
2053 qp = sort_divs(qp);
2054 if (qp && qp->div->n_row < n_div)
2055 return reduce_divs(qp);
2056
2057 return qp;
2058 error:
2059 isl_qpolynomial_free(qp);
2060 isl_vec_free(aff);
2061 return NULL;
2062 }
2063
2064 /* Assumes each div only depends on earlier divs.
2065 */
2066 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2067 int power)
2068 {
2069 struct isl_qpolynomial *qp = NULL;
2070 struct isl_upoly_rec *rec;
2071 struct isl_upoly_cst *cst;
2072 int i, d;
2073 int pos;
2074
2075 if (!div)
2076 return NULL;
2077
2078 d = div->line - div->bmap->div;
2079
2080 pos = isl_dim_total(div->bmap->dim) + d;
2081 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2082 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2083 div->bmap->n_div, &rec->up);
2084 if (!qp)
2085 goto error;
2086
2087 for (i = 0; i < div->bmap->n_div; ++i)
2088 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2089
2090 for (i = 0; i < 1 + power; ++i) {
2091 rec->p[i] = isl_upoly_zero(div->ctx);
2092 if (!rec->p[i])
2093 goto error;
2094 rec->n++;
2095 }
2096 cst = isl_upoly_as_cst(rec->p[power]);
2097 isl_int_set_si(cst->n, 1);
2098
2099 isl_div_free(div);
2100
2101 qp = reduce_divs(qp);
2102
2103 return qp;
2104 error:
2105 isl_qpolynomial_free(qp);
2106 isl_div_free(div);
2107 return NULL;
2108 }
2109
2110 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2111 {
2112 return isl_qpolynomial_div_pow(div, 1);
2113 }
2114
2115 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2116 const isl_int n, const isl_int d)
2117 {
2118 struct isl_qpolynomial *qp;
2119 struct isl_upoly_cst *cst;
2120
2121 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2122 if (!qp)
2123 return NULL;
2124
2125 cst = isl_upoly_as_cst(qp->upoly);
2126 isl_int_set(cst->n, n);
2127 isl_int_set(cst->d, d);
2128
2129 return qp;
2130 }
2131
2132 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2133 {
2134 struct isl_upoly_rec *rec;
2135 int i;
2136
2137 if (!up)
2138 return -1;
2139
2140 if (isl_upoly_is_cst(up))
2141 return 0;
2142
2143 if (up->var < d)
2144 active[up->var] = 1;
2145
2146 rec = isl_upoly_as_rec(up);
2147 for (i = 0; i < rec->n; ++i)
2148 if (up_set_active(rec->p[i], active, d) < 0)
2149 return -1;
2150
2151 return 0;
2152 }
2153
2154 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2155 {
2156 int i, j;
2157 int d = isl_dim_total(qp->dim);
2158
2159 if (!qp || !active)
2160 return -1;
2161
2162 for (i = 0; i < d; ++i)
2163 for (j = 0; j < qp->div->n_row; ++j) {
2164 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2165 continue;
2166 active[i] = 1;
2167 break;
2168 }
2169
2170 return up_set_active(qp->upoly, active, d);
2171 }
2172
2173 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2174 enum isl_dim_type type, unsigned first, unsigned n)
2175 {
2176 int i;
2177 int *active = NULL;
2178 int involves = 0;
2179
2180 if (!qp)
2181 return -1;
2182 if (n == 0)
2183 return 0;
2184
2185 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2186 return -1);
2187 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2188 type == isl_dim_set, return -1);
2189
2190 active = isl_calloc_array(qp->dim->ctx, int, isl_dim_total(qp->dim));
2191 if (set_active(qp, active) < 0)
2192 goto error;
2193
2194 if (type == isl_dim_set)
2195 first += isl_dim_size(qp->dim, isl_dim_param);
2196 for (i = 0; i < n; ++i)
2197 if (active[first + i]) {
2198 involves = 1;
2199 break;
2200 }
2201
2202 free(active);
2203
2204 return involves;
2205 error:
2206 free(active);
2207 return -1;
2208 }
2209
2210 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2211 * of the divs that do appear in the quasi-polynomial.
2212 */
2213 static __isl_give isl_qpolynomial *remove_redundant_divs(
2214 __isl_take isl_qpolynomial *qp)
2215 {
2216 int i, j;
2217 int d;
2218 int len;
2219 int skip;
2220 int *active = NULL;
2221 int *reordering = NULL;
2222 int redundant = 0;
2223 int n_div;
2224 isl_ctx *ctx;
2225
2226 if (!qp)
2227 return NULL;
2228 if (qp->div->n_row == 0)
2229 return qp;
2230
2231 d = isl_dim_total(qp->dim);
2232 len = qp->div->n_col - 2;
2233 ctx = isl_qpolynomial_get_ctx(qp);
2234 active = isl_calloc_array(ctx, int, len);
2235 if (!active)
2236 goto error;
2237
2238 if (up_set_active(qp->upoly, active, len) < 0)
2239 goto error;
2240
2241 for (i = qp->div->n_row - 1; i >= 0; --i) {
2242 if (!active[d + i]) {
2243 redundant = 1;
2244 continue;
2245 }
2246 for (j = 0; j < i; ++j) {
2247 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2248 continue;
2249 active[d + j] = 1;
2250 break;
2251 }
2252 }
2253
2254 if (!redundant) {
2255 free(active);
2256 return qp;
2257 }
2258
2259 reordering = isl_alloc_array(qp->div->ctx, int, len);
2260 if (!reordering)
2261 goto error;
2262
2263 for (i = 0; i < d; ++i)
2264 reordering[i] = i;
2265
2266 skip = 0;
2267 n_div = qp->div->n_row;
2268 for (i = 0; i < n_div; ++i) {
2269 if (!active[d + i]) {
2270 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2271 qp->div = isl_mat_drop_cols(qp->div,
2272 2 + d + i - skip, 1);
2273 skip++;
2274 }
2275 reordering[d + i] = d + i - skip;
2276 }
2277
2278 qp->upoly = reorder(qp->upoly, reordering);
2279
2280 if (!qp->upoly || !qp->div)
2281 goto error;
2282
2283 free(active);
2284 free(reordering);
2285
2286 return qp;
2287 error:
2288 free(active);
2289 free(reordering);
2290 isl_qpolynomial_free(qp);
2291 return NULL;
2292 }
2293
2294 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2295 unsigned first, unsigned n)
2296 {
2297 int i;
2298 struct isl_upoly_rec *rec;
2299
2300 if (!up)
2301 return NULL;
2302 if (n == 0 || up->var < 0 || up->var < first)
2303 return up;
2304 if (up->var < first + n) {
2305 up = replace_by_constant_term(up);
2306 return isl_upoly_drop(up, first, n);
2307 }
2308 up = isl_upoly_cow(up);
2309 if (!up)
2310 return NULL;
2311 up->var -= n;
2312 rec = isl_upoly_as_rec(up);
2313 if (!rec)
2314 goto error;
2315
2316 for (i = 0; i < rec->n; ++i) {
2317 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2318 if (!rec->p[i])
2319 goto error;
2320 }
2321
2322 return up;
2323 error:
2324 isl_upoly_free(up);
2325 return NULL;
2326 }
2327
2328 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2329 __isl_take isl_qpolynomial *qp,
2330 enum isl_dim_type type, unsigned pos, const char *s)
2331 {
2332 qp = isl_qpolynomial_cow(qp);
2333 if (!qp)
2334 return NULL;
2335 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2336 if (!qp->dim)
2337 goto error;
2338 return qp;
2339 error:
2340 isl_qpolynomial_free(qp);
2341 return NULL;
2342 }
2343
2344 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2345 __isl_take isl_qpolynomial *qp,
2346 enum isl_dim_type type, unsigned first, unsigned n)
2347 {
2348 if (!qp)
2349 return NULL;
2350 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2351 return qp;
2352
2353 qp = isl_qpolynomial_cow(qp);
2354 if (!qp)
2355 return NULL;
2356
2357 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2358 goto error);
2359 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2360 type == isl_dim_set, goto error);
2361
2362 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2363 if (!qp->dim)
2364 goto error;
2365
2366 if (type == isl_dim_set)
2367 first += isl_dim_size(qp->dim, isl_dim_param);
2368
2369 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2370 if (!qp->div)
2371 goto error;
2372
2373 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2374 if (!qp->upoly)
2375 goto error;
2376
2377 return qp;
2378 error:
2379 isl_qpolynomial_free(qp);
2380 return NULL;
2381 }
2382
2383 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2384 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2385 {
2386 int i, j, k;
2387 isl_int denom;
2388 unsigned total;
2389 unsigned n_div;
2390 struct isl_upoly *up;
2391
2392 if (!eq)
2393 goto error;
2394 if (eq->n_eq == 0) {
2395 isl_basic_set_free(eq);
2396 return qp;
2397 }
2398
2399 qp = isl_qpolynomial_cow(qp);
2400 if (!qp)
2401 goto error;
2402 qp->div = isl_mat_cow(qp->div);
2403 if (!qp->div)
2404 goto error;
2405
2406 total = 1 + isl_dim_total(eq->dim);
2407 n_div = eq->n_div;
2408 isl_int_init(denom);
2409 for (i = 0; i < eq->n_eq; ++i) {
2410 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2411 if (j < 0 || j == 0 || j >= total)
2412 continue;
2413
2414 for (k = 0; k < qp->div->n_row; ++k) {
2415 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2416 continue;
2417 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2418 &qp->div->row[k][0]);
2419 normalize_div(qp, k);
2420 }
2421
2422 if (isl_int_is_pos(eq->eq[i][j]))
2423 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2424 isl_int_abs(denom, eq->eq[i][j]);
2425 isl_int_set_si(eq->eq[i][j], 0);
2426
2427 up = isl_upoly_from_affine(qp->dim->ctx,
2428 eq->eq[i], denom, total);
2429 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2430 isl_upoly_free(up);
2431 }
2432 isl_int_clear(denom);
2433
2434 if (!qp->upoly)
2435 goto error;
2436
2437 isl_basic_set_free(eq);
2438
2439 qp = substitute_non_divs(qp);
2440 qp = sort_divs(qp);
2441
2442 return qp;
2443 error:
2444 isl_basic_set_free(eq);
2445 isl_qpolynomial_free(qp);
2446 return NULL;
2447 }
2448
2449 static __isl_give isl_basic_set *add_div_constraints(
2450 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2451 {
2452 int i;
2453 unsigned total;
2454
2455 if (!bset || !div)
2456 goto error;
2457
2458 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2459 if (!bset)
2460 goto error;
2461 total = isl_basic_set_total_dim(bset);
2462 for (i = 0; i < div->n_row; ++i)
2463 if (isl_basic_set_add_div_constraints_var(bset,
2464 total - div->n_row + i, div->row[i]) < 0)
2465 goto error;
2466
2467 isl_mat_free(div);
2468 return bset;
2469 error:
2470 isl_mat_free(div);
2471 isl_basic_set_free(bset);
2472 return NULL;
2473 }
2474
2475 /* Look for equalities among the variables shared by context and qp
2476 * and the integer divisions of qp, if any.
2477 * The equalities are then used to eliminate variables and/or integer
2478 * divisions from qp.
2479 */
2480 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2481 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2482 {
2483 isl_basic_set *aff;
2484
2485 if (!qp)
2486 goto error;
2487 if (qp->div->n_row > 0) {
2488 isl_basic_set *bset;
2489 context = isl_set_add_dims(context, isl_dim_set,
2490 qp->div->n_row);
2491 bset = isl_basic_set_universe(isl_set_get_dim(context));
2492 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2493 context = isl_set_intersect(context,
2494 isl_set_from_basic_set(bset));
2495 }
2496
2497 aff = isl_set_affine_hull(context);
2498 return isl_qpolynomial_substitute_equalities(qp, aff);
2499 error:
2500 isl_qpolynomial_free(qp);
2501 isl_set_free(context);
2502 return NULL;
2503 }
2504
2505 #undef PW
2506 #define PW isl_pw_qpolynomial
2507 #undef EL
2508 #define EL isl_qpolynomial
2509 #undef EL_IS_ZERO
2510 #define EL_IS_ZERO is_zero
2511 #undef ZERO
2512 #define ZERO zero
2513 #undef IS_ZERO
2514 #define IS_ZERO is_zero
2515 #undef FIELD
2516 #define FIELD qp
2517
2518 #include <isl_pw_templ.c>
2519
2520 #undef UNION
2521 #define UNION isl_union_pw_qpolynomial
2522 #undef PART
2523 #define PART isl_pw_qpolynomial
2524 #undef PARTS
2525 #define PARTS pw_qpolynomial
2526
2527 #include <isl_union_templ.c>
2528
2529 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2530 {
2531 if (!pwqp)
2532 return -1;
2533
2534 if (pwqp->n != -1)
2535 return 0;
2536
2537 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2538 return 0;
2539
2540 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2541 }
2542
2543 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2544 __isl_take isl_pw_qpolynomial *pwqp1,
2545 __isl_take isl_pw_qpolynomial *pwqp2)
2546 {
2547 int i, j, n;
2548 struct isl_pw_qpolynomial *res;
2549
2550 if (!pwqp1 || !pwqp2)
2551 goto error;
2552
2553 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2554 goto error);
2555
2556 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2557 isl_pw_qpolynomial_free(pwqp2);
2558 return pwqp1;
2559 }
2560
2561 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2562 isl_pw_qpolynomial_free(pwqp1);
2563 return pwqp2;
2564 }
2565
2566 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2567 isl_pw_qpolynomial_free(pwqp1);
2568 return pwqp2;
2569 }
2570
2571 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2572 isl_pw_qpolynomial_free(pwqp2);
2573 return pwqp1;
2574 }
2575
2576 n = pwqp1->n * pwqp2->n;
2577 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2578
2579 for (i = 0; i < pwqp1->n; ++i) {
2580 for (j = 0; j < pwqp2->n; ++j) {
2581 struct isl_set *common;
2582 struct isl_qpolynomial *prod;
2583 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2584 isl_set_copy(pwqp2->p[j].set));
2585 if (isl_set_plain_is_empty(common)) {
2586 isl_set_free(common);
2587 continue;
2588 }
2589
2590 prod = isl_qpolynomial_mul(
2591 isl_qpolynomial_copy(pwqp1->p[i].qp),
2592 isl_qpolynomial_copy(pwqp2->p[j].qp));
2593
2594 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2595 }
2596 }
2597
2598 isl_pw_qpolynomial_free(pwqp1);
2599 isl_pw_qpolynomial_free(pwqp2);
2600
2601 return res;
2602 error:
2603 isl_pw_qpolynomial_free(pwqp1);
2604 isl_pw_qpolynomial_free(pwqp2);
2605 return NULL;
2606 }
2607
2608 __isl_give struct isl_upoly *isl_upoly_eval(
2609 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2610 {
2611 int i;
2612 struct isl_upoly_rec *rec;
2613 struct isl_upoly *res;
2614 struct isl_upoly *base;
2615
2616 if (isl_upoly_is_cst(up)) {
2617 isl_vec_free(vec);
2618 return up;
2619 }
2620
2621 rec = isl_upoly_as_rec(up);
2622 if (!rec)
2623 goto error;
2624
2625 isl_assert(up->ctx, rec->n >= 1, goto error);
2626
2627 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2628
2629 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2630 isl_vec_copy(vec));
2631
2632 for (i = rec->n - 2; i >= 0; --i) {
2633 res = isl_upoly_mul(res, isl_upoly_copy(base));
2634 res = isl_upoly_sum(res,
2635 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2636 isl_vec_copy(vec)));
2637 }
2638
2639 isl_upoly_free(base);
2640 isl_upoly_free(up);
2641 isl_vec_free(vec);
2642 return res;
2643 error:
2644 isl_upoly_free(up);
2645 isl_vec_free(vec);
2646 return NULL;
2647 }
2648
2649 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2650 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2651 {
2652 isl_vec *ext;
2653 struct isl_upoly *up;
2654 isl_dim *dim;
2655
2656 if (!qp || !pnt)
2657 goto error;
2658 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2659
2660 if (qp->div->n_row == 0)
2661 ext = isl_vec_copy(pnt->vec);
2662 else {
2663 int i;
2664 unsigned dim = isl_dim_total(qp->dim);
2665 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2666 if (!ext)
2667 goto error;
2668
2669 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2670 for (i = 0; i < qp->div->n_row; ++i) {
2671 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2672 1 + dim + i, &ext->el[1+dim+i]);
2673 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2674 qp->div->row[i][0]);
2675 }
2676 }
2677
2678 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2679 if (!up)
2680 goto error;
2681
2682 dim = isl_dim_copy(qp->dim);
2683 isl_qpolynomial_free(qp);
2684 isl_point_free(pnt);
2685
2686 return isl_qpolynomial_alloc(dim, 0, up);
2687 error:
2688 isl_qpolynomial_free(qp);
2689 isl_point_free(pnt);
2690 return NULL;
2691 }
2692
2693 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2694 __isl_keep struct isl_upoly_cst *cst2)
2695 {
2696 int cmp;
2697 isl_int t;
2698 isl_int_init(t);
2699 isl_int_mul(t, cst1->n, cst2->d);
2700 isl_int_submul(t, cst2->n, cst1->d);
2701 cmp = isl_int_sgn(t);
2702 isl_int_clear(t);
2703 return cmp;
2704 }
2705
2706 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2707 __isl_keep isl_qpolynomial *qp2)
2708 {
2709 struct isl_upoly_cst *cst1, *cst2;
2710
2711 if (!qp1 || !qp2)
2712 return -1;
2713 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2714 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2715 if (isl_qpolynomial_is_nan(qp1))
2716 return -1;
2717 if (isl_qpolynomial_is_nan(qp2))
2718 return -1;
2719 cst1 = isl_upoly_as_cst(qp1->upoly);
2720 cst2 = isl_upoly_as_cst(qp2->upoly);
2721
2722 return isl_upoly_cmp(cst1, cst2) <= 0;
2723 }
2724
2725 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2726 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2727 {
2728 struct isl_upoly_cst *cst1, *cst2;
2729 int cmp;
2730
2731 if (!qp1 || !qp2)
2732 goto error;
2733 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2734 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2735 cst1 = isl_upoly_as_cst(qp1->upoly);
2736 cst2 = isl_upoly_as_cst(qp2->upoly);
2737 cmp = isl_upoly_cmp(cst1, cst2);
2738
2739 if (cmp <= 0) {
2740 isl_qpolynomial_free(qp2);
2741 } else {
2742 isl_qpolynomial_free(qp1);
2743 qp1 = qp2;
2744 }
2745 return qp1;
2746 error:
2747 isl_qpolynomial_free(qp1);
2748 isl_qpolynomial_free(qp2);
2749 return NULL;
2750 }
2751
2752 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2753 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2754 {
2755 struct isl_upoly_cst *cst1, *cst2;
2756 int cmp;
2757
2758 if (!qp1 || !qp2)
2759 goto error;
2760 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2761 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2762 cst1 = isl_upoly_as_cst(qp1->upoly);
2763 cst2 = isl_upoly_as_cst(qp2->upoly);
2764 cmp = isl_upoly_cmp(cst1, cst2);
2765
2766 if (cmp >= 0) {
2767 isl_qpolynomial_free(qp2);
2768 } else {
2769 isl_qpolynomial_free(qp1);
2770 qp1 = qp2;
2771 }
2772 return qp1;
2773 error:
2774 isl_qpolynomial_free(qp1);
2775 isl_qpolynomial_free(qp2);
2776 return NULL;
2777 }
2778
2779 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2780 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2781 unsigned first, unsigned n)
2782 {
2783 unsigned total;
2784 unsigned g_pos;
2785 int *exp;
2786
2787 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2788 return qp;
2789
2790 qp = isl_qpolynomial_cow(qp);
2791 if (!qp)
2792 return NULL;
2793
2794 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2795 goto error);
2796
2797 g_pos = pos(qp->dim, type) + first;
2798
2799 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2800 if (!qp->div)
2801 goto error;
2802
2803 total = qp->div->n_col - 2;
2804 if (total > g_pos) {
2805 int i;
2806 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2807 if (!exp)
2808 goto error;
2809 for (i = 0; i < total - g_pos; ++i)
2810 exp[i] = i + n;
2811 qp->upoly = expand(qp->upoly, exp, g_pos);
2812 free(exp);
2813 if (!qp->upoly)
2814 goto error;
2815 }
2816
2817 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2818 if (!qp->dim)
2819 goto error;
2820
2821 return qp;
2822 error:
2823 isl_qpolynomial_free(qp);
2824 return NULL;
2825 }
2826
2827 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2828 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2829 {
2830 unsigned pos;
2831
2832 pos = isl_qpolynomial_dim(qp, type);
2833
2834 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2835 }
2836
2837 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2838 __isl_take isl_pw_qpolynomial *pwqp,
2839 enum isl_dim_type type, unsigned n)
2840 {
2841 unsigned pos;
2842
2843 pos = isl_pw_qpolynomial_dim(pwqp, type);
2844
2845 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2846 }
2847
2848 static int *reordering_move(isl_ctx *ctx,
2849 unsigned len, unsigned dst, unsigned src, unsigned n)
2850 {
2851 int i;
2852 int *reordering;
2853
2854 reordering = isl_alloc_array(ctx, int, len);
2855 if (!reordering)
2856 return NULL;
2857
2858 if (dst <= src) {
2859 for (i = 0; i < dst; ++i)
2860 reordering[i] = i;
2861 for (i = 0; i < n; ++i)
2862 reordering[src + i] = dst + i;
2863 for (i = 0; i < src - dst; ++i)
2864 reordering[dst + i] = dst + n + i;
2865 for (i = 0; i < len - src - n; ++i)
2866 reordering[src + n + i] = src + n + i;
2867 } else {
2868 for (i = 0; i < src; ++i)
2869 reordering[i] = i;
2870 for (i = 0; i < n; ++i)
2871 reordering[src + i] = dst + i;
2872 for (i = 0; i < dst - src; ++i)
2873 reordering[src + n + i] = src + i;
2874 for (i = 0; i < len - dst - n; ++i)
2875 reordering[dst + n + i] = dst + n + i;
2876 }
2877
2878 return reordering;
2879 }
2880
2881 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2882 __isl_take isl_qpolynomial *qp,
2883 enum isl_dim_type dst_type, unsigned dst_pos,
2884 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2885 {
2886 unsigned g_dst_pos;
2887 unsigned g_src_pos;
2888 int *reordering;
2889
2890 qp = isl_qpolynomial_cow(qp);
2891 if (!qp)
2892 return NULL;
2893
2894 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2895 goto error);
2896
2897 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2898 g_src_pos = pos(qp->dim, src_type) + src_pos;
2899 if (dst_type > src_type)
2900 g_dst_pos -= n;
2901
2902 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2903 if (!qp->div)
2904 goto error;
2905 qp = sort_divs(qp);
2906 if (!qp)
2907 goto error;
2908
2909 reordering = reordering_move(qp->dim->ctx,
2910 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2911 if (!reordering)
2912 goto error;
2913
2914 qp->upoly = reorder(qp->upoly, reordering);
2915 free(reordering);
2916 if (!qp->upoly)
2917 goto error;
2918
2919 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2920 if (!qp->dim)
2921 goto error;
2922
2923 return qp;
2924 error:
2925 isl_qpolynomial_free(qp);
2926 return NULL;
2927 }
2928
2929 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2930 isl_int *f, isl_int denom)
2931 {
2932 struct isl_upoly *up;
2933
2934 if (!dim)
2935 return NULL;
2936
2937 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2938
2939 return isl_qpolynomial_alloc(dim, 0, up);
2940 }
2941
2942 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
2943 {
2944 isl_ctx *ctx;
2945 struct isl_upoly *up;
2946 isl_qpolynomial *qp;
2947
2948 if (!aff)
2949 return NULL;
2950
2951 ctx = isl_aff_get_ctx(aff);
2952 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
2953 aff->v->size - 1);
2954
2955 qp = isl_qpolynomial_alloc(isl_aff_get_dim(aff),
2956 aff->ls->div->n_row, up);
2957 if (!qp)
2958 goto error;
2959
2960 isl_mat_free(qp->div);
2961 qp->div = isl_mat_copy(aff->ls->div);
2962 qp->div = isl_mat_cow(qp->div);
2963 if (!qp->div)
2964 goto error;
2965
2966 isl_aff_free(aff);
2967 qp = reduce_divs(qp);
2968 qp = remove_redundant_divs(qp);
2969 return qp;
2970 error:
2971 isl_aff_free(aff);
2972 return NULL;
2973 }
2974
2975 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2976 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2977 {
2978 isl_aff *aff;
2979
2980 aff = isl_constraint_get_bound(c, type, pos);
2981 isl_constraint_free(c);
2982 return isl_qpolynomial_from_aff(aff);
2983 }
2984
2985 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2986 * in "qp" by subs[i].
2987 */
2988 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2989 __isl_take isl_qpolynomial *qp,
2990 enum isl_dim_type type, unsigned first, unsigned n,
2991 __isl_keep isl_qpolynomial **subs)
2992 {
2993 int i;
2994 struct isl_upoly **ups;
2995
2996 if (n == 0)
2997 return qp;
2998
2999 qp = isl_qpolynomial_cow(qp);
3000 if (!qp)
3001 return NULL;
3002 for (i = 0; i < n; ++i)
3003 if (!subs[i])
3004 goto error;
3005
3006 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
3007 goto error);
3008
3009 for (i = 0; i < n; ++i)
3010 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
3011 goto error);
3012
3013 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3014 for (i = 0; i < n; ++i)
3015 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3016
3017 first += pos(qp->dim, type);
3018
3019 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3020 if (!ups)
3021 goto error;
3022 for (i = 0; i < n; ++i)
3023 ups[i] = subs[i]->upoly;
3024
3025 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3026
3027 free(ups);
3028
3029 if (!qp->upoly)
3030 goto error;
3031
3032 return qp;
3033 error:
3034 isl_qpolynomial_free(qp);
3035 return NULL;
3036 }
3037
3038 /* Extend "bset" with extra set dimensions for each integer division
3039 * in "qp" and then call "fn" with the extended bset and the polynomial
3040 * that results from replacing each of the integer divisions by the
3041 * corresponding extra set dimension.
3042 */
3043 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3044 __isl_keep isl_basic_set *bset,
3045 int (*fn)(__isl_take isl_basic_set *bset,
3046 __isl_take isl_qpolynomial *poly, void *user), void *user)
3047 {
3048 isl_dim *dim;
3049 isl_mat *div;
3050 isl_qpolynomial *poly;
3051
3052 if (!qp || !bset)
3053 goto error;
3054 if (qp->div->n_row == 0)
3055 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3056 user);
3057
3058 div = isl_mat_copy(qp->div);
3059 dim = isl_dim_copy(qp->dim);
3060 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3061 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3062 bset = isl_basic_set_copy(bset);
3063 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3064 bset = add_div_constraints(bset, div);
3065
3066 return fn(bset, poly, user);
3067 error:
3068 return -1;
3069 }
3070
3071 /* Return total degree in variables first (inclusive) up to last (exclusive).
3072 */
3073 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3074 {
3075 int deg = -1;
3076 int i;
3077 struct isl_upoly_rec *rec;
3078
3079 if (!up)
3080 return -2;
3081 if (isl_upoly_is_zero(up))
3082 return -1;
3083 if (isl_upoly_is_cst(up) || up->var < first)
3084 return 0;
3085
3086 rec = isl_upoly_as_rec(up);
3087 if (!rec)
3088 return -2;
3089
3090 for (i = 0; i < rec->n; ++i) {
3091 int d;
3092
3093 if (isl_upoly_is_zero(rec->p[i]))
3094 continue;
3095 d = isl_upoly_degree(rec->p[i], first, last);
3096 if (up->var < last)
3097 d += i;
3098 if (d > deg)
3099 deg = d;
3100 }
3101
3102 return deg;
3103 }
3104
3105 /* Return total degree in set variables.
3106 */
3107 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3108 {
3109 unsigned ovar;
3110 unsigned nvar;
3111
3112 if (!poly)
3113 return -2;
3114
3115 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3116 nvar = isl_dim_size(poly->dim, isl_dim_set);
3117 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3118 }
3119
3120 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3121 unsigned pos, int deg)
3122 {
3123 int i;
3124 struct isl_upoly_rec *rec;
3125
3126 if (!up)
3127 return NULL;
3128
3129 if (isl_upoly_is_cst(up) || up->var < pos) {
3130 if (deg == 0)
3131 return isl_upoly_copy(up);
3132 else
3133 return isl_upoly_zero(up->ctx);
3134 }
3135
3136 rec = isl_upoly_as_rec(up);
3137 if (!rec)
3138 return NULL;
3139
3140 if (up->var == pos) {
3141 if (deg < rec->n)
3142 return isl_upoly_copy(rec->p[deg]);
3143 else
3144 return isl_upoly_zero(up->ctx);
3145 }
3146
3147 up = isl_upoly_copy(up);
3148 up = isl_upoly_cow(up);
3149 rec = isl_upoly_as_rec(up);
3150 if (!rec)
3151 goto error;
3152
3153 for (i = 0; i < rec->n; ++i) {
3154 struct isl_upoly *t;
3155 t = isl_upoly_coeff(rec->p[i], pos, deg);
3156 if (!t)
3157 goto error;
3158 isl_upoly_free(rec->p[i]);
3159 rec->p[i] = t;
3160 }
3161
3162 return up;
3163 error:
3164 isl_upoly_free(up);
3165 return NULL;
3166 }
3167
3168 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3169 */
3170 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3171 __isl_keep isl_qpolynomial *qp,
3172 enum isl_dim_type type, unsigned t_pos, int deg)
3173 {
3174 unsigned g_pos;
3175 struct isl_upoly *up;
3176 isl_qpolynomial *c;
3177
3178 if (!qp)
3179 return NULL;
3180
3181 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3182 return NULL);
3183
3184 g_pos = pos(qp->dim, type) + t_pos;
3185 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3186
3187 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3188 if (!c)
3189 return NULL;
3190 isl_mat_free(c->div);
3191 c->div = isl_mat_copy(qp->div);
3192 if (!c->div)
3193 goto error;
3194 return c;
3195 error:
3196 isl_qpolynomial_free(c);
3197 return NULL;
3198 }
3199
3200 /* Homogenize the polynomial in the variables first (inclusive) up to
3201 * last (exclusive) by inserting powers of variable first.
3202 * Variable first is assumed not to appear in the input.
3203 */
3204 __isl_give struct isl_upoly *isl_upoly_homogenize(
3205 __isl_take struct isl_upoly *up, int deg, int target,
3206 int first, int last)
3207 {
3208 int i;
3209 struct isl_upoly_rec *rec;
3210
3211 if (!up)
3212 return NULL;
3213 if (isl_upoly_is_zero(up))
3214 return up;
3215 if (deg == target)
3216 return up;
3217 if (isl_upoly_is_cst(up) || up->var < first) {
3218 struct isl_upoly *hom;
3219
3220 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3221 if (!hom)
3222 goto error;
3223 rec = isl_upoly_as_rec(hom);
3224 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3225
3226 return hom;
3227 }
3228
3229 up = isl_upoly_cow(up);
3230 rec = isl_upoly_as_rec(up);
3231 if (!rec)
3232 goto error;
3233
3234 for (i = 0; i < rec->n; ++i) {
3235 if (isl_upoly_is_zero(rec->p[i]))
3236 continue;
3237 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3238 up->var < last ? deg + i : i, target,
3239 first, last);
3240 if (!rec->p[i])
3241 goto error;
3242 }
3243
3244 return up;
3245 error:
3246 isl_upoly_free(up);
3247 return NULL;
3248 }
3249
3250 /* Homogenize the polynomial in the set variables by introducing
3251 * powers of an extra set variable at position 0.
3252 */
3253 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3254 __isl_take isl_qpolynomial *poly)
3255 {
3256 unsigned ovar;
3257 unsigned nvar;
3258 int deg = isl_qpolynomial_degree(poly);
3259
3260 if (deg < -1)
3261 goto error;
3262
3263 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3264 poly = isl_qpolynomial_cow(poly);
3265 if (!poly)
3266 goto error;
3267
3268 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3269 nvar = isl_dim_size(poly->dim, isl_dim_set);
3270 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3271 ovar, ovar + nvar);
3272 if (!poly->upoly)
3273 goto error;
3274
3275 return poly;
3276 error:
3277 isl_qpolynomial_free(poly);
3278 return NULL;
3279 }
3280
3281 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3282 __isl_take isl_mat *div)
3283 {
3284 isl_term *term;
3285 int n;
3286
3287 if (!dim || !div)
3288 goto error;
3289
3290 n = isl_dim_total(dim) + div->n_row;
3291
3292 term = isl_calloc(dim->ctx, struct isl_term,
3293 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3294 if (!term)
3295 goto error;
3296
3297 term->ref = 1;
3298 term->dim = dim;
3299 term->div = div;
3300 isl_int_init(term->n);
3301 isl_int_init(term->d);
3302
3303 return term;
3304 error:
3305 isl_dim_free(dim);
3306 isl_mat_free(div);
3307 return NULL;
3308 }
3309
3310 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3311 {
3312 if (!term)
3313 return NULL;
3314
3315 term->ref++;
3316 return term;
3317 }
3318
3319 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3320 {
3321 int i;
3322 isl_term *dup;
3323 unsigned total;
3324
3325 if (term)
3326 return NULL;
3327
3328 total = isl_dim_total(term->dim) + term->div->n_row;
3329
3330 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3331 if (!dup)
3332 return NULL;
3333
3334 isl_int_set(dup->n, term->n);
3335 isl_int_set(dup->d, term->d);
3336
3337 for (i = 0; i < total; ++i)
3338 dup->pow[i] = term->pow[i];
3339
3340 return dup;
3341 }
3342
3343 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3344 {
3345 if (!term)
3346 return NULL;
3347
3348 if (term->ref == 1)
3349 return term;
3350 term->ref--;
3351 return isl_term_dup(term);
3352 }
3353
3354 void isl_term_free(__isl_take isl_term *term)
3355 {
3356 if (!term)
3357 return;
3358
3359 if (--term->ref > 0)
3360 return;
3361
3362 isl_dim_free(term->dim);
3363 isl_mat_free(term->div);
3364 isl_int_clear(term->n);
3365 isl_int_clear(term->d);
3366 free(term);
3367 }
3368
3369 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3370 {
3371 if (!term)
3372 return 0;
3373
3374 switch (type) {
3375 case isl_dim_param:
3376 case isl_dim_in:
3377 case isl_dim_out: return isl_dim_size(term->dim, type);
3378 case isl_dim_div: return term->div->n_row;
3379 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3380 default: return 0;
3381 }
3382 }
3383
3384 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3385 {
3386 return term ? term->dim->ctx : NULL;
3387 }
3388
3389 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3390 {
3391 if (!term)
3392 return;
3393 isl_int_set(*n, term->n);
3394 }
3395
3396 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3397 {
3398 if (!term)
3399 return;
3400 isl_int_set(*d, term->d);
3401 }
3402
3403 int isl_term_get_exp(__isl_keep isl_term *term,
3404 enum isl_dim_type type, unsigned pos)
3405 {
3406 if (!term)
3407 return -1;
3408
3409 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3410
3411 if (type >= isl_dim_set)
3412 pos += isl_dim_size(term->dim, isl_dim_param);
3413 if (type >= isl_dim_div)
3414 pos += isl_dim_size(term->dim, isl_dim_set);
3415
3416 return term->pow[pos];
3417 }
3418
3419 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3420 {
3421 isl_basic_map *bmap;
3422 unsigned total;
3423 int k;
3424
3425 if (!term)
3426 return NULL;
3427
3428 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3429 return NULL);
3430
3431 total = term->div->n_col - term->div->n_row - 2;
3432 /* No nested divs for now */
3433 isl_assert(term->dim->ctx,
3434 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3435 term->div->n_row) == -1,
3436 return NULL);
3437
3438 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3439 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3440 goto error;
3441
3442 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3443
3444 return isl_basic_map_div(bmap, k);
3445 error:
3446 isl_basic_map_free(bmap);
3447 return NULL;
3448 }
3449
3450 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3451 int (*fn)(__isl_take isl_term *term, void *user),
3452 __isl_take isl_term *term, void *user)
3453 {
3454 int i;
3455 struct isl_upoly_rec *rec;
3456
3457 if (!up || !term)
3458 goto error;
3459
3460 if (isl_upoly_is_zero(up))
3461 return term;
3462
3463 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3464 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3465 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3466
3467 if (isl_upoly_is_cst(up)) {
3468 struct isl_upoly_cst *cst;
3469 cst = isl_upoly_as_cst(up);
3470 if (!cst)
3471 goto error;
3472 term = isl_term_cow(term);
3473 if (!term)
3474 goto error;
3475 isl_int_set(term->n, cst->n);
3476 isl_int_set(term->d, cst->d);
3477 if (fn(isl_term_copy(term), user) < 0)
3478 goto error;
3479 return term;
3480 }
3481
3482 rec = isl_upoly_as_rec(up);
3483 if (!rec)
3484 goto error;
3485
3486 for (i = 0; i < rec->n; ++i) {
3487 term = isl_term_cow(term);
3488 if (!term)
3489 goto error;
3490 term->pow[up->var] = i;
3491 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3492 if (!term)
3493 goto error;
3494 }
3495 term->pow[up->var] = 0;
3496
3497 return term;
3498 error:
3499 isl_term_free(term);
3500 return NULL;
3501 }
3502
3503 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3504 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3505 {
3506 isl_term *term;
3507
3508 if (!qp)
3509 return -1;
3510
3511 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3512 if (!term)
3513 return -1;
3514
3515 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3516
3517 isl_term_free(term);
3518
3519 return term ? 0 : -1;
3520 }
3521
3522 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3523 {
3524 struct isl_upoly *up;
3525 isl_qpolynomial *qp;
3526 int i, n;
3527
3528 if (!term)
3529 return NULL;
3530
3531 n = isl_dim_total(term->dim) + term->div->n_row;
3532
3533 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3534 for (i = 0; i < n; ++i) {
3535 if (!term->pow[i])
3536 continue;
3537 up = isl_upoly_mul(up,
3538 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3539 }
3540
3541 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3542 if (!qp)
3543 goto error;
3544 isl_mat_free(qp->div);
3545 qp->div = isl_mat_copy(term->div);
3546 if (!qp->div)
3547 goto error;
3548
3549 isl_term_free(term);
3550 return qp;
3551 error:
3552 isl_qpolynomial_free(qp);
3553 isl_term_free(term);
3554 return NULL;
3555 }
3556
3557 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3558 __isl_take isl_dim *dim)
3559 {
3560 int i;
3561 int extra;
3562 unsigned total;
3563
3564 if (!qp || !dim)
3565 goto error;
3566
3567 if (isl_dim_equal(qp->dim, dim)) {
3568 isl_dim_free(dim);
3569 return qp;
3570 }
3571
3572 qp = isl_qpolynomial_cow(qp);
3573 if (!qp)
3574 goto error;
3575
3576 extra = isl_dim_size(dim, isl_dim_set) -
3577 isl_dim_size(qp->dim, isl_dim_set);
3578 total = isl_dim_total(qp->dim);
3579 if (qp->div->n_row) {
3580 int *exp;
3581
3582 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3583 if (!exp)
3584 goto error;
3585 for (i = 0; i < qp->div->n_row; ++i)
3586 exp[i] = extra + i;
3587 qp->upoly = expand(qp->upoly, exp, total);
3588 free(exp);
3589 if (!qp->upoly)
3590 goto error;
3591 }
3592 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3593 if (!qp->div)
3594 goto error;
3595 for (i = 0; i < qp->div->n_row; ++i)
3596 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3597
3598 isl_dim_free(qp->dim);
3599 qp->dim = dim;
3600
3601 return qp;
3602 error:
3603 isl_dim_free(dim);
3604 isl_qpolynomial_free(qp);
3605 return NULL;
3606 }
3607
3608 /* For each parameter or variable that does not appear in qp,
3609 * first eliminate the variable from all constraints and then set it to zero.
3610 */
3611 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3612 __isl_keep isl_qpolynomial *qp)
3613 {
3614 int *active = NULL;
3615 int i;
3616 int d;
3617 unsigned nparam;
3618 unsigned nvar;
3619
3620 if (!set || !qp)
3621 goto error;
3622
3623 d = isl_dim_total(set->dim);
3624 active = isl_calloc_array(set->ctx, int, d);
3625 if (set_active(qp, active) < 0)
3626 goto error;
3627
3628 for (i = 0; i < d; ++i)
3629 if (!active[i])
3630 break;
3631
3632 if (i == d) {
3633 free(active);
3634 return set;
3635 }
3636
3637 nparam = isl_dim_size(set->dim, isl_dim_param);
3638 nvar = isl_dim_size(set->dim, isl_dim_set);
3639 for (i = 0; i < nparam; ++i) {
3640 if (active[i])
3641 continue;
3642 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3643 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3644 }
3645 for (i = 0; i < nvar; ++i) {
3646 if (active[nparam + i])
3647 continue;
3648 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3649 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3650 }
3651
3652 free(active);
3653
3654 return set;
3655 error:
3656 free(active);
3657 isl_set_free(set);
3658 return NULL;
3659 }
3660
3661 struct isl_opt_data {
3662 isl_qpolynomial *qp;
3663 int first;
3664 isl_qpolynomial *opt;
3665 int max;
3666 };
3667
3668 static int opt_fn(__isl_take isl_point *pnt, void *user)
3669 {
3670 struct isl_opt_data *data = (struct isl_opt_data *)user;
3671 isl_qpolynomial *val;
3672
3673 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3674 if (data->first) {
3675 data->first = 0;
3676 data->opt = val;
3677 } else if (data->max) {
3678 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3679 } else {
3680 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3681 }
3682
3683 return 0;
3684 }
3685
3686 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3687 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3688 {
3689 struct isl_opt_data data = { NULL, 1, NULL, max };
3690
3691 if (!set || !qp)
3692 goto error;
3693
3694 if (isl_upoly_is_cst(qp->upoly)) {
3695 isl_set_free(set);
3696 return qp;
3697 }
3698
3699 set = fix_inactive(set, qp);
3700
3701 data.qp = qp;
3702 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3703 goto error;
3704
3705 if (data.first)
3706 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3707
3708 isl_set_free(set);
3709 isl_qpolynomial_free(qp);
3710 return data.opt;
3711 error:
3712 isl_set_free(set);
3713 isl_qpolynomial_free(qp);
3714 isl_qpolynomial_free(data.opt);
3715 return NULL;
3716 }
3717
3718 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3719 __isl_take isl_morph *morph)
3720 {
3721 int i;
3722 int n_sub;
3723 isl_ctx *ctx;
3724 struct isl_upoly **subs;
3725 isl_mat *mat;
3726
3727 qp = isl_qpolynomial_cow(qp);
3728 if (!qp || !morph)
3729 goto error;
3730
3731 ctx = qp->dim->ctx;
3732 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3733
3734 n_sub = morph->inv->n_row - 1;
3735 if (morph->inv->n_row != morph->inv->n_col)
3736 n_sub += qp->div->n_row;
3737 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3738 if (!subs)
3739 goto error;
3740
3741 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3742 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3743 morph->inv->row[0][0], morph->inv->n_col);
3744 if (morph->inv->n_row != morph->inv->n_col)
3745 for (i = 0; i < qp->div->n_row; ++i)
3746 subs[morph->inv->n_row - 1 + i] =
3747 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3748
3749 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3750
3751 for (i = 0; i < n_sub; ++i)
3752 isl_upoly_free(subs[i]);
3753 free(subs);
3754
3755 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3756 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3757 qp->div = isl_mat_product(qp->div, mat);
3758 isl_dim_free(qp->dim);
3759 qp->dim = isl_dim_copy(morph->ran->dim);
3760
3761 if (!qp->upoly || !qp->div || !qp->dim)
3762 goto error;
3763
3764 isl_morph_free(morph);
3765
3766 return qp;
3767 error:
3768 isl_qpolynomial_free(qp);
3769 isl_morph_free(morph);
3770 return NULL;
3771 }
3772
3773 static int neg_entry(void **entry, void *user)
3774 {
3775 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3776
3777 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3778
3779 return *pwqp ? 0 : -1;
3780 }
3781
3782 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3783 __isl_take isl_union_pw_qpolynomial *upwqp)
3784 {
3785 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3786 if (!upwqp)
3787 return NULL;
3788
3789 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3790 &neg_entry, NULL) < 0)
3791 goto error;
3792
3793 return upwqp;
3794 error:
3795 isl_union_pw_qpolynomial_free(upwqp);
3796 return NULL;
3797 }
3798
3799 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3800 __isl_take isl_union_pw_qpolynomial *upwqp1,
3801 __isl_take isl_union_pw_qpolynomial *upwqp2)
3802 {
3803 return isl_union_pw_qpolynomial_add(upwqp1,
3804 isl_union_pw_qpolynomial_neg(upwqp2));
3805 }
3806
3807 static int mul_entry(void **entry, void *user)
3808 {
3809 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3810 uint32_t hash;
3811 struct isl_hash_table_entry *entry2;
3812 isl_pw_qpolynomial *pwpq = *entry;
3813 int empty;
3814
3815 hash = isl_dim_get_hash(pwpq->dim);
3816 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3817 hash, &has_dim, pwpq->dim, 0);
3818 if (!entry2)
3819 return 0;
3820
3821 pwpq = isl_pw_qpolynomial_copy(pwpq);
3822 pwpq = isl_pw_qpolynomial_mul(pwpq,
3823 isl_pw_qpolynomial_copy(entry2->data));
3824
3825 empty = isl_pw_qpolynomial_is_zero(pwpq);
3826 if (empty < 0) {
3827 isl_pw_qpolynomial_free(pwpq);
3828 return -1;
3829 }
3830 if (empty) {
3831 isl_pw_qpolynomial_free(pwpq);
3832 return 0;
3833 }
3834
3835 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3836
3837 return 0;
3838 }
3839
3840 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3841 __isl_take isl_union_pw_qpolynomial *upwqp1,
3842 __isl_take isl_union_pw_qpolynomial *upwqp2)
3843 {
3844 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3845 }
3846
3847 /* Reorder the columns of the given div definitions according to the
3848 * given reordering.
3849 */
3850 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3851 __isl_take isl_reordering *r)
3852 {
3853 int i, j;
3854 isl_mat *mat;
3855 int extra;
3856
3857 if (!div || !r)
3858 goto error;
3859
3860 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3861 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3862 if (!mat)
3863 goto error;
3864
3865 for (i = 0; i < div->n_row; ++i) {
3866 isl_seq_cpy(mat->row[i], div->row[i], 2);
3867 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3868 for (j = 0; j < r->len; ++j)
3869 isl_int_set(mat->row[i][2 + r->pos[j]],
3870 div->row[i][2 + j]);
3871 }
3872
3873 isl_reordering_free(r);
3874 isl_mat_free(div);
3875 return mat;
3876 error:
3877 isl_reordering_free(r);
3878 isl_mat_free(div);
3879 return NULL;
3880 }
3881
3882 /* Reorder the dimension of "qp" according to the given reordering.
3883 */
3884 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3885 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3886 {
3887 qp = isl_qpolynomial_cow(qp);
3888 if (!qp)
3889 goto error;
3890
3891 r = isl_reordering_extend(r, qp->div->n_row);
3892 if (!r)
3893 goto error;
3894
3895 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3896 if (!qp->div)
3897 goto error;
3898
3899 qp->upoly = reorder(qp->upoly, r->pos);
3900 if (!qp->upoly)
3901 goto error;
3902
3903 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3904
3905 isl_reordering_free(r);
3906 return qp;
3907 error:
3908 isl_qpolynomial_free(qp);
3909 isl_reordering_free(r);
3910 return NULL;
3911 }
3912
3913 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3914 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3915 {
3916 if (!qp || !model)
3917 goto error;
3918
3919 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
3920 isl_reordering *exp;
3921
3922 model = isl_dim_drop(model, isl_dim_in,
3923 0, isl_dim_size(model, isl_dim_in));
3924 model = isl_dim_drop(model, isl_dim_out,
3925 0, isl_dim_size(model, isl_dim_out));
3926 exp = isl_parameter_alignment_reordering(qp->dim, model);
3927 exp = isl_reordering_extend_dim(exp,
3928 isl_qpolynomial_get_dim(qp));
3929 qp = isl_qpolynomial_realign(qp, exp);
3930 }
3931
3932 isl_dim_free(model);
3933 return qp;
3934 error:
3935 isl_dim_free(model);
3936 isl_qpolynomial_free(qp);
3937 return NULL;
3938 }
3939
3940 struct isl_split_periods_data {
3941 int max_periods;
3942 isl_pw_qpolynomial *res;
3943 };
3944
3945 /* Create a slice where the integer division "div" has the fixed value "v".
3946 * In particular, if "div" refers to floor(f/m), then create a slice
3947 *
3948 * m v <= f <= m v + (m - 1)
3949 *
3950 * or
3951 *
3952 * f - m v >= 0
3953 * -f + m v + (m - 1) >= 0
3954 */
3955 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3956 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3957 {
3958 int total;
3959 isl_basic_set *bset = NULL;
3960 int k;
3961
3962 if (!dim || !qp)
3963 goto error;
3964
3965 total = isl_dim_total(dim);
3966 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3967
3968 k = isl_basic_set_alloc_inequality(bset);
3969 if (k < 0)
3970 goto error;
3971 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3972 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3973
3974 k = isl_basic_set_alloc_inequality(bset);
3975 if (k < 0)
3976 goto error;
3977 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3978 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3979 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3980 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3981
3982 isl_dim_free(dim);
3983 return isl_set_from_basic_set(bset);
3984 error:
3985 isl_basic_set_free(bset);
3986 isl_dim_free(dim);
3987 return NULL;
3988 }
3989
3990 static int split_periods(__isl_take isl_set *set,
3991 __isl_take isl_qpolynomial *qp, void *user);
3992
3993 /* Create a slice of the domain "set" such that integer division "div"
3994 * has the fixed value "v" and add the results to data->res,
3995 * replacing the integer division by "v" in "qp".
3996 */
3997 static int set_div(__isl_take isl_set *set,
3998 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3999 struct isl_split_periods_data *data)
4000 {
4001 int i;
4002 int total;
4003 isl_set *slice;
4004 struct isl_upoly *cst;
4005
4006 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
4007 set = isl_set_intersect(set, slice);
4008
4009 if (!qp)
4010 goto error;
4011
4012 total = isl_dim_total(qp->dim);
4013
4014 for (i = div + 1; i < qp->div->n_row; ++i) {
4015 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4016 continue;
4017 isl_int_addmul(qp->div->row[i][1],
4018 qp->div->row[i][2 + total + div], v);
4019 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4020 }
4021
4022 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4023 qp = substitute_div(qp, div, cst);
4024
4025 return split_periods(set, qp, data);
4026 error:
4027 isl_set_free(set);
4028 isl_qpolynomial_free(qp);
4029 return -1;
4030 }
4031
4032 /* Split the domain "set" such that integer division "div"
4033 * has a fixed value (ranging from "min" to "max") on each slice
4034 * and add the results to data->res.
4035 */
4036 static int split_div(__isl_take isl_set *set,
4037 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4038 struct isl_split_periods_data *data)
4039 {
4040 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4041 isl_set *set_i = isl_set_copy(set);
4042 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4043
4044 if (set_div(set_i, qp_i, div, min, data) < 0)
4045 goto error;
4046 }
4047 isl_set_free(set);
4048 isl_qpolynomial_free(qp);
4049 return 0;
4050 error:
4051 isl_set_free(set);
4052 isl_qpolynomial_free(qp);
4053 return -1;
4054 }
4055
4056 /* If "qp" refers to any integer division
4057 * that can only attain "max_periods" distinct values on "set"
4058 * then split the domain along those distinct values.
4059 * Add the results (or the original if no splitting occurs)
4060 * to data->res.
4061 */
4062 static int split_periods(__isl_take isl_set *set,
4063 __isl_take isl_qpolynomial *qp, void *user)
4064 {
4065 int i;
4066 isl_pw_qpolynomial *pwqp;
4067 struct isl_split_periods_data *data;
4068 isl_int min, max;
4069 int total;
4070 int r = 0;
4071
4072 data = (struct isl_split_periods_data *)user;
4073
4074 if (!set || !qp)
4075 goto error;
4076
4077 if (qp->div->n_row == 0) {
4078 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4079 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4080 return 0;
4081 }
4082
4083 isl_int_init(min);
4084 isl_int_init(max);
4085 total = isl_dim_total(qp->dim);
4086 for (i = 0; i < qp->div->n_row; ++i) {
4087 enum isl_lp_result lp_res;
4088
4089 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4090 qp->div->n_row) != -1)
4091 continue;
4092
4093 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4094 set->ctx->one, &min, NULL, NULL);
4095 if (lp_res == isl_lp_error)
4096 goto error2;
4097 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4098 continue;
4099 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4100
4101 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4102 set->ctx->one, &max, NULL, NULL);
4103 if (lp_res == isl_lp_error)
4104 goto error2;
4105 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4106 continue;
4107 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4108
4109 isl_int_sub(max, max, min);
4110 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4111 isl_int_add(max, max, min);
4112 break;
4113 }
4114 }
4115
4116 if (i < qp->div->n_row) {
4117 r = split_div(set, qp, i, min, max, data);
4118 } else {
4119 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4120 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4121 }
4122
4123 isl_int_clear(max);
4124 isl_int_clear(min);
4125
4126 return r;
4127 error2:
4128 isl_int_clear(max);
4129 isl_int_clear(min);
4130 error:
4131 isl_set_free(set);
4132 isl_qpolynomial_free(qp);
4133 return -1;
4134 }
4135
4136 /* If any quasi-polynomial in pwqp refers to any integer division
4137 * that can only attain "max_periods" distinct values on its domain
4138 * then split the domain along those distinct values.
4139 */
4140 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4141 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4142 {
4143 struct isl_split_periods_data data;
4144
4145 data.max_periods = max_periods;
4146 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4147
4148 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4149 goto error;
4150
4151 isl_pw_qpolynomial_free(pwqp);
4152
4153 return data.res;
4154 error:
4155 isl_pw_qpolynomial_free(data.res);
4156 isl_pw_qpolynomial_free(pwqp);
4157 return NULL;
4158 }
4159
4160 /* Construct a piecewise quasipolynomial that is constant on the given
4161 * domain. In particular, it is
4162 * 0 if cst == 0
4163 * 1 if cst == 1
4164 * infinity if cst == -1
4165 */
4166 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4167 __isl_take isl_basic_set *bset, int cst)
4168 {
4169 isl_dim *dim;
4170 isl_qpolynomial *qp;
4171
4172 if (!bset)
4173 return NULL;
4174
4175 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4176 dim = isl_basic_set_get_dim(bset);
4177 if (cst < 0)
4178 qp = isl_qpolynomial_infty(dim);
4179 else if (cst == 0)
4180 qp = isl_qpolynomial_zero(dim);
4181 else
4182 qp = isl_qpolynomial_one(dim);
4183 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4184 }
4185
4186 /* Factor bset, call fn on each of the factors and return the product.
4187 *
4188 * If no factors can be found, simply call fn on the input.
4189 * Otherwise, construct the factors based on the factorizer,
4190 * call fn on each factor and compute the product.
4191 */
4192 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4193 __isl_take isl_basic_set *bset,
4194 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4195 {
4196 int i, n;
4197 isl_dim *dim;
4198 isl_set *set;
4199 isl_factorizer *f;
4200 isl_qpolynomial *qp;
4201 isl_pw_qpolynomial *pwqp;
4202 unsigned nparam;
4203 unsigned nvar;
4204
4205 f = isl_basic_set_factorizer(bset);
4206 if (!f)
4207 goto error;
4208 if (f->n_group == 0) {
4209 isl_factorizer_free(f);
4210 return fn(bset);
4211 }
4212
4213 nparam = isl_basic_set_dim(bset, isl_dim_param);
4214 nvar = isl_basic_set_dim(bset, isl_dim_set);
4215
4216 dim = isl_basic_set_get_dim(bset);
4217 dim = isl_dim_domain(dim);
4218 set = isl_set_universe(isl_dim_copy(dim));
4219 qp = isl_qpolynomial_one(dim);
4220 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4221
4222 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4223
4224 for (i = 0, n = 0; i < f->n_group; ++i) {
4225 isl_basic_set *bset_i;
4226 isl_pw_qpolynomial *pwqp_i;
4227
4228 bset_i = isl_basic_set_copy(bset);
4229 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4230 nparam + n + f->len[i], nvar - n - f->len[i]);
4231 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4232 nparam, n);
4233 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4234 n + f->len[i], nvar - n - f->len[i]);
4235 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4236
4237 pwqp_i = fn(bset_i);
4238 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4239
4240 n += f->len[i];
4241 }
4242
4243 isl_basic_set_free(bset);
4244 isl_factorizer_free(f);
4245
4246 return pwqp;
4247 error:
4248 isl_basic_set_free(bset);
4249 return NULL;
4250 }
4251
4252 /* Factor bset, call fn on each of the factors and return the product.
4253 * The function is assumed to evaluate to zero on empty domains,
4254 * to one on zero-dimensional domains and to infinity on unbounded domains
4255 * and will not be called explicitly on zero-dimensional or unbounded domains.
4256 *
4257 * We first check for some special cases and remove all equalities.
4258 * Then we hand over control to compressed_multiplicative_call.
4259 */
4260 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4261 __isl_take isl_basic_set *bset,
4262 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4263 {
4264 int bounded;
4265 isl_morph *morph;
4266 isl_pw_qpolynomial *pwqp;
4267 unsigned orig_nvar, final_nvar;
4268
4269 if (!bset)
4270 return NULL;
4271
4272 if (isl_basic_set_plain_is_empty(bset))
4273 return constant_on_domain(bset, 0);
4274
4275 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4276
4277 if (orig_nvar == 0)
4278 return constant_on_domain(bset, 1);
4279
4280 bounded = isl_basic_set_is_bounded(bset);
4281 if (bounded < 0)
4282 goto error;
4283 if (!bounded)
4284 return constant_on_domain(bset, -1);
4285
4286 if (bset->n_eq == 0)
4287 return compressed_multiplicative_call(bset, fn);
4288
4289 morph = isl_basic_set_full_compression(bset);
4290 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4291
4292 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4293
4294 pwqp = compressed_multiplicative_call(bset, fn);
4295
4296 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4297 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4298 morph = isl_morph_inverse(morph);
4299
4300 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4301
4302 return pwqp;
4303 error:
4304 isl_basic_set_free(bset);
4305 return NULL;
4306 }
4307
4308 /* Drop all floors in "qp", turning each integer division [a/m] into
4309 * a rational division a/m. If "down" is set, then the integer division
4310 * is replaces by (a-(m-1))/m instead.
4311 */
4312 static __isl_give isl_qpolynomial *qp_drop_floors(
4313 __isl_take isl_qpolynomial *qp, int down)
4314 {
4315 int i;
4316 struct isl_upoly *s;
4317
4318 if (!qp)
4319 return NULL;
4320 if (qp->div->n_row == 0)
4321 return qp;
4322
4323 qp = isl_qpolynomial_cow(qp);
4324 if (!qp)
4325 return NULL;
4326
4327 for (i = qp->div->n_row - 1; i >= 0; --i) {
4328 if (down) {
4329 isl_int_sub(qp->div->row[i][1],
4330 qp->div->row[i][1], qp->div->row[i][0]);
4331 isl_int_add_ui(qp->div->row[i][1],
4332 qp->div->row[i][1], 1);
4333 }
4334 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4335 qp->div->row[i][0], qp->div->n_col - 1);
4336 qp = substitute_div(qp, i, s);
4337 if (!qp)
4338 return NULL;
4339 }
4340
4341 return qp;
4342 }
4343
4344 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4345 * a rational division a/m.
4346 */
4347 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4348 __isl_take isl_pw_qpolynomial *pwqp)
4349 {
4350 int i;
4351
4352 if (!pwqp)
4353 return NULL;
4354
4355 if (isl_pw_qpolynomial_is_zero(pwqp))
4356 return pwqp;
4357
4358 pwqp = isl_pw_qpolynomial_cow(pwqp);
4359 if (!pwqp)
4360 return NULL;
4361
4362 for (i = 0; i < pwqp->n; ++i) {
4363 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4364 if (!pwqp->p[i].qp)
4365 goto error;
4366 }
4367
4368 return pwqp;
4369 error:
4370 isl_pw_qpolynomial_free(pwqp);
4371 return NULL;
4372 }
4373
4374 /* Adjust all the integer divisions in "qp" such that they are at least
4375 * one over the given orthant (identified by "signs"). This ensures
4376 * that they will still be non-negative even after subtracting (m-1)/m.
4377 *
4378 * In particular, f is replaced by f' + v, changing f = [a/m]
4379 * to f' = [(a - m v)/m].
4380 * If the constant term k in a is smaller than m,
4381 * the constant term of v is set to floor(k/m) - 1.
4382 * For any other term, if the coefficient c and the variable x have
4383 * the same sign, then no changes are needed.
4384 * Otherwise, if the variable is positive (and c is negative),
4385 * then the coefficient of x in v is set to floor(c/m).
4386 * If the variable is negative (and c is positive),
4387 * then the coefficient of x in v is set to ceil(c/m).
4388 */
4389 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4390 int *signs)
4391 {
4392 int i, j;
4393 int total;
4394 isl_vec *v = NULL;
4395 struct isl_upoly *s;
4396
4397 qp = isl_qpolynomial_cow(qp);
4398 if (!qp)
4399 return NULL;
4400 qp->div = isl_mat_cow(qp->div);
4401 if (!qp->div)
4402 goto error;
4403
4404 total = isl_dim_total(qp->dim);
4405 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4406
4407 for (i = 0; i < qp->div->n_row; ++i) {
4408 isl_int *row = qp->div->row[i];
4409 v = isl_vec_clr(v);
4410 if (!v)
4411 goto error;
4412 if (isl_int_lt(row[1], row[0])) {
4413 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4414 isl_int_sub_ui(v->el[0], v->el[0], 1);
4415 isl_int_submul(row[1], row[0], v->el[0]);
4416 }
4417 for (j = 0; j < total; ++j) {
4418 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4419 continue;
4420 if (signs[j] < 0)
4421 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4422 else
4423 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4424 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4425 }
4426 for (j = 0; j < i; ++j) {
4427 if (isl_int_sgn(row[2 + total + j]) >= 0)
4428 continue;
4429 isl_int_fdiv_q(v->el[1 + total + j],
4430 row[2 + total + j], row[0]);
4431 isl_int_submul(row[2 + total + j],
4432 row[0], v->el[1 + total + j]);
4433 }
4434 for (j = i + 1; j < qp->div->n_row; ++j) {
4435 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4436 continue;
4437 isl_seq_combine(qp->div->row[j] + 1,
4438 qp->div->ctx->one, qp->div->row[j] + 1,
4439 qp->div->row[j][2 + total + i], v->el, v->size);
4440 }
4441 isl_int_set_si(v->el[1 + total + i], 1);
4442 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4443 qp->div->ctx->one, v->size);
4444 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4445 isl_upoly_free(s);
4446 if (!qp->upoly)
4447 goto error;
4448 }
4449
4450 isl_vec_free(v);
4451 return qp;
4452 error:
4453 isl_vec_free(v);
4454 isl_qpolynomial_free(qp);
4455 return NULL;
4456 }
4457
4458 struct isl_to_poly_data {
4459 int sign;
4460 isl_pw_qpolynomial *res;
4461 isl_qpolynomial *qp;
4462 };
4463
4464 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4465 * We first make all integer divisions positive and then split the
4466 * quasipolynomials into terms with sign data->sign (the direction
4467 * of the requested approximation) and terms with the opposite sign.
4468 * In the first set of terms, each integer division [a/m] is
4469 * overapproximated by a/m, while in the second it is underapproximated
4470 * by (a-(m-1))/m.
4471 */
4472 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4473 void *user)
4474 {
4475 struct isl_to_poly_data *data = user;
4476 isl_pw_qpolynomial *t;
4477 isl_qpolynomial *qp, *up, *down;
4478
4479 qp = isl_qpolynomial_copy(data->qp);
4480 qp = make_divs_pos(qp, signs);
4481
4482 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4483 up = qp_drop_floors(up, 0);
4484 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4485 down = qp_drop_floors(down, 1);
4486
4487 isl_qpolynomial_free(qp);
4488 qp = isl_qpolynomial_add(up, down);
4489
4490 t = isl_pw_qpolynomial_alloc(orthant, qp);
4491 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4492
4493 return 0;
4494 }
4495
4496 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4497 * the polynomial will be an overapproximation. If "sign" is negative,
4498 * it will be an underapproximation. If "sign" is zero, the approximation
4499 * will lie somewhere in between.
4500 *
4501 * In particular, is sign == 0, we simply drop the floors, turning
4502 * the integer divisions into rational divisions.
4503 * Otherwise, we split the domains into orthants, make all integer divisions
4504 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4505 * depending on the requested sign and the sign of the term in which
4506 * the integer division appears.
4507 */
4508 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4509 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4510 {
4511 int i;
4512 struct isl_to_poly_data data;
4513
4514 if (sign == 0)
4515 return pwqp_drop_floors(pwqp);
4516
4517 if (!pwqp)
4518 return NULL;
4519
4520 data.sign = sign;
4521 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4522
4523 for (i = 0; i < pwqp->n; ++i) {
4524 if (pwqp->p[i].qp->div->n_row == 0) {
4525 isl_pw_qpolynomial *t;
4526 t = isl_pw_qpolynomial_alloc(
4527 isl_set_copy(pwqp->p[i].set),
4528 isl_qpolynomial_copy(pwqp->p[i].qp));
4529 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4530 continue;
4531 }
4532 data.qp = pwqp->p[i].qp;
4533 if (isl_set_foreach_orthant(pwqp->p[i].set,
4534 &to_polynomial_on_orthant, &data) < 0)
4535 goto error;
4536 }
4537
4538 isl_pw_qpolynomial_free(pwqp);
4539
4540 return data.res;
4541 error:
4542 isl_pw_qpolynomial_free(pwqp);
4543 isl_pw_qpolynomial_free(data.res);
4544 return NULL;
4545 }
4546
4547 static int poly_entry(void **entry, void *user)
4548 {
4549 int *sign = user;
4550 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4551
4552 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4553
4554 return *pwqp ? 0 : -1;
4555 }
4556
4557 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4558 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4559 {
4560 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4561 if (!upwqp)
4562 return NULL;
4563
4564 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4565 &poly_entry, &sign) < 0)
4566 goto error;
4567
4568 return upwqp;
4569 error:
4570 isl_union_pw_qpolynomial_free(upwqp);
4571 return NULL;
4572 }
4573
4574 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4575 __isl_take isl_qpolynomial *qp)
4576 {
4577 int i, k;
4578 isl_dim *dim;
4579 isl_vec *aff = NULL;
4580 isl_basic_map *bmap = NULL;
4581 unsigned pos;
4582 unsigned n_div;
4583
4584 if (!qp)
4585 return NULL;
4586 if (!isl_upoly_is_affine(qp->upoly))
4587 isl_die(qp->dim->ctx, isl_error_invalid,
4588 "input quasi-polynomial not affine", goto error);
4589 aff = isl_qpolynomial_extract_affine(qp);
4590 if (!aff)
4591 goto error;
4592 dim = isl_qpolynomial_get_dim(qp);
4593 dim = isl_dim_from_domain(dim);
4594 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4595 dim = isl_dim_add(dim, isl_dim_out, 1);
4596 n_div = qp->div->n_row;
4597 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4598
4599 for (i = 0; i < n_div; ++i) {
4600 k = isl_basic_map_alloc_div(bmap);
4601 if (k < 0)
4602 goto error;
4603 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4604 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4605 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4606 goto error;
4607 }
4608 k = isl_basic_map_alloc_equality(bmap);
4609 if (k < 0)
4610 goto error;
4611 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4612 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4613 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4614
4615 isl_vec_free(aff);
4616 isl_qpolynomial_free(qp);
4617 bmap = isl_basic_map_finalize(bmap);
4618 return bmap;
4619 error:
4620 isl_vec_free(aff);
4621 isl_qpolynomial_free(qp);
4622 isl_basic_map_free(bmap);
4623 return NULL;
4624 }
Integer set library