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add private isl_local_space_realign
[isl.git] / isl_polynomial.c
blob69e01c8918762f3337dff74ade858d6e130e0202
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 isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2609 __isl_take isl_pw_qpolynomial *pwqp1,
2610 __isl_take isl_pw_qpolynomial *pwqp2)
2611 {
2612 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2613 }
2614
2615 __isl_give struct isl_upoly *isl_upoly_eval(
2616 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2617 {
2618 int i;
2619 struct isl_upoly_rec *rec;
2620 struct isl_upoly *res;
2621 struct isl_upoly *base;
2622
2623 if (isl_upoly_is_cst(up)) {
2624 isl_vec_free(vec);
2625 return up;
2626 }
2627
2628 rec = isl_upoly_as_rec(up);
2629 if (!rec)
2630 goto error;
2631
2632 isl_assert(up->ctx, rec->n >= 1, goto error);
2633
2634 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2635
2636 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2637 isl_vec_copy(vec));
2638
2639 for (i = rec->n - 2; i >= 0; --i) {
2640 res = isl_upoly_mul(res, isl_upoly_copy(base));
2641 res = isl_upoly_sum(res,
2642 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2643 isl_vec_copy(vec)));
2644 }
2645
2646 isl_upoly_free(base);
2647 isl_upoly_free(up);
2648 isl_vec_free(vec);
2649 return res;
2650 error:
2651 isl_upoly_free(up);
2652 isl_vec_free(vec);
2653 return NULL;
2654 }
2655
2656 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2657 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2658 {
2659 isl_vec *ext;
2660 struct isl_upoly *up;
2661 isl_dim *dim;
2662
2663 if (!qp || !pnt)
2664 goto error;
2665 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2666
2667 if (qp->div->n_row == 0)
2668 ext = isl_vec_copy(pnt->vec);
2669 else {
2670 int i;
2671 unsigned dim = isl_dim_total(qp->dim);
2672 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2673 if (!ext)
2674 goto error;
2675
2676 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2677 for (i = 0; i < qp->div->n_row; ++i) {
2678 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2679 1 + dim + i, &ext->el[1+dim+i]);
2680 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2681 qp->div->row[i][0]);
2682 }
2683 }
2684
2685 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2686 if (!up)
2687 goto error;
2688
2689 dim = isl_dim_copy(qp->dim);
2690 isl_qpolynomial_free(qp);
2691 isl_point_free(pnt);
2692
2693 return isl_qpolynomial_alloc(dim, 0, up);
2694 error:
2695 isl_qpolynomial_free(qp);
2696 isl_point_free(pnt);
2697 return NULL;
2698 }
2699
2700 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2701 __isl_keep struct isl_upoly_cst *cst2)
2702 {
2703 int cmp;
2704 isl_int t;
2705 isl_int_init(t);
2706 isl_int_mul(t, cst1->n, cst2->d);
2707 isl_int_submul(t, cst2->n, cst1->d);
2708 cmp = isl_int_sgn(t);
2709 isl_int_clear(t);
2710 return cmp;
2711 }
2712
2713 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2714 __isl_keep isl_qpolynomial *qp2)
2715 {
2716 struct isl_upoly_cst *cst1, *cst2;
2717
2718 if (!qp1 || !qp2)
2719 return -1;
2720 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2721 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2722 if (isl_qpolynomial_is_nan(qp1))
2723 return -1;
2724 if (isl_qpolynomial_is_nan(qp2))
2725 return -1;
2726 cst1 = isl_upoly_as_cst(qp1->upoly);
2727 cst2 = isl_upoly_as_cst(qp2->upoly);
2728
2729 return isl_upoly_cmp(cst1, cst2) <= 0;
2730 }
2731
2732 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2733 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2734 {
2735 struct isl_upoly_cst *cst1, *cst2;
2736 int cmp;
2737
2738 if (!qp1 || !qp2)
2739 goto error;
2740 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2741 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2742 cst1 = isl_upoly_as_cst(qp1->upoly);
2743 cst2 = isl_upoly_as_cst(qp2->upoly);
2744 cmp = isl_upoly_cmp(cst1, cst2);
2745
2746 if (cmp <= 0) {
2747 isl_qpolynomial_free(qp2);
2748 } else {
2749 isl_qpolynomial_free(qp1);
2750 qp1 = qp2;
2751 }
2752 return qp1;
2753 error:
2754 isl_qpolynomial_free(qp1);
2755 isl_qpolynomial_free(qp2);
2756 return NULL;
2757 }
2758
2759 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2760 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2761 {
2762 struct isl_upoly_cst *cst1, *cst2;
2763 int cmp;
2764
2765 if (!qp1 || !qp2)
2766 goto error;
2767 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2768 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2769 cst1 = isl_upoly_as_cst(qp1->upoly);
2770 cst2 = isl_upoly_as_cst(qp2->upoly);
2771 cmp = isl_upoly_cmp(cst1, cst2);
2772
2773 if (cmp >= 0) {
2774 isl_qpolynomial_free(qp2);
2775 } else {
2776 isl_qpolynomial_free(qp1);
2777 qp1 = qp2;
2778 }
2779 return qp1;
2780 error:
2781 isl_qpolynomial_free(qp1);
2782 isl_qpolynomial_free(qp2);
2783 return NULL;
2784 }
2785
2786 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2787 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2788 unsigned first, unsigned n)
2789 {
2790 unsigned total;
2791 unsigned g_pos;
2792 int *exp;
2793
2794 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2795 return qp;
2796
2797 qp = isl_qpolynomial_cow(qp);
2798 if (!qp)
2799 return NULL;
2800
2801 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2802 goto error);
2803
2804 g_pos = pos(qp->dim, type) + first;
2805
2806 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2807 if (!qp->div)
2808 goto error;
2809
2810 total = qp->div->n_col - 2;
2811 if (total > g_pos) {
2812 int i;
2813 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2814 if (!exp)
2815 goto error;
2816 for (i = 0; i < total - g_pos; ++i)
2817 exp[i] = i + n;
2818 qp->upoly = expand(qp->upoly, exp, g_pos);
2819 free(exp);
2820 if (!qp->upoly)
2821 goto error;
2822 }
2823
2824 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2825 if (!qp->dim)
2826 goto error;
2827
2828 return qp;
2829 error:
2830 isl_qpolynomial_free(qp);
2831 return NULL;
2832 }
2833
2834 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2835 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2836 {
2837 unsigned pos;
2838
2839 pos = isl_qpolynomial_dim(qp, type);
2840
2841 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2842 }
2843
2844 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2845 __isl_take isl_pw_qpolynomial *pwqp,
2846 enum isl_dim_type type, unsigned n)
2847 {
2848 unsigned pos;
2849
2850 pos = isl_pw_qpolynomial_dim(pwqp, type);
2851
2852 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2853 }
2854
2855 static int *reordering_move(isl_ctx *ctx,
2856 unsigned len, unsigned dst, unsigned src, unsigned n)
2857 {
2858 int i;
2859 int *reordering;
2860
2861 reordering = isl_alloc_array(ctx, int, len);
2862 if (!reordering)
2863 return NULL;
2864
2865 if (dst <= src) {
2866 for (i = 0; i < dst; ++i)
2867 reordering[i] = i;
2868 for (i = 0; i < n; ++i)
2869 reordering[src + i] = dst + i;
2870 for (i = 0; i < src - dst; ++i)
2871 reordering[dst + i] = dst + n + i;
2872 for (i = 0; i < len - src - n; ++i)
2873 reordering[src + n + i] = src + n + i;
2874 } else {
2875 for (i = 0; i < src; ++i)
2876 reordering[i] = i;
2877 for (i = 0; i < n; ++i)
2878 reordering[src + i] = dst + i;
2879 for (i = 0; i < dst - src; ++i)
2880 reordering[src + n + i] = src + i;
2881 for (i = 0; i < len - dst - n; ++i)
2882 reordering[dst + n + i] = dst + n + i;
2883 }
2884
2885 return reordering;
2886 }
2887
2888 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2889 __isl_take isl_qpolynomial *qp,
2890 enum isl_dim_type dst_type, unsigned dst_pos,
2891 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2892 {
2893 unsigned g_dst_pos;
2894 unsigned g_src_pos;
2895 int *reordering;
2896
2897 qp = isl_qpolynomial_cow(qp);
2898 if (!qp)
2899 return NULL;
2900
2901 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2902 goto error);
2903
2904 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2905 g_src_pos = pos(qp->dim, src_type) + src_pos;
2906 if (dst_type > src_type)
2907 g_dst_pos -= n;
2908
2909 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2910 if (!qp->div)
2911 goto error;
2912 qp = sort_divs(qp);
2913 if (!qp)
2914 goto error;
2915
2916 reordering = reordering_move(qp->dim->ctx,
2917 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2918 if (!reordering)
2919 goto error;
2920
2921 qp->upoly = reorder(qp->upoly, reordering);
2922 free(reordering);
2923 if (!qp->upoly)
2924 goto error;
2925
2926 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2927 if (!qp->dim)
2928 goto error;
2929
2930 return qp;
2931 error:
2932 isl_qpolynomial_free(qp);
2933 return NULL;
2934 }
2935
2936 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2937 isl_int *f, isl_int denom)
2938 {
2939 struct isl_upoly *up;
2940
2941 if (!dim)
2942 return NULL;
2943
2944 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2945
2946 return isl_qpolynomial_alloc(dim, 0, up);
2947 }
2948
2949 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
2950 {
2951 isl_ctx *ctx;
2952 struct isl_upoly *up;
2953 isl_qpolynomial *qp;
2954
2955 if (!aff)
2956 return NULL;
2957
2958 ctx = isl_aff_get_ctx(aff);
2959 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
2960 aff->v->size - 1);
2961
2962 qp = isl_qpolynomial_alloc(isl_aff_get_dim(aff),
2963 aff->ls->div->n_row, up);
2964 if (!qp)
2965 goto error;
2966
2967 isl_mat_free(qp->div);
2968 qp->div = isl_mat_copy(aff->ls->div);
2969 qp->div = isl_mat_cow(qp->div);
2970 if (!qp->div)
2971 goto error;
2972
2973 isl_aff_free(aff);
2974 qp = reduce_divs(qp);
2975 qp = remove_redundant_divs(qp);
2976 return qp;
2977 error:
2978 isl_aff_free(aff);
2979 return NULL;
2980 }
2981
2982 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2983 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2984 {
2985 isl_aff *aff;
2986
2987 aff = isl_constraint_get_bound(c, type, pos);
2988 isl_constraint_free(c);
2989 return isl_qpolynomial_from_aff(aff);
2990 }
2991
2992 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2993 * in "qp" by subs[i].
2994 */
2995 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2996 __isl_take isl_qpolynomial *qp,
2997 enum isl_dim_type type, unsigned first, unsigned n,
2998 __isl_keep isl_qpolynomial **subs)
2999 {
3000 int i;
3001 struct isl_upoly **ups;
3002
3003 if (n == 0)
3004 return qp;
3005
3006 qp = isl_qpolynomial_cow(qp);
3007 if (!qp)
3008 return NULL;
3009 for (i = 0; i < n; ++i)
3010 if (!subs[i])
3011 goto error;
3012
3013 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
3014 goto error);
3015
3016 for (i = 0; i < n; ++i)
3017 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
3018 goto error);
3019
3020 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3021 for (i = 0; i < n; ++i)
3022 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3023
3024 first += pos(qp->dim, type);
3025
3026 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3027 if (!ups)
3028 goto error;
3029 for (i = 0; i < n; ++i)
3030 ups[i] = subs[i]->upoly;
3031
3032 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3033
3034 free(ups);
3035
3036 if (!qp->upoly)
3037 goto error;
3038
3039 return qp;
3040 error:
3041 isl_qpolynomial_free(qp);
3042 return NULL;
3043 }
3044
3045 /* Extend "bset" with extra set dimensions for each integer division
3046 * in "qp" and then call "fn" with the extended bset and the polynomial
3047 * that results from replacing each of the integer divisions by the
3048 * corresponding extra set dimension.
3049 */
3050 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3051 __isl_keep isl_basic_set *bset,
3052 int (*fn)(__isl_take isl_basic_set *bset,
3053 __isl_take isl_qpolynomial *poly, void *user), void *user)
3054 {
3055 isl_dim *dim;
3056 isl_mat *div;
3057 isl_qpolynomial *poly;
3058
3059 if (!qp || !bset)
3060 goto error;
3061 if (qp->div->n_row == 0)
3062 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3063 user);
3064
3065 div = isl_mat_copy(qp->div);
3066 dim = isl_dim_copy(qp->dim);
3067 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3068 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3069 bset = isl_basic_set_copy(bset);
3070 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3071 bset = add_div_constraints(bset, div);
3072
3073 return fn(bset, poly, user);
3074 error:
3075 return -1;
3076 }
3077
3078 /* Return total degree in variables first (inclusive) up to last (exclusive).
3079 */
3080 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3081 {
3082 int deg = -1;
3083 int i;
3084 struct isl_upoly_rec *rec;
3085
3086 if (!up)
3087 return -2;
3088 if (isl_upoly_is_zero(up))
3089 return -1;
3090 if (isl_upoly_is_cst(up) || up->var < first)
3091 return 0;
3092
3093 rec = isl_upoly_as_rec(up);
3094 if (!rec)
3095 return -2;
3096
3097 for (i = 0; i < rec->n; ++i) {
3098 int d;
3099
3100 if (isl_upoly_is_zero(rec->p[i]))
3101 continue;
3102 d = isl_upoly_degree(rec->p[i], first, last);
3103 if (up->var < last)
3104 d += i;
3105 if (d > deg)
3106 deg = d;
3107 }
3108
3109 return deg;
3110 }
3111
3112 /* Return total degree in set variables.
3113 */
3114 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3115 {
3116 unsigned ovar;
3117 unsigned nvar;
3118
3119 if (!poly)
3120 return -2;
3121
3122 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3123 nvar = isl_dim_size(poly->dim, isl_dim_set);
3124 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3125 }
3126
3127 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3128 unsigned pos, int deg)
3129 {
3130 int i;
3131 struct isl_upoly_rec *rec;
3132
3133 if (!up)
3134 return NULL;
3135
3136 if (isl_upoly_is_cst(up) || up->var < pos) {
3137 if (deg == 0)
3138 return isl_upoly_copy(up);
3139 else
3140 return isl_upoly_zero(up->ctx);
3141 }
3142
3143 rec = isl_upoly_as_rec(up);
3144 if (!rec)
3145 return NULL;
3146
3147 if (up->var == pos) {
3148 if (deg < rec->n)
3149 return isl_upoly_copy(rec->p[deg]);
3150 else
3151 return isl_upoly_zero(up->ctx);
3152 }
3153
3154 up = isl_upoly_copy(up);
3155 up = isl_upoly_cow(up);
3156 rec = isl_upoly_as_rec(up);
3157 if (!rec)
3158 goto error;
3159
3160 for (i = 0; i < rec->n; ++i) {
3161 struct isl_upoly *t;
3162 t = isl_upoly_coeff(rec->p[i], pos, deg);
3163 if (!t)
3164 goto error;
3165 isl_upoly_free(rec->p[i]);
3166 rec->p[i] = t;
3167 }
3168
3169 return up;
3170 error:
3171 isl_upoly_free(up);
3172 return NULL;
3173 }
3174
3175 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3176 */
3177 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3178 __isl_keep isl_qpolynomial *qp,
3179 enum isl_dim_type type, unsigned t_pos, int deg)
3180 {
3181 unsigned g_pos;
3182 struct isl_upoly *up;
3183 isl_qpolynomial *c;
3184
3185 if (!qp)
3186 return NULL;
3187
3188 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3189 return NULL);
3190
3191 g_pos = pos(qp->dim, type) + t_pos;
3192 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3193
3194 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3195 if (!c)
3196 return NULL;
3197 isl_mat_free(c->div);
3198 c->div = isl_mat_copy(qp->div);
3199 if (!c->div)
3200 goto error;
3201 return c;
3202 error:
3203 isl_qpolynomial_free(c);
3204 return NULL;
3205 }
3206
3207 /* Homogenize the polynomial in the variables first (inclusive) up to
3208 * last (exclusive) by inserting powers of variable first.
3209 * Variable first is assumed not to appear in the input.
3210 */
3211 __isl_give struct isl_upoly *isl_upoly_homogenize(
3212 __isl_take struct isl_upoly *up, int deg, int target,
3213 int first, int last)
3214 {
3215 int i;
3216 struct isl_upoly_rec *rec;
3217
3218 if (!up)
3219 return NULL;
3220 if (isl_upoly_is_zero(up))
3221 return up;
3222 if (deg == target)
3223 return up;
3224 if (isl_upoly_is_cst(up) || up->var < first) {
3225 struct isl_upoly *hom;
3226
3227 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3228 if (!hom)
3229 goto error;
3230 rec = isl_upoly_as_rec(hom);
3231 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3232
3233 return hom;
3234 }
3235
3236 up = isl_upoly_cow(up);
3237 rec = isl_upoly_as_rec(up);
3238 if (!rec)
3239 goto error;
3240
3241 for (i = 0; i < rec->n; ++i) {
3242 if (isl_upoly_is_zero(rec->p[i]))
3243 continue;
3244 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3245 up->var < last ? deg + i : i, target,
3246 first, last);
3247 if (!rec->p[i])
3248 goto error;
3249 }
3250
3251 return up;
3252 error:
3253 isl_upoly_free(up);
3254 return NULL;
3255 }
3256
3257 /* Homogenize the polynomial in the set variables by introducing
3258 * powers of an extra set variable at position 0.
3259 */
3260 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3261 __isl_take isl_qpolynomial *poly)
3262 {
3263 unsigned ovar;
3264 unsigned nvar;
3265 int deg = isl_qpolynomial_degree(poly);
3266
3267 if (deg < -1)
3268 goto error;
3269
3270 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3271 poly = isl_qpolynomial_cow(poly);
3272 if (!poly)
3273 goto error;
3274
3275 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3276 nvar = isl_dim_size(poly->dim, isl_dim_set);
3277 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3278 ovar, ovar + nvar);
3279 if (!poly->upoly)
3280 goto error;
3281
3282 return poly;
3283 error:
3284 isl_qpolynomial_free(poly);
3285 return NULL;
3286 }
3287
3288 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3289 __isl_take isl_mat *div)
3290 {
3291 isl_term *term;
3292 int n;
3293
3294 if (!dim || !div)
3295 goto error;
3296
3297 n = isl_dim_total(dim) + div->n_row;
3298
3299 term = isl_calloc(dim->ctx, struct isl_term,
3300 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3301 if (!term)
3302 goto error;
3303
3304 term->ref = 1;
3305 term->dim = dim;
3306 term->div = div;
3307 isl_int_init(term->n);
3308 isl_int_init(term->d);
3309
3310 return term;
3311 error:
3312 isl_dim_free(dim);
3313 isl_mat_free(div);
3314 return NULL;
3315 }
3316
3317 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3318 {
3319 if (!term)
3320 return NULL;
3321
3322 term->ref++;
3323 return term;
3324 }
3325
3326 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3327 {
3328 int i;
3329 isl_term *dup;
3330 unsigned total;
3331
3332 if (term)
3333 return NULL;
3334
3335 total = isl_dim_total(term->dim) + term->div->n_row;
3336
3337 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3338 if (!dup)
3339 return NULL;
3340
3341 isl_int_set(dup->n, term->n);
3342 isl_int_set(dup->d, term->d);
3343
3344 for (i = 0; i < total; ++i)
3345 dup->pow[i] = term->pow[i];
3346
3347 return dup;
3348 }
3349
3350 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3351 {
3352 if (!term)
3353 return NULL;
3354
3355 if (term->ref == 1)
3356 return term;
3357 term->ref--;
3358 return isl_term_dup(term);
3359 }
3360
3361 void isl_term_free(__isl_take isl_term *term)
3362 {
3363 if (!term)
3364 return;
3365
3366 if (--term->ref > 0)
3367 return;
3368
3369 isl_dim_free(term->dim);
3370 isl_mat_free(term->div);
3371 isl_int_clear(term->n);
3372 isl_int_clear(term->d);
3373 free(term);
3374 }
3375
3376 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3377 {
3378 if (!term)
3379 return 0;
3380
3381 switch (type) {
3382 case isl_dim_param:
3383 case isl_dim_in:
3384 case isl_dim_out: return isl_dim_size(term->dim, type);
3385 case isl_dim_div: return term->div->n_row;
3386 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3387 default: return 0;
3388 }
3389 }
3390
3391 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3392 {
3393 return term ? term->dim->ctx : NULL;
3394 }
3395
3396 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3397 {
3398 if (!term)
3399 return;
3400 isl_int_set(*n, term->n);
3401 }
3402
3403 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3404 {
3405 if (!term)
3406 return;
3407 isl_int_set(*d, term->d);
3408 }
3409
3410 int isl_term_get_exp(__isl_keep isl_term *term,
3411 enum isl_dim_type type, unsigned pos)
3412 {
3413 if (!term)
3414 return -1;
3415
3416 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3417
3418 if (type >= isl_dim_set)
3419 pos += isl_dim_size(term->dim, isl_dim_param);
3420 if (type >= isl_dim_div)
3421 pos += isl_dim_size(term->dim, isl_dim_set);
3422
3423 return term->pow[pos];
3424 }
3425
3426 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3427 {
3428 isl_basic_map *bmap;
3429 unsigned total;
3430 int k;
3431
3432 if (!term)
3433 return NULL;
3434
3435 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3436 return NULL);
3437
3438 total = term->div->n_col - term->div->n_row - 2;
3439 /* No nested divs for now */
3440 isl_assert(term->dim->ctx,
3441 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3442 term->div->n_row) == -1,
3443 return NULL);
3444
3445 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3446 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3447 goto error;
3448
3449 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3450
3451 return isl_basic_map_div(bmap, k);
3452 error:
3453 isl_basic_map_free(bmap);
3454 return NULL;
3455 }
3456
3457 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3458 int (*fn)(__isl_take isl_term *term, void *user),
3459 __isl_take isl_term *term, void *user)
3460 {
3461 int i;
3462 struct isl_upoly_rec *rec;
3463
3464 if (!up || !term)
3465 goto error;
3466
3467 if (isl_upoly_is_zero(up))
3468 return term;
3469
3470 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3471 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3472 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3473
3474 if (isl_upoly_is_cst(up)) {
3475 struct isl_upoly_cst *cst;
3476 cst = isl_upoly_as_cst(up);
3477 if (!cst)
3478 goto error;
3479 term = isl_term_cow(term);
3480 if (!term)
3481 goto error;
3482 isl_int_set(term->n, cst->n);
3483 isl_int_set(term->d, cst->d);
3484 if (fn(isl_term_copy(term), user) < 0)
3485 goto error;
3486 return term;
3487 }
3488
3489 rec = isl_upoly_as_rec(up);
3490 if (!rec)
3491 goto error;
3492
3493 for (i = 0; i < rec->n; ++i) {
3494 term = isl_term_cow(term);
3495 if (!term)
3496 goto error;
3497 term->pow[up->var] = i;
3498 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3499 if (!term)
3500 goto error;
3501 }
3502 term->pow[up->var] = 0;
3503
3504 return term;
3505 error:
3506 isl_term_free(term);
3507 return NULL;
3508 }
3509
3510 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3511 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3512 {
3513 isl_term *term;
3514
3515 if (!qp)
3516 return -1;
3517
3518 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3519 if (!term)
3520 return -1;
3521
3522 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3523
3524 isl_term_free(term);
3525
3526 return term ? 0 : -1;
3527 }
3528
3529 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3530 {
3531 struct isl_upoly *up;
3532 isl_qpolynomial *qp;
3533 int i, n;
3534
3535 if (!term)
3536 return NULL;
3537
3538 n = isl_dim_total(term->dim) + term->div->n_row;
3539
3540 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3541 for (i = 0; i < n; ++i) {
3542 if (!term->pow[i])
3543 continue;
3544 up = isl_upoly_mul(up,
3545 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3546 }
3547
3548 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3549 if (!qp)
3550 goto error;
3551 isl_mat_free(qp->div);
3552 qp->div = isl_mat_copy(term->div);
3553 if (!qp->div)
3554 goto error;
3555
3556 isl_term_free(term);
3557 return qp;
3558 error:
3559 isl_qpolynomial_free(qp);
3560 isl_term_free(term);
3561 return NULL;
3562 }
3563
3564 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3565 __isl_take isl_dim *dim)
3566 {
3567 int i;
3568 int extra;
3569 unsigned total;
3570
3571 if (!qp || !dim)
3572 goto error;
3573
3574 if (isl_dim_equal(qp->dim, dim)) {
3575 isl_dim_free(dim);
3576 return qp;
3577 }
3578
3579 qp = isl_qpolynomial_cow(qp);
3580 if (!qp)
3581 goto error;
3582
3583 extra = isl_dim_size(dim, isl_dim_set) -
3584 isl_dim_size(qp->dim, isl_dim_set);
3585 total = isl_dim_total(qp->dim);
3586 if (qp->div->n_row) {
3587 int *exp;
3588
3589 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3590 if (!exp)
3591 goto error;
3592 for (i = 0; i < qp->div->n_row; ++i)
3593 exp[i] = extra + i;
3594 qp->upoly = expand(qp->upoly, exp, total);
3595 free(exp);
3596 if (!qp->upoly)
3597 goto error;
3598 }
3599 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3600 if (!qp->div)
3601 goto error;
3602 for (i = 0; i < qp->div->n_row; ++i)
3603 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3604
3605 isl_dim_free(qp->dim);
3606 qp->dim = dim;
3607
3608 return qp;
3609 error:
3610 isl_dim_free(dim);
3611 isl_qpolynomial_free(qp);
3612 return NULL;
3613 }
3614
3615 /* For each parameter or variable that does not appear in qp,
3616 * first eliminate the variable from all constraints and then set it to zero.
3617 */
3618 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3619 __isl_keep isl_qpolynomial *qp)
3620 {
3621 int *active = NULL;
3622 int i;
3623 int d;
3624 unsigned nparam;
3625 unsigned nvar;
3626
3627 if (!set || !qp)
3628 goto error;
3629
3630 d = isl_dim_total(set->dim);
3631 active = isl_calloc_array(set->ctx, int, d);
3632 if (set_active(qp, active) < 0)
3633 goto error;
3634
3635 for (i = 0; i < d; ++i)
3636 if (!active[i])
3637 break;
3638
3639 if (i == d) {
3640 free(active);
3641 return set;
3642 }
3643
3644 nparam = isl_dim_size(set->dim, isl_dim_param);
3645 nvar = isl_dim_size(set->dim, isl_dim_set);
3646 for (i = 0; i < nparam; ++i) {
3647 if (active[i])
3648 continue;
3649 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3650 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3651 }
3652 for (i = 0; i < nvar; ++i) {
3653 if (active[nparam + i])
3654 continue;
3655 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3656 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3657 }
3658
3659 free(active);
3660
3661 return set;
3662 error:
3663 free(active);
3664 isl_set_free(set);
3665 return NULL;
3666 }
3667
3668 struct isl_opt_data {
3669 isl_qpolynomial *qp;
3670 int first;
3671 isl_qpolynomial *opt;
3672 int max;
3673 };
3674
3675 static int opt_fn(__isl_take isl_point *pnt, void *user)
3676 {
3677 struct isl_opt_data *data = (struct isl_opt_data *)user;
3678 isl_qpolynomial *val;
3679
3680 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3681 if (data->first) {
3682 data->first = 0;
3683 data->opt = val;
3684 } else if (data->max) {
3685 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3686 } else {
3687 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3688 }
3689
3690 return 0;
3691 }
3692
3693 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3694 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3695 {
3696 struct isl_opt_data data = { NULL, 1, NULL, max };
3697
3698 if (!set || !qp)
3699 goto error;
3700
3701 if (isl_upoly_is_cst(qp->upoly)) {
3702 isl_set_free(set);
3703 return qp;
3704 }
3705
3706 set = fix_inactive(set, qp);
3707
3708 data.qp = qp;
3709 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3710 goto error;
3711
3712 if (data.first)
3713 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3714
3715 isl_set_free(set);
3716 isl_qpolynomial_free(qp);
3717 return data.opt;
3718 error:
3719 isl_set_free(set);
3720 isl_qpolynomial_free(qp);
3721 isl_qpolynomial_free(data.opt);
3722 return NULL;
3723 }
3724
3725 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3726 __isl_take isl_morph *morph)
3727 {
3728 int i;
3729 int n_sub;
3730 isl_ctx *ctx;
3731 struct isl_upoly **subs;
3732 isl_mat *mat;
3733
3734 qp = isl_qpolynomial_cow(qp);
3735 if (!qp || !morph)
3736 goto error;
3737
3738 ctx = qp->dim->ctx;
3739 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3740
3741 n_sub = morph->inv->n_row - 1;
3742 if (morph->inv->n_row != morph->inv->n_col)
3743 n_sub += qp->div->n_row;
3744 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3745 if (!subs)
3746 goto error;
3747
3748 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3749 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3750 morph->inv->row[0][0], morph->inv->n_col);
3751 if (morph->inv->n_row != morph->inv->n_col)
3752 for (i = 0; i < qp->div->n_row; ++i)
3753 subs[morph->inv->n_row - 1 + i] =
3754 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3755
3756 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3757
3758 for (i = 0; i < n_sub; ++i)
3759 isl_upoly_free(subs[i]);
3760 free(subs);
3761
3762 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3763 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3764 qp->div = isl_mat_product(qp->div, mat);
3765 isl_dim_free(qp->dim);
3766 qp->dim = isl_dim_copy(morph->ran->dim);
3767
3768 if (!qp->upoly || !qp->div || !qp->dim)
3769 goto error;
3770
3771 isl_morph_free(morph);
3772
3773 return qp;
3774 error:
3775 isl_qpolynomial_free(qp);
3776 isl_morph_free(morph);
3777 return NULL;
3778 }
3779
3780 static int neg_entry(void **entry, void *user)
3781 {
3782 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3783
3784 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3785
3786 return *pwqp ? 0 : -1;
3787 }
3788
3789 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3790 __isl_take isl_union_pw_qpolynomial *upwqp)
3791 {
3792 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3793 if (!upwqp)
3794 return NULL;
3795
3796 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3797 &neg_entry, NULL) < 0)
3798 goto error;
3799
3800 return upwqp;
3801 error:
3802 isl_union_pw_qpolynomial_free(upwqp);
3803 return NULL;
3804 }
3805
3806 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3807 __isl_take isl_union_pw_qpolynomial *upwqp1,
3808 __isl_take isl_union_pw_qpolynomial *upwqp2)
3809 {
3810 return isl_union_pw_qpolynomial_add(upwqp1,
3811 isl_union_pw_qpolynomial_neg(upwqp2));
3812 }
3813
3814 static int mul_entry(void **entry, void *user)
3815 {
3816 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3817 uint32_t hash;
3818 struct isl_hash_table_entry *entry2;
3819 isl_pw_qpolynomial *pwpq = *entry;
3820 int empty;
3821
3822 hash = isl_dim_get_hash(pwpq->dim);
3823 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3824 hash, &has_dim, pwpq->dim, 0);
3825 if (!entry2)
3826 return 0;
3827
3828 pwpq = isl_pw_qpolynomial_copy(pwpq);
3829 pwpq = isl_pw_qpolynomial_mul(pwpq,
3830 isl_pw_qpolynomial_copy(entry2->data));
3831
3832 empty = isl_pw_qpolynomial_is_zero(pwpq);
3833 if (empty < 0) {
3834 isl_pw_qpolynomial_free(pwpq);
3835 return -1;
3836 }
3837 if (empty) {
3838 isl_pw_qpolynomial_free(pwpq);
3839 return 0;
3840 }
3841
3842 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3843
3844 return 0;
3845 }
3846
3847 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3848 __isl_take isl_union_pw_qpolynomial *upwqp1,
3849 __isl_take isl_union_pw_qpolynomial *upwqp2)
3850 {
3851 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3852 }
3853
3854 /* Reorder the columns of the given div definitions according to the
3855 * given reordering.
3856 */
3857 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3858 __isl_take isl_reordering *r)
3859 {
3860 int i, j;
3861 isl_mat *mat;
3862 int extra;
3863
3864 if (!div || !r)
3865 goto error;
3866
3867 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3868 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3869 if (!mat)
3870 goto error;
3871
3872 for (i = 0; i < div->n_row; ++i) {
3873 isl_seq_cpy(mat->row[i], div->row[i], 2);
3874 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3875 for (j = 0; j < r->len; ++j)
3876 isl_int_set(mat->row[i][2 + r->pos[j]],
3877 div->row[i][2 + j]);
3878 }
3879
3880 isl_reordering_free(r);
3881 isl_mat_free(div);
3882 return mat;
3883 error:
3884 isl_reordering_free(r);
3885 isl_mat_free(div);
3886 return NULL;
3887 }
3888
3889 /* Reorder the dimension of "qp" according to the given reordering.
3890 */
3891 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3892 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3893 {
3894 qp = isl_qpolynomial_cow(qp);
3895 if (!qp)
3896 goto error;
3897
3898 r = isl_reordering_extend(r, qp->div->n_row);
3899 if (!r)
3900 goto error;
3901
3902 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3903 if (!qp->div)
3904 goto error;
3905
3906 qp->upoly = reorder(qp->upoly, r->pos);
3907 if (!qp->upoly)
3908 goto error;
3909
3910 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3911
3912 isl_reordering_free(r);
3913 return qp;
3914 error:
3915 isl_qpolynomial_free(qp);
3916 isl_reordering_free(r);
3917 return NULL;
3918 }
3919
3920 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3921 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3922 {
3923 if (!qp || !model)
3924 goto error;
3925
3926 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
3927 isl_reordering *exp;
3928
3929 model = isl_dim_drop(model, isl_dim_in,
3930 0, isl_dim_size(model, isl_dim_in));
3931 model = isl_dim_drop(model, isl_dim_out,
3932 0, isl_dim_size(model, isl_dim_out));
3933 exp = isl_parameter_alignment_reordering(qp->dim, model);
3934 exp = isl_reordering_extend_dim(exp,
3935 isl_qpolynomial_get_dim(qp));
3936 qp = isl_qpolynomial_realign(qp, exp);
3937 }
3938
3939 isl_dim_free(model);
3940 return qp;
3941 error:
3942 isl_dim_free(model);
3943 isl_qpolynomial_free(qp);
3944 return NULL;
3945 }
3946
3947 struct isl_split_periods_data {
3948 int max_periods;
3949 isl_pw_qpolynomial *res;
3950 };
3951
3952 /* Create a slice where the integer division "div" has the fixed value "v".
3953 * In particular, if "div" refers to floor(f/m), then create a slice
3954 *
3955 * m v <= f <= m v + (m - 1)
3956 *
3957 * or
3958 *
3959 * f - m v >= 0
3960 * -f + m v + (m - 1) >= 0
3961 */
3962 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3963 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3964 {
3965 int total;
3966 isl_basic_set *bset = NULL;
3967 int k;
3968
3969 if (!dim || !qp)
3970 goto error;
3971
3972 total = isl_dim_total(dim);
3973 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3974
3975 k = isl_basic_set_alloc_inequality(bset);
3976 if (k < 0)
3977 goto error;
3978 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3979 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3980
3981 k = isl_basic_set_alloc_inequality(bset);
3982 if (k < 0)
3983 goto error;
3984 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3985 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3986 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3987 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3988
3989 isl_dim_free(dim);
3990 return isl_set_from_basic_set(bset);
3991 error:
3992 isl_basic_set_free(bset);
3993 isl_dim_free(dim);
3994 return NULL;
3995 }
3996
3997 static int split_periods(__isl_take isl_set *set,
3998 __isl_take isl_qpolynomial *qp, void *user);
3999
4000 /* Create a slice of the domain "set" such that integer division "div"
4001 * has the fixed value "v" and add the results to data->res,
4002 * replacing the integer division by "v" in "qp".
4003 */
4004 static int set_div(__isl_take isl_set *set,
4005 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4006 struct isl_split_periods_data *data)
4007 {
4008 int i;
4009 int total;
4010 isl_set *slice;
4011 struct isl_upoly *cst;
4012
4013 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
4014 set = isl_set_intersect(set, slice);
4015
4016 if (!qp)
4017 goto error;
4018
4019 total = isl_dim_total(qp->dim);
4020
4021 for (i = div + 1; i < qp->div->n_row; ++i) {
4022 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4023 continue;
4024 isl_int_addmul(qp->div->row[i][1],
4025 qp->div->row[i][2 + total + div], v);
4026 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4027 }
4028
4029 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4030 qp = substitute_div(qp, div, cst);
4031
4032 return split_periods(set, qp, data);
4033 error:
4034 isl_set_free(set);
4035 isl_qpolynomial_free(qp);
4036 return -1;
4037 }
4038
4039 /* Split the domain "set" such that integer division "div"
4040 * has a fixed value (ranging from "min" to "max") on each slice
4041 * and add the results to data->res.
4042 */
4043 static int split_div(__isl_take isl_set *set,
4044 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4045 struct isl_split_periods_data *data)
4046 {
4047 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4048 isl_set *set_i = isl_set_copy(set);
4049 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4050
4051 if (set_div(set_i, qp_i, div, min, data) < 0)
4052 goto error;
4053 }
4054 isl_set_free(set);
4055 isl_qpolynomial_free(qp);
4056 return 0;
4057 error:
4058 isl_set_free(set);
4059 isl_qpolynomial_free(qp);
4060 return -1;
4061 }
4062
4063 /* If "qp" refers to any integer division
4064 * that can only attain "max_periods" distinct values on "set"
4065 * then split the domain along those distinct values.
4066 * Add the results (or the original if no splitting occurs)
4067 * to data->res.
4068 */
4069 static int split_periods(__isl_take isl_set *set,
4070 __isl_take isl_qpolynomial *qp, void *user)
4071 {
4072 int i;
4073 isl_pw_qpolynomial *pwqp;
4074 struct isl_split_periods_data *data;
4075 isl_int min, max;
4076 int total;
4077 int r = 0;
4078
4079 data = (struct isl_split_periods_data *)user;
4080
4081 if (!set || !qp)
4082 goto error;
4083
4084 if (qp->div->n_row == 0) {
4085 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4086 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4087 return 0;
4088 }
4089
4090 isl_int_init(min);
4091 isl_int_init(max);
4092 total = isl_dim_total(qp->dim);
4093 for (i = 0; i < qp->div->n_row; ++i) {
4094 enum isl_lp_result lp_res;
4095
4096 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4097 qp->div->n_row) != -1)
4098 continue;
4099
4100 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4101 set->ctx->one, &min, NULL, NULL);
4102 if (lp_res == isl_lp_error)
4103 goto error2;
4104 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4105 continue;
4106 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4107
4108 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4109 set->ctx->one, &max, NULL, NULL);
4110 if (lp_res == isl_lp_error)
4111 goto error2;
4112 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4113 continue;
4114 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4115
4116 isl_int_sub(max, max, min);
4117 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4118 isl_int_add(max, max, min);
4119 break;
4120 }
4121 }
4122
4123 if (i < qp->div->n_row) {
4124 r = split_div(set, qp, i, min, max, data);
4125 } else {
4126 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4127 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4128 }
4129
4130 isl_int_clear(max);
4131 isl_int_clear(min);
4132
4133 return r;
4134 error2:
4135 isl_int_clear(max);
4136 isl_int_clear(min);
4137 error:
4138 isl_set_free(set);
4139 isl_qpolynomial_free(qp);
4140 return -1;
4141 }
4142
4143 /* If any quasi-polynomial in pwqp refers to any integer division
4144 * that can only attain "max_periods" distinct values on its domain
4145 * then split the domain along those distinct values.
4146 */
4147 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4148 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4149 {
4150 struct isl_split_periods_data data;
4151
4152 data.max_periods = max_periods;
4153 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4154
4155 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4156 goto error;
4157
4158 isl_pw_qpolynomial_free(pwqp);
4159
4160 return data.res;
4161 error:
4162 isl_pw_qpolynomial_free(data.res);
4163 isl_pw_qpolynomial_free(pwqp);
4164 return NULL;
4165 }
4166
4167 /* Construct a piecewise quasipolynomial that is constant on the given
4168 * domain. In particular, it is
4169 * 0 if cst == 0
4170 * 1 if cst == 1
4171 * infinity if cst == -1
4172 */
4173 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4174 __isl_take isl_basic_set *bset, int cst)
4175 {
4176 isl_dim *dim;
4177 isl_qpolynomial *qp;
4178
4179 if (!bset)
4180 return NULL;
4181
4182 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4183 dim = isl_basic_set_get_dim(bset);
4184 if (cst < 0)
4185 qp = isl_qpolynomial_infty(dim);
4186 else if (cst == 0)
4187 qp = isl_qpolynomial_zero(dim);
4188 else
4189 qp = isl_qpolynomial_one(dim);
4190 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4191 }
4192
4193 /* Factor bset, call fn on each of the factors and return the product.
4194 *
4195 * If no factors can be found, simply call fn on the input.
4196 * Otherwise, construct the factors based on the factorizer,
4197 * call fn on each factor and compute the product.
4198 */
4199 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4200 __isl_take isl_basic_set *bset,
4201 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4202 {
4203 int i, n;
4204 isl_dim *dim;
4205 isl_set *set;
4206 isl_factorizer *f;
4207 isl_qpolynomial *qp;
4208 isl_pw_qpolynomial *pwqp;
4209 unsigned nparam;
4210 unsigned nvar;
4211
4212 f = isl_basic_set_factorizer(bset);
4213 if (!f)
4214 goto error;
4215 if (f->n_group == 0) {
4216 isl_factorizer_free(f);
4217 return fn(bset);
4218 }
4219
4220 nparam = isl_basic_set_dim(bset, isl_dim_param);
4221 nvar = isl_basic_set_dim(bset, isl_dim_set);
4222
4223 dim = isl_basic_set_get_dim(bset);
4224 dim = isl_dim_domain(dim);
4225 set = isl_set_universe(isl_dim_copy(dim));
4226 qp = isl_qpolynomial_one(dim);
4227 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4228
4229 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4230
4231 for (i = 0, n = 0; i < f->n_group; ++i) {
4232 isl_basic_set *bset_i;
4233 isl_pw_qpolynomial *pwqp_i;
4234
4235 bset_i = isl_basic_set_copy(bset);
4236 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4237 nparam + n + f->len[i], nvar - n - f->len[i]);
4238 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4239 nparam, n);
4240 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4241 n + f->len[i], nvar - n - f->len[i]);
4242 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4243
4244 pwqp_i = fn(bset_i);
4245 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4246
4247 n += f->len[i];
4248 }
4249
4250 isl_basic_set_free(bset);
4251 isl_factorizer_free(f);
4252
4253 return pwqp;
4254 error:
4255 isl_basic_set_free(bset);
4256 return NULL;
4257 }
4258
4259 /* Factor bset, call fn on each of the factors and return the product.
4260 * The function is assumed to evaluate to zero on empty domains,
4261 * to one on zero-dimensional domains and to infinity on unbounded domains
4262 * and will not be called explicitly on zero-dimensional or unbounded domains.
4263 *
4264 * We first check for some special cases and remove all equalities.
4265 * Then we hand over control to compressed_multiplicative_call.
4266 */
4267 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4268 __isl_take isl_basic_set *bset,
4269 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4270 {
4271 int bounded;
4272 isl_morph *morph;
4273 isl_pw_qpolynomial *pwqp;
4274 unsigned orig_nvar, final_nvar;
4275
4276 if (!bset)
4277 return NULL;
4278
4279 if (isl_basic_set_plain_is_empty(bset))
4280 return constant_on_domain(bset, 0);
4281
4282 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4283
4284 if (orig_nvar == 0)
4285 return constant_on_domain(bset, 1);
4286
4287 bounded = isl_basic_set_is_bounded(bset);
4288 if (bounded < 0)
4289 goto error;
4290 if (!bounded)
4291 return constant_on_domain(bset, -1);
4292
4293 if (bset->n_eq == 0)
4294 return compressed_multiplicative_call(bset, fn);
4295
4296 morph = isl_basic_set_full_compression(bset);
4297 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4298
4299 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4300
4301 pwqp = compressed_multiplicative_call(bset, fn);
4302
4303 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4304 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4305 morph = isl_morph_inverse(morph);
4306
4307 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4308
4309 return pwqp;
4310 error:
4311 isl_basic_set_free(bset);
4312 return NULL;
4313 }
4314
4315 /* Drop all floors in "qp", turning each integer division [a/m] into
4316 * a rational division a/m. If "down" is set, then the integer division
4317 * is replaces by (a-(m-1))/m instead.
4318 */
4319 static __isl_give isl_qpolynomial *qp_drop_floors(
4320 __isl_take isl_qpolynomial *qp, int down)
4321 {
4322 int i;
4323 struct isl_upoly *s;
4324
4325 if (!qp)
4326 return NULL;
4327 if (qp->div->n_row == 0)
4328 return qp;
4329
4330 qp = isl_qpolynomial_cow(qp);
4331 if (!qp)
4332 return NULL;
4333
4334 for (i = qp->div->n_row - 1; i >= 0; --i) {
4335 if (down) {
4336 isl_int_sub(qp->div->row[i][1],
4337 qp->div->row[i][1], qp->div->row[i][0]);
4338 isl_int_add_ui(qp->div->row[i][1],
4339 qp->div->row[i][1], 1);
4340 }
4341 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4342 qp->div->row[i][0], qp->div->n_col - 1);
4343 qp = substitute_div(qp, i, s);
4344 if (!qp)
4345 return NULL;
4346 }
4347
4348 return qp;
4349 }
4350
4351 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4352 * a rational division a/m.
4353 */
4354 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4355 __isl_take isl_pw_qpolynomial *pwqp)
4356 {
4357 int i;
4358
4359 if (!pwqp)
4360 return NULL;
4361
4362 if (isl_pw_qpolynomial_is_zero(pwqp))
4363 return pwqp;
4364
4365 pwqp = isl_pw_qpolynomial_cow(pwqp);
4366 if (!pwqp)
4367 return NULL;
4368
4369 for (i = 0; i < pwqp->n; ++i) {
4370 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4371 if (!pwqp->p[i].qp)
4372 goto error;
4373 }
4374
4375 return pwqp;
4376 error:
4377 isl_pw_qpolynomial_free(pwqp);
4378 return NULL;
4379 }
4380
4381 /* Adjust all the integer divisions in "qp" such that they are at least
4382 * one over the given orthant (identified by "signs"). This ensures
4383 * that they will still be non-negative even after subtracting (m-1)/m.
4384 *
4385 * In particular, f is replaced by f' + v, changing f = [a/m]
4386 * to f' = [(a - m v)/m].
4387 * If the constant term k in a is smaller than m,
4388 * the constant term of v is set to floor(k/m) - 1.
4389 * For any other term, if the coefficient c and the variable x have
4390 * the same sign, then no changes are needed.
4391 * Otherwise, if the variable is positive (and c is negative),
4392 * then the coefficient of x in v is set to floor(c/m).
4393 * If the variable is negative (and c is positive),
4394 * then the coefficient of x in v is set to ceil(c/m).
4395 */
4396 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4397 int *signs)
4398 {
4399 int i, j;
4400 int total;
4401 isl_vec *v = NULL;
4402 struct isl_upoly *s;
4403
4404 qp = isl_qpolynomial_cow(qp);
4405 if (!qp)
4406 return NULL;
4407 qp->div = isl_mat_cow(qp->div);
4408 if (!qp->div)
4409 goto error;
4410
4411 total = isl_dim_total(qp->dim);
4412 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4413
4414 for (i = 0; i < qp->div->n_row; ++i) {
4415 isl_int *row = qp->div->row[i];
4416 v = isl_vec_clr(v);
4417 if (!v)
4418 goto error;
4419 if (isl_int_lt(row[1], row[0])) {
4420 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4421 isl_int_sub_ui(v->el[0], v->el[0], 1);
4422 isl_int_submul(row[1], row[0], v->el[0]);
4423 }
4424 for (j = 0; j < total; ++j) {
4425 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4426 continue;
4427 if (signs[j] < 0)
4428 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4429 else
4430 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4431 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4432 }
4433 for (j = 0; j < i; ++j) {
4434 if (isl_int_sgn(row[2 + total + j]) >= 0)
4435 continue;
4436 isl_int_fdiv_q(v->el[1 + total + j],
4437 row[2 + total + j], row[0]);
4438 isl_int_submul(row[2 + total + j],
4439 row[0], v->el[1 + total + j]);
4440 }
4441 for (j = i + 1; j < qp->div->n_row; ++j) {
4442 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4443 continue;
4444 isl_seq_combine(qp->div->row[j] + 1,
4445 qp->div->ctx->one, qp->div->row[j] + 1,
4446 qp->div->row[j][2 + total + i], v->el, v->size);
4447 }
4448 isl_int_set_si(v->el[1 + total + i], 1);
4449 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4450 qp->div->ctx->one, v->size);
4451 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4452 isl_upoly_free(s);
4453 if (!qp->upoly)
4454 goto error;
4455 }
4456
4457 isl_vec_free(v);
4458 return qp;
4459 error:
4460 isl_vec_free(v);
4461 isl_qpolynomial_free(qp);
4462 return NULL;
4463 }
4464
4465 struct isl_to_poly_data {
4466 int sign;
4467 isl_pw_qpolynomial *res;
4468 isl_qpolynomial *qp;
4469 };
4470
4471 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4472 * We first make all integer divisions positive and then split the
4473 * quasipolynomials into terms with sign data->sign (the direction
4474 * of the requested approximation) and terms with the opposite sign.
4475 * In the first set of terms, each integer division [a/m] is
4476 * overapproximated by a/m, while in the second it is underapproximated
4477 * by (a-(m-1))/m.
4478 */
4479 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4480 void *user)
4481 {
4482 struct isl_to_poly_data *data = user;
4483 isl_pw_qpolynomial *t;
4484 isl_qpolynomial *qp, *up, *down;
4485
4486 qp = isl_qpolynomial_copy(data->qp);
4487 qp = make_divs_pos(qp, signs);
4488
4489 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4490 up = qp_drop_floors(up, 0);
4491 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4492 down = qp_drop_floors(down, 1);
4493
4494 isl_qpolynomial_free(qp);
4495 qp = isl_qpolynomial_add(up, down);
4496
4497 t = isl_pw_qpolynomial_alloc(orthant, qp);
4498 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4499
4500 return 0;
4501 }
4502
4503 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4504 * the polynomial will be an overapproximation. If "sign" is negative,
4505 * it will be an underapproximation. If "sign" is zero, the approximation
4506 * will lie somewhere in between.
4507 *
4508 * In particular, is sign == 0, we simply drop the floors, turning
4509 * the integer divisions into rational divisions.
4510 * Otherwise, we split the domains into orthants, make all integer divisions
4511 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4512 * depending on the requested sign and the sign of the term in which
4513 * the integer division appears.
4514 */
4515 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4516 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4517 {
4518 int i;
4519 struct isl_to_poly_data data;
4520
4521 if (sign == 0)
4522 return pwqp_drop_floors(pwqp);
4523
4524 if (!pwqp)
4525 return NULL;
4526
4527 data.sign = sign;
4528 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4529
4530 for (i = 0; i < pwqp->n; ++i) {
4531 if (pwqp->p[i].qp->div->n_row == 0) {
4532 isl_pw_qpolynomial *t;
4533 t = isl_pw_qpolynomial_alloc(
4534 isl_set_copy(pwqp->p[i].set),
4535 isl_qpolynomial_copy(pwqp->p[i].qp));
4536 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4537 continue;
4538 }
4539 data.qp = pwqp->p[i].qp;
4540 if (isl_set_foreach_orthant(pwqp->p[i].set,
4541 &to_polynomial_on_orthant, &data) < 0)
4542 goto error;
4543 }
4544
4545 isl_pw_qpolynomial_free(pwqp);
4546
4547 return data.res;
4548 error:
4549 isl_pw_qpolynomial_free(pwqp);
4550 isl_pw_qpolynomial_free(data.res);
4551 return NULL;
4552 }
4553
4554 static int poly_entry(void **entry, void *user)
4555 {
4556 int *sign = user;
4557 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4558
4559 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4560
4561 return *pwqp ? 0 : -1;
4562 }
4563
4564 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4565 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4566 {
4567 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4568 if (!upwqp)
4569 return NULL;
4570
4571 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4572 &poly_entry, &sign) < 0)
4573 goto error;
4574
4575 return upwqp;
4576 error:
4577 isl_union_pw_qpolynomial_free(upwqp);
4578 return NULL;
4579 }
4580
4581 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4582 __isl_take isl_qpolynomial *qp)
4583 {
4584 int i, k;
4585 isl_dim *dim;
4586 isl_vec *aff = NULL;
4587 isl_basic_map *bmap = NULL;
4588 unsigned pos;
4589 unsigned n_div;
4590
4591 if (!qp)
4592 return NULL;
4593 if (!isl_upoly_is_affine(qp->upoly))
4594 isl_die(qp->dim->ctx, isl_error_invalid,
4595 "input quasi-polynomial not affine", goto error);
4596 aff = isl_qpolynomial_extract_affine(qp);
4597 if (!aff)
4598 goto error;
4599 dim = isl_qpolynomial_get_dim(qp);
4600 dim = isl_dim_from_domain(dim);
4601 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4602 dim = isl_dim_add(dim, isl_dim_out, 1);
4603 n_div = qp->div->n_row;
4604 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4605
4606 for (i = 0; i < n_div; ++i) {
4607 k = isl_basic_map_alloc_div(bmap);
4608 if (k < 0)
4609 goto error;
4610 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4611 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4612 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4613 goto error;
4614 }
4615 k = isl_basic_map_alloc_equality(bmap);
4616 if (k < 0)
4617 goto error;
4618 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4619 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4620 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4621
4622 isl_vec_free(aff);
4623 isl_qpolynomial_free(qp);
4624 bmap = isl_basic_map_finalize(bmap);
4625 return bmap;
4626 error:
4627 isl_vec_free(aff);
4628 isl_qpolynomial_free(qp);
4629 isl_basic_map_free(bmap);
4630 return NULL;
4631 }
Integer set library