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export isl_pw_aff_coalesce
[isl.git] / isl_polynomial.c
blobce9158138542e324a5135f17b37aef9e60ed1511
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_polynomial_private.h>
19 #include <isl_point_private.h>
20 #include <isl_dim_private.h>
21 #include <isl_div_private.h>
22 #include <isl_mat_private.h>
23 #include <isl_range.h>
24 #include <isl_local_space_private.h>
25 #include <isl_aff_private.h>
26 #include <isl_config.h>
27
28 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
29 {
30 switch (type) {
31 case isl_dim_param: return 0;
32 case isl_dim_in: return dim->nparam;
33 case isl_dim_out: return dim->nparam + dim->n_in;
34 default: return 0;
35 }
36 }
37
38 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
39 {
40 if (!up)
41 return -1;
42
43 return up->var < 0;
44 }
45
46 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
47 {
48 if (!up)
49 return NULL;
50
51 isl_assert(up->ctx, up->var < 0, return NULL);
52
53 return (struct isl_upoly_cst *)up;
54 }
55
56 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
57 {
58 if (!up)
59 return NULL;
60
61 isl_assert(up->ctx, up->var >= 0, return NULL);
62
63 return (struct isl_upoly_rec *)up;
64 }
65
66 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
67 __isl_keep struct isl_upoly *up2)
68 {
69 int i;
70 struct isl_upoly_rec *rec1, *rec2;
71
72 if (!up1 || !up2)
73 return -1;
74 if (up1 == up2)
75 return 1;
76 if (up1->var != up2->var)
77 return 0;
78 if (isl_upoly_is_cst(up1)) {
79 struct isl_upoly_cst *cst1, *cst2;
80 cst1 = isl_upoly_as_cst(up1);
81 cst2 = isl_upoly_as_cst(up2);
82 if (!cst1 || !cst2)
83 return -1;
84 return isl_int_eq(cst1->n, cst2->n) &&
85 isl_int_eq(cst1->d, cst2->d);
86 }
87
88 rec1 = isl_upoly_as_rec(up1);
89 rec2 = isl_upoly_as_rec(up2);
90 if (!rec1 || !rec2)
91 return -1;
92
93 if (rec1->n != rec2->n)
94 return 0;
95
96 for (i = 0; i < rec1->n; ++i) {
97 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
98 if (eq < 0 || !eq)
99 return eq;
100 }
101
102 return 1;
103 }
104
105 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
106 {
107 struct isl_upoly_cst *cst;
108
109 if (!up)
110 return -1;
111 if (!isl_upoly_is_cst(up))
112 return 0;
113
114 cst = isl_upoly_as_cst(up);
115 if (!cst)
116 return -1;
117
118 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
119 }
120
121 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
122 {
123 struct isl_upoly_cst *cst;
124
125 if (!up)
126 return 0;
127 if (!isl_upoly_is_cst(up))
128 return 0;
129
130 cst = isl_upoly_as_cst(up);
131 if (!cst)
132 return 0;
133
134 return isl_int_sgn(cst->n);
135 }
136
137 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
138 {
139 struct isl_upoly_cst *cst;
140
141 if (!up)
142 return -1;
143 if (!isl_upoly_is_cst(up))
144 return 0;
145
146 cst = isl_upoly_as_cst(up);
147 if (!cst)
148 return -1;
149
150 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
151 }
152
153 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
154 {
155 struct isl_upoly_cst *cst;
156
157 if (!up)
158 return -1;
159 if (!isl_upoly_is_cst(up))
160 return 0;
161
162 cst = isl_upoly_as_cst(up);
163 if (!cst)
164 return -1;
165
166 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
167 }
168
169 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
170 {
171 struct isl_upoly_cst *cst;
172
173 if (!up)
174 return -1;
175 if (!isl_upoly_is_cst(up))
176 return 0;
177
178 cst = isl_upoly_as_cst(up);
179 if (!cst)
180 return -1;
181
182 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
183 }
184
185 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
186 {
187 struct isl_upoly_cst *cst;
188
189 if (!up)
190 return -1;
191 if (!isl_upoly_is_cst(up))
192 return 0;
193
194 cst = isl_upoly_as_cst(up);
195 if (!cst)
196 return -1;
197
198 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
199 }
200
201 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
202 {
203 struct isl_upoly_cst *cst;
204
205 if (!up)
206 return -1;
207 if (!isl_upoly_is_cst(up))
208 return 0;
209
210 cst = isl_upoly_as_cst(up);
211 if (!cst)
212 return -1;
213
214 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
215 }
216
217 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
218 {
219 struct isl_upoly_cst *cst;
220
221 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
222 if (!cst)
223 return NULL;
224
225 cst->up.ref = 1;
226 cst->up.ctx = ctx;
227 isl_ctx_ref(ctx);
228 cst->up.var = -1;
229
230 isl_int_init(cst->n);
231 isl_int_init(cst->d);
232
233 return cst;
234 }
235
236 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
237 {
238 struct isl_upoly_cst *cst;
239
240 cst = isl_upoly_cst_alloc(ctx);
241 if (!cst)
242 return NULL;
243
244 isl_int_set_si(cst->n, 0);
245 isl_int_set_si(cst->d, 1);
246
247 return &cst->up;
248 }
249
250 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
251 {
252 struct isl_upoly_cst *cst;
253
254 cst = isl_upoly_cst_alloc(ctx);
255 if (!cst)
256 return NULL;
257
258 isl_int_set_si(cst->n, 1);
259 isl_int_set_si(cst->d, 1);
260
261 return &cst->up;
262 }
263
264 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
265 {
266 struct isl_upoly_cst *cst;
267
268 cst = isl_upoly_cst_alloc(ctx);
269 if (!cst)
270 return NULL;
271
272 isl_int_set_si(cst->n, 1);
273 isl_int_set_si(cst->d, 0);
274
275 return &cst->up;
276 }
277
278 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
279 {
280 struct isl_upoly_cst *cst;
281
282 cst = isl_upoly_cst_alloc(ctx);
283 if (!cst)
284 return NULL;
285
286 isl_int_set_si(cst->n, -1);
287 isl_int_set_si(cst->d, 0);
288
289 return &cst->up;
290 }
291
292 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
293 {
294 struct isl_upoly_cst *cst;
295
296 cst = isl_upoly_cst_alloc(ctx);
297 if (!cst)
298 return NULL;
299
300 isl_int_set_si(cst->n, 0);
301 isl_int_set_si(cst->d, 0);
302
303 return &cst->up;
304 }
305
306 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
307 isl_int n, isl_int d)
308 {
309 struct isl_upoly_cst *cst;
310
311 cst = isl_upoly_cst_alloc(ctx);
312 if (!cst)
313 return NULL;
314
315 isl_int_set(cst->n, n);
316 isl_int_set(cst->d, d);
317
318 return &cst->up;
319 }
320
321 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
322 int var, int size)
323 {
324 struct isl_upoly_rec *rec;
325
326 isl_assert(ctx, var >= 0, return NULL);
327 isl_assert(ctx, size >= 0, return NULL);
328 rec = isl_calloc(ctx, struct isl_upoly_rec,
329 sizeof(struct isl_upoly_rec) +
330 size * sizeof(struct isl_upoly *));
331 if (!rec)
332 return NULL;
333
334 rec->up.ref = 1;
335 rec->up.ctx = ctx;
336 isl_ctx_ref(ctx);
337 rec->up.var = var;
338
339 rec->n = 0;
340 rec->size = size;
341
342 return rec;
343 }
344
345 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
346 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
347 {
348 qp = isl_qpolynomial_cow(qp);
349 if (!qp || !dim)
350 goto error;
351
352 isl_dim_free(qp->dim);
353 qp->dim = dim;
354
355 return qp;
356 error:
357 isl_qpolynomial_free(qp);
358 isl_dim_free(dim);
359 return NULL;
360 }
361
362 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
363 {
364 return qp ? qp->dim->ctx : NULL;
365 }
366
367 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
368 {
369 return qp ? isl_dim_copy(qp->dim) : NULL;
370 }
371
372 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
373 enum isl_dim_type type)
374 {
375 return qp ? isl_dim_size(qp->dim, type) : 0;
376 }
377
378 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
379 {
380 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
381 }
382
383 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
384 {
385 return qp ? isl_upoly_is_one(qp->upoly) : -1;
386 }
387
388 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
389 {
390 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
391 }
392
393 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
394 {
395 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
396 }
397
398 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
399 {
400 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
401 }
402
403 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
404 {
405 return qp ? isl_upoly_sgn(qp->upoly) : 0;
406 }
407
408 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
409 {
410 isl_int_clear(cst->n);
411 isl_int_clear(cst->d);
412 }
413
414 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
415 {
416 int i;
417
418 for (i = 0; i < rec->n; ++i)
419 isl_upoly_free(rec->p[i]);
420 }
421
422 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
423 {
424 if (!up)
425 return NULL;
426
427 up->ref++;
428 return up;
429 }
430
431 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
432 {
433 struct isl_upoly_cst *cst;
434 struct isl_upoly_cst *dup;
435
436 cst = isl_upoly_as_cst(up);
437 if (!cst)
438 return NULL;
439
440 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
441 if (!dup)
442 return NULL;
443 isl_int_set(dup->n, cst->n);
444 isl_int_set(dup->d, cst->d);
445
446 return &dup->up;
447 }
448
449 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
450 {
451 int i;
452 struct isl_upoly_rec *rec;
453 struct isl_upoly_rec *dup;
454
455 rec = isl_upoly_as_rec(up);
456 if (!rec)
457 return NULL;
458
459 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
460 if (!dup)
461 return NULL;
462
463 for (i = 0; i < rec->n; ++i) {
464 dup->p[i] = isl_upoly_copy(rec->p[i]);
465 if (!dup->p[i])
466 goto error;
467 dup->n++;
468 }
469
470 return &dup->up;
471 error:
472 isl_upoly_free(&dup->up);
473 return NULL;
474 }
475
476 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
477 {
478 if (!up)
479 return NULL;
480
481 if (isl_upoly_is_cst(up))
482 return isl_upoly_dup_cst(up);
483 else
484 return isl_upoly_dup_rec(up);
485 }
486
487 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
488 {
489 if (!up)
490 return NULL;
491
492 if (up->ref == 1)
493 return up;
494 up->ref--;
495 return isl_upoly_dup(up);
496 }
497
498 void isl_upoly_free(__isl_take struct isl_upoly *up)
499 {
500 if (!up)
501 return;
502
503 if (--up->ref > 0)
504 return;
505
506 if (up->var < 0)
507 upoly_free_cst((struct isl_upoly_cst *)up);
508 else
509 upoly_free_rec((struct isl_upoly_rec *)up);
510
511 isl_ctx_deref(up->ctx);
512 free(up);
513 }
514
515 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
516 {
517 isl_int gcd;
518
519 isl_int_init(gcd);
520 isl_int_gcd(gcd, cst->n, cst->d);
521 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
522 isl_int_divexact(cst->n, cst->n, gcd);
523 isl_int_divexact(cst->d, cst->d, gcd);
524 }
525 isl_int_clear(gcd);
526 }
527
528 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
529 __isl_take struct isl_upoly *up2)
530 {
531 struct isl_upoly_cst *cst1;
532 struct isl_upoly_cst *cst2;
533
534 up1 = isl_upoly_cow(up1);
535 if (!up1 || !up2)
536 goto error;
537
538 cst1 = isl_upoly_as_cst(up1);
539 cst2 = isl_upoly_as_cst(up2);
540
541 if (isl_int_eq(cst1->d, cst2->d))
542 isl_int_add(cst1->n, cst1->n, cst2->n);
543 else {
544 isl_int_mul(cst1->n, cst1->n, cst2->d);
545 isl_int_addmul(cst1->n, cst2->n, cst1->d);
546 isl_int_mul(cst1->d, cst1->d, cst2->d);
547 }
548
549 isl_upoly_cst_reduce(cst1);
550
551 isl_upoly_free(up2);
552 return up1;
553 error:
554 isl_upoly_free(up1);
555 isl_upoly_free(up2);
556 return NULL;
557 }
558
559 static __isl_give struct isl_upoly *replace_by_zero(
560 __isl_take struct isl_upoly *up)
561 {
562 struct isl_ctx *ctx;
563
564 if (!up)
565 return NULL;
566 ctx = up->ctx;
567 isl_upoly_free(up);
568 return isl_upoly_zero(ctx);
569 }
570
571 static __isl_give struct isl_upoly *replace_by_constant_term(
572 __isl_take struct isl_upoly *up)
573 {
574 struct isl_upoly_rec *rec;
575 struct isl_upoly *cst;
576
577 if (!up)
578 return NULL;
579
580 rec = isl_upoly_as_rec(up);
581 if (!rec)
582 goto error;
583 cst = isl_upoly_copy(rec->p[0]);
584 isl_upoly_free(up);
585 return cst;
586 error:
587 isl_upoly_free(up);
588 return NULL;
589 }
590
591 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
592 __isl_take struct isl_upoly *up2)
593 {
594 int i;
595 struct isl_upoly_rec *rec1, *rec2;
596
597 if (!up1 || !up2)
598 goto error;
599
600 if (isl_upoly_is_nan(up1)) {
601 isl_upoly_free(up2);
602 return up1;
603 }
604
605 if (isl_upoly_is_nan(up2)) {
606 isl_upoly_free(up1);
607 return up2;
608 }
609
610 if (isl_upoly_is_zero(up1)) {
611 isl_upoly_free(up1);
612 return up2;
613 }
614
615 if (isl_upoly_is_zero(up2)) {
616 isl_upoly_free(up2);
617 return up1;
618 }
619
620 if (up1->var < up2->var)
621 return isl_upoly_sum(up2, up1);
622
623 if (up2->var < up1->var) {
624 struct isl_upoly_rec *rec;
625 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
626 isl_upoly_free(up1);
627 return up2;
628 }
629 up1 = isl_upoly_cow(up1);
630 rec = isl_upoly_as_rec(up1);
631 if (!rec)
632 goto error;
633 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
634 if (rec->n == 1)
635 up1 = replace_by_constant_term(up1);
636 return up1;
637 }
638
639 if (isl_upoly_is_cst(up1))
640 return isl_upoly_sum_cst(up1, up2);
641
642 rec1 = isl_upoly_as_rec(up1);
643 rec2 = isl_upoly_as_rec(up2);
644 if (!rec1 || !rec2)
645 goto error;
646
647 if (rec1->n < rec2->n)
648 return isl_upoly_sum(up2, up1);
649
650 up1 = isl_upoly_cow(up1);
651 rec1 = isl_upoly_as_rec(up1);
652 if (!rec1)
653 goto error;
654
655 for (i = rec2->n - 1; i >= 0; --i) {
656 rec1->p[i] = isl_upoly_sum(rec1->p[i],
657 isl_upoly_copy(rec2->p[i]));
658 if (!rec1->p[i])
659 goto error;
660 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
661 isl_upoly_free(rec1->p[i]);
662 rec1->n--;
663 }
664 }
665
666 if (rec1->n == 0)
667 up1 = replace_by_zero(up1);
668 else if (rec1->n == 1)
669 up1 = replace_by_constant_term(up1);
670
671 isl_upoly_free(up2);
672
673 return up1;
674 error:
675 isl_upoly_free(up1);
676 isl_upoly_free(up2);
677 return NULL;
678 }
679
680 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
681 __isl_take struct isl_upoly *up, isl_int v)
682 {
683 struct isl_upoly_cst *cst;
684
685 up = isl_upoly_cow(up);
686 if (!up)
687 return NULL;
688
689 cst = isl_upoly_as_cst(up);
690
691 isl_int_addmul(cst->n, cst->d, v);
692
693 return up;
694 }
695
696 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
697 __isl_take struct isl_upoly *up, isl_int v)
698 {
699 struct isl_upoly_rec *rec;
700
701 if (!up)
702 return NULL;
703
704 if (isl_upoly_is_cst(up))
705 return isl_upoly_cst_add_isl_int(up, v);
706
707 up = isl_upoly_cow(up);
708 rec = isl_upoly_as_rec(up);
709 if (!rec)
710 goto error;
711
712 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
713 if (!rec->p[0])
714 goto error;
715
716 return up;
717 error:
718 isl_upoly_free(up);
719 return NULL;
720 }
721
722 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
723 __isl_take struct isl_upoly *up, isl_int v)
724 {
725 struct isl_upoly_cst *cst;
726
727 if (isl_upoly_is_zero(up))
728 return up;
729
730 up = isl_upoly_cow(up);
731 if (!up)
732 return NULL;
733
734 cst = isl_upoly_as_cst(up);
735
736 isl_int_mul(cst->n, cst->n, v);
737
738 return up;
739 }
740
741 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
742 __isl_take struct isl_upoly *up, isl_int v)
743 {
744 int i;
745 struct isl_upoly_rec *rec;
746
747 if (!up)
748 return NULL;
749
750 if (isl_upoly_is_cst(up))
751 return isl_upoly_cst_mul_isl_int(up, v);
752
753 up = isl_upoly_cow(up);
754 rec = isl_upoly_as_rec(up);
755 if (!rec)
756 goto error;
757
758 for (i = 0; i < rec->n; ++i) {
759 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
760 if (!rec->p[i])
761 goto error;
762 }
763
764 return up;
765 error:
766 isl_upoly_free(up);
767 return NULL;
768 }
769
770 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
771 __isl_take struct isl_upoly *up2)
772 {
773 struct isl_upoly_cst *cst1;
774 struct isl_upoly_cst *cst2;
775
776 up1 = isl_upoly_cow(up1);
777 if (!up1 || !up2)
778 goto error;
779
780 cst1 = isl_upoly_as_cst(up1);
781 cst2 = isl_upoly_as_cst(up2);
782
783 isl_int_mul(cst1->n, cst1->n, cst2->n);
784 isl_int_mul(cst1->d, cst1->d, cst2->d);
785
786 isl_upoly_cst_reduce(cst1);
787
788 isl_upoly_free(up2);
789 return up1;
790 error:
791 isl_upoly_free(up1);
792 isl_upoly_free(up2);
793 return NULL;
794 }
795
796 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
797 __isl_take struct isl_upoly *up2)
798 {
799 struct isl_upoly_rec *rec1;
800 struct isl_upoly_rec *rec2;
801 struct isl_upoly_rec *res = NULL;
802 int i, j;
803 int size;
804
805 rec1 = isl_upoly_as_rec(up1);
806 rec2 = isl_upoly_as_rec(up2);
807 if (!rec1 || !rec2)
808 goto error;
809 size = rec1->n + rec2->n - 1;
810 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
811 if (!res)
812 goto error;
813
814 for (i = 0; i < rec1->n; ++i) {
815 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
816 isl_upoly_copy(rec1->p[i]));
817 if (!res->p[i])
818 goto error;
819 res->n++;
820 }
821 for (; i < size; ++i) {
822 res->p[i] = isl_upoly_zero(up1->ctx);
823 if (!res->p[i])
824 goto error;
825 res->n++;
826 }
827 for (i = 0; i < rec1->n; ++i) {
828 for (j = 1; j < rec2->n; ++j) {
829 struct isl_upoly *up;
830 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
831 isl_upoly_copy(rec1->p[i]));
832 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
833 if (!res->p[i + j])
834 goto error;
835 }
836 }
837
838 isl_upoly_free(up1);
839 isl_upoly_free(up2);
840
841 return &res->up;
842 error:
843 isl_upoly_free(up1);
844 isl_upoly_free(up2);
845 isl_upoly_free(&res->up);
846 return NULL;
847 }
848
849 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
850 __isl_take struct isl_upoly *up2)
851 {
852 if (!up1 || !up2)
853 goto error;
854
855 if (isl_upoly_is_nan(up1)) {
856 isl_upoly_free(up2);
857 return up1;
858 }
859
860 if (isl_upoly_is_nan(up2)) {
861 isl_upoly_free(up1);
862 return up2;
863 }
864
865 if (isl_upoly_is_zero(up1)) {
866 isl_upoly_free(up2);
867 return up1;
868 }
869
870 if (isl_upoly_is_zero(up2)) {
871 isl_upoly_free(up1);
872 return up2;
873 }
874
875 if (isl_upoly_is_one(up1)) {
876 isl_upoly_free(up1);
877 return up2;
878 }
879
880 if (isl_upoly_is_one(up2)) {
881 isl_upoly_free(up2);
882 return up1;
883 }
884
885 if (up1->var < up2->var)
886 return isl_upoly_mul(up2, up1);
887
888 if (up2->var < up1->var) {
889 int i;
890 struct isl_upoly_rec *rec;
891 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
892 isl_ctx *ctx = up1->ctx;
893 isl_upoly_free(up1);
894 isl_upoly_free(up2);
895 return isl_upoly_nan(ctx);
896 }
897 up1 = isl_upoly_cow(up1);
898 rec = isl_upoly_as_rec(up1);
899 if (!rec)
900 goto error;
901
902 for (i = 0; i < rec->n; ++i) {
903 rec->p[i] = isl_upoly_mul(rec->p[i],
904 isl_upoly_copy(up2));
905 if (!rec->p[i])
906 goto error;
907 }
908 isl_upoly_free(up2);
909 return up1;
910 }
911
912 if (isl_upoly_is_cst(up1))
913 return isl_upoly_mul_cst(up1, up2);
914
915 return isl_upoly_mul_rec(up1, up2);
916 error:
917 isl_upoly_free(up1);
918 isl_upoly_free(up2);
919 return NULL;
920 }
921
922 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
923 unsigned power)
924 {
925 struct isl_upoly *res;
926
927 if (!up)
928 return NULL;
929 if (power == 1)
930 return up;
931
932 if (power % 2)
933 res = isl_upoly_copy(up);
934 else
935 res = isl_upoly_one(up->ctx);
936
937 while (power >>= 1) {
938 up = isl_upoly_mul(up, isl_upoly_copy(up));
939 if (power % 2)
940 res = isl_upoly_mul(res, isl_upoly_copy(up));
941 }
942
943 isl_upoly_free(up);
944 return res;
945 }
946
947 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
948 unsigned n_div, __isl_take struct isl_upoly *up)
949 {
950 struct isl_qpolynomial *qp = NULL;
951 unsigned total;
952
953 if (!dim || !up)
954 goto error;
955
956 total = isl_dim_total(dim);
957
958 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
959 if (!qp)
960 goto error;
961
962 qp->ref = 1;
963 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
964 if (!qp->div)
965 goto error;
966
967 qp->dim = dim;
968 qp->upoly = up;
969
970 return qp;
971 error:
972 isl_dim_free(dim);
973 isl_upoly_free(up);
974 isl_qpolynomial_free(qp);
975 return NULL;
976 }
977
978 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
979 {
980 if (!qp)
981 return NULL;
982
983 qp->ref++;
984 return qp;
985 }
986
987 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
988 {
989 struct isl_qpolynomial *dup;
990
991 if (!qp)
992 return NULL;
993
994 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
995 isl_upoly_copy(qp->upoly));
996 if (!dup)
997 return NULL;
998 isl_mat_free(dup->div);
999 dup->div = isl_mat_copy(qp->div);
1000 if (!dup->div)
1001 goto error;
1002
1003 return dup;
1004 error:
1005 isl_qpolynomial_free(dup);
1006 return NULL;
1007 }
1008
1009 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1010 {
1011 if (!qp)
1012 return NULL;
1013
1014 if (qp->ref == 1)
1015 return qp;
1016 qp->ref--;
1017 return isl_qpolynomial_dup(qp);
1018 }
1019
1020 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1021 {
1022 if (!qp)
1023 return;
1024
1025 if (--qp->ref > 0)
1026 return;
1027
1028 isl_dim_free(qp->dim);
1029 isl_mat_free(qp->div);
1030 isl_upoly_free(qp->upoly);
1031
1032 free(qp);
1033 }
1034
1035 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1036 {
1037 int i;
1038 struct isl_upoly_rec *rec;
1039 struct isl_upoly_cst *cst;
1040
1041 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1042 if (!rec)
1043 return NULL;
1044 for (i = 0; i < 1 + power; ++i) {
1045 rec->p[i] = isl_upoly_zero(ctx);
1046 if (!rec->p[i])
1047 goto error;
1048 rec->n++;
1049 }
1050 cst = isl_upoly_as_cst(rec->p[power]);
1051 isl_int_set_si(cst->n, 1);
1052
1053 return &rec->up;
1054 error:
1055 isl_upoly_free(&rec->up);
1056 return NULL;
1057 }
1058
1059 /* r array maps original positions to new positions.
1060 */
1061 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1062 int *r)
1063 {
1064 int i;
1065 struct isl_upoly_rec *rec;
1066 struct isl_upoly *base;
1067 struct isl_upoly *res;
1068
1069 if (isl_upoly_is_cst(up))
1070 return up;
1071
1072 rec = isl_upoly_as_rec(up);
1073 if (!rec)
1074 goto error;
1075
1076 isl_assert(up->ctx, rec->n >= 1, goto error);
1077
1078 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1079 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1080
1081 for (i = rec->n - 2; i >= 0; --i) {
1082 res = isl_upoly_mul(res, isl_upoly_copy(base));
1083 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1084 }
1085
1086 isl_upoly_free(base);
1087 isl_upoly_free(up);
1088
1089 return res;
1090 error:
1091 isl_upoly_free(up);
1092 return NULL;
1093 }
1094
1095 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1096 {
1097 int n_row, n_col;
1098 int equal;
1099
1100 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1101 div1->n_col >= div2->n_col, return -1);
1102
1103 if (div1->n_row == div2->n_row)
1104 return isl_mat_is_equal(div1, div2);
1105
1106 n_row = div1->n_row;
1107 n_col = div1->n_col;
1108 div1->n_row = div2->n_row;
1109 div1->n_col = div2->n_col;
1110
1111 equal = isl_mat_is_equal(div1, div2);
1112
1113 div1->n_row = n_row;
1114 div1->n_col = n_col;
1115
1116 return equal;
1117 }
1118
1119 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1120 {
1121 int li, lj;
1122
1123 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1124 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1125
1126 if (li != lj)
1127 return li - lj;
1128
1129 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1130 }
1131
1132 struct isl_div_sort_info {
1133 isl_mat *div;
1134 int row;
1135 };
1136
1137 static int div_sort_cmp(const void *p1, const void *p2)
1138 {
1139 const struct isl_div_sort_info *i1, *i2;
1140 i1 = (const struct isl_div_sort_info *) p1;
1141 i2 = (const struct isl_div_sort_info *) p2;
1142
1143 return cmp_row(i1->div, i1->row, i2->row);
1144 }
1145
1146 /* Sort divs and remove duplicates.
1147 */
1148 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1149 {
1150 int i;
1151 int skip;
1152 int len;
1153 struct isl_div_sort_info *array = NULL;
1154 int *pos = NULL, *at = NULL;
1155 int *reordering = NULL;
1156 unsigned div_pos;
1157
1158 if (!qp)
1159 return NULL;
1160 if (qp->div->n_row <= 1)
1161 return qp;
1162
1163 div_pos = isl_dim_total(qp->dim);
1164
1165 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1166 qp->div->n_row);
1167 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1168 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1169 len = qp->div->n_col - 2;
1170 reordering = isl_alloc_array(qp->div->ctx, int, len);
1171 if (!array || !pos || !at || !reordering)
1172 goto error;
1173
1174 for (i = 0; i < qp->div->n_row; ++i) {
1175 array[i].div = qp->div;
1176 array[i].row = i;
1177 pos[i] = i;
1178 at[i] = i;
1179 }
1180
1181 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1182 div_sort_cmp);
1183
1184 for (i = 0; i < div_pos; ++i)
1185 reordering[i] = i;
1186
1187 for (i = 0; i < qp->div->n_row; ++i) {
1188 if (pos[array[i].row] == i)
1189 continue;
1190 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1191 pos[at[i]] = pos[array[i].row];
1192 at[pos[array[i].row]] = at[i];
1193 at[i] = array[i].row;
1194 pos[array[i].row] = i;
1195 }
1196
1197 skip = 0;
1198 for (i = 0; i < len - div_pos; ++i) {
1199 if (i > 0 &&
1200 isl_seq_eq(qp->div->row[i - skip - 1],
1201 qp->div->row[i - skip], qp->div->n_col)) {
1202 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1203 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1204 2 + div_pos + i - skip);
1205 qp->div = isl_mat_drop_cols(qp->div,
1206 2 + div_pos + i - skip, 1);
1207 skip++;
1208 }
1209 reordering[div_pos + array[i].row] = div_pos + i - skip;
1210 }
1211
1212 qp->upoly = reorder(qp->upoly, reordering);
1213
1214 if (!qp->upoly || !qp->div)
1215 goto error;
1216
1217 free(at);
1218 free(pos);
1219 free(array);
1220 free(reordering);
1221
1222 return qp;
1223 error:
1224 free(at);
1225 free(pos);
1226 free(array);
1227 free(reordering);
1228 isl_qpolynomial_free(qp);
1229 return NULL;
1230 }
1231
1232 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1233 int *exp, int first)
1234 {
1235 int i;
1236 struct isl_upoly_rec *rec;
1237
1238 if (isl_upoly_is_cst(up))
1239 return up;
1240
1241 if (up->var < first)
1242 return up;
1243
1244 if (exp[up->var - first] == up->var - first)
1245 return up;
1246
1247 up = isl_upoly_cow(up);
1248 if (!up)
1249 goto error;
1250
1251 up->var = exp[up->var - first] + first;
1252
1253 rec = isl_upoly_as_rec(up);
1254 if (!rec)
1255 goto error;
1256
1257 for (i = 0; i < rec->n; ++i) {
1258 rec->p[i] = expand(rec->p[i], exp, first);
1259 if (!rec->p[i])
1260 goto error;
1261 }
1262
1263 return up;
1264 error:
1265 isl_upoly_free(up);
1266 return NULL;
1267 }
1268
1269 static __isl_give isl_qpolynomial *with_merged_divs(
1270 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1271 __isl_take isl_qpolynomial *qp2),
1272 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1273 {
1274 int *exp1 = NULL;
1275 int *exp2 = NULL;
1276 isl_mat *div = NULL;
1277
1278 qp1 = isl_qpolynomial_cow(qp1);
1279 qp2 = isl_qpolynomial_cow(qp2);
1280
1281 if (!qp1 || !qp2)
1282 goto error;
1283
1284 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1285 qp1->div->n_col >= qp2->div->n_col, goto error);
1286
1287 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1288 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1289 if (!exp1 || !exp2)
1290 goto error;
1291
1292 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1293 if (!div)
1294 goto error;
1295
1296 isl_mat_free(qp1->div);
1297 qp1->div = isl_mat_copy(div);
1298 isl_mat_free(qp2->div);
1299 qp2->div = isl_mat_copy(div);
1300
1301 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1302 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1303
1304 if (!qp1->upoly || !qp2->upoly)
1305 goto error;
1306
1307 isl_mat_free(div);
1308 free(exp1);
1309 free(exp2);
1310
1311 return fn(qp1, qp2);
1312 error:
1313 isl_mat_free(div);
1314 free(exp1);
1315 free(exp2);
1316 isl_qpolynomial_free(qp1);
1317 isl_qpolynomial_free(qp2);
1318 return NULL;
1319 }
1320
1321 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1322 __isl_take isl_qpolynomial *qp2)
1323 {
1324 qp1 = isl_qpolynomial_cow(qp1);
1325
1326 if (!qp1 || !qp2)
1327 goto error;
1328
1329 if (qp1->div->n_row < qp2->div->n_row)
1330 return isl_qpolynomial_add(qp2, qp1);
1331
1332 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1333 if (!compatible_divs(qp1->div, qp2->div))
1334 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1335
1336 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1337 if (!qp1->upoly)
1338 goto error;
1339
1340 isl_qpolynomial_free(qp2);
1341
1342 return qp1;
1343 error:
1344 isl_qpolynomial_free(qp1);
1345 isl_qpolynomial_free(qp2);
1346 return NULL;
1347 }
1348
1349 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1350 __isl_keep isl_set *dom,
1351 __isl_take isl_qpolynomial *qp1,
1352 __isl_take isl_qpolynomial *qp2)
1353 {
1354 qp1 = isl_qpolynomial_add(qp1, qp2);
1355 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1356 return qp1;
1357 }
1358
1359 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1360 __isl_take isl_qpolynomial *qp2)
1361 {
1362 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1363 }
1364
1365 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1366 __isl_take isl_qpolynomial *qp, isl_int v)
1367 {
1368 if (isl_int_is_zero(v))
1369 return qp;
1370
1371 qp = isl_qpolynomial_cow(qp);
1372 if (!qp)
1373 return NULL;
1374
1375 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1376 if (!qp->upoly)
1377 goto error;
1378
1379 return qp;
1380 error:
1381 isl_qpolynomial_free(qp);
1382 return NULL;
1383
1384 }
1385
1386 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1387 {
1388 if (!qp)
1389 return NULL;
1390
1391 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1392 }
1393
1394 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1395 __isl_take isl_qpolynomial *qp, isl_int v)
1396 {
1397 if (isl_int_is_one(v))
1398 return qp;
1399
1400 if (qp && isl_int_is_zero(v)) {
1401 isl_qpolynomial *zero;
1402 zero = isl_qpolynomial_zero(isl_dim_copy(qp->dim));
1403 isl_qpolynomial_free(qp);
1404 return zero;
1405 }
1406
1407 qp = isl_qpolynomial_cow(qp);
1408 if (!qp)
1409 return NULL;
1410
1411 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1412 if (!qp->upoly)
1413 goto error;
1414
1415 return qp;
1416 error:
1417 isl_qpolynomial_free(qp);
1418 return NULL;
1419 }
1420
1421 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
1422 __isl_take isl_qpolynomial *qp, isl_int v)
1423 {
1424 return isl_qpolynomial_mul_isl_int(qp, v);
1425 }
1426
1427 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1428 __isl_take isl_qpolynomial *qp2)
1429 {
1430 qp1 = isl_qpolynomial_cow(qp1);
1431
1432 if (!qp1 || !qp2)
1433 goto error;
1434
1435 if (qp1->div->n_row < qp2->div->n_row)
1436 return isl_qpolynomial_mul(qp2, qp1);
1437
1438 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1439 if (!compatible_divs(qp1->div, qp2->div))
1440 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1441
1442 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1443 if (!qp1->upoly)
1444 goto error;
1445
1446 isl_qpolynomial_free(qp2);
1447
1448 return qp1;
1449 error:
1450 isl_qpolynomial_free(qp1);
1451 isl_qpolynomial_free(qp2);
1452 return NULL;
1453 }
1454
1455 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1456 unsigned power)
1457 {
1458 qp = isl_qpolynomial_cow(qp);
1459
1460 if (!qp)
1461 return NULL;
1462
1463 qp->upoly = isl_upoly_pow(qp->upoly, power);
1464 if (!qp->upoly)
1465 goto error;
1466
1467 return qp;
1468 error:
1469 isl_qpolynomial_free(qp);
1470 return NULL;
1471 }
1472
1473 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1474 {
1475 if (!dim)
1476 return NULL;
1477 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1478 }
1479
1480 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1481 {
1482 if (!dim)
1483 return NULL;
1484 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1485 }
1486
1487 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1488 {
1489 if (!dim)
1490 return NULL;
1491 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1492 }
1493
1494 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1495 {
1496 if (!dim)
1497 return NULL;
1498 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1499 }
1500
1501 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1502 {
1503 if (!dim)
1504 return NULL;
1505 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1506 }
1507
1508 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1509 isl_int v)
1510 {
1511 struct isl_qpolynomial *qp;
1512 struct isl_upoly_cst *cst;
1513
1514 if (!dim)
1515 return NULL;
1516
1517 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1518 if (!qp)
1519 return NULL;
1520
1521 cst = isl_upoly_as_cst(qp->upoly);
1522 isl_int_set(cst->n, v);
1523
1524 return qp;
1525 }
1526
1527 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1528 isl_int *n, isl_int *d)
1529 {
1530 struct isl_upoly_cst *cst;
1531
1532 if (!qp)
1533 return -1;
1534
1535 if (!isl_upoly_is_cst(qp->upoly))
1536 return 0;
1537
1538 cst = isl_upoly_as_cst(qp->upoly);
1539 if (!cst)
1540 return -1;
1541
1542 if (n)
1543 isl_int_set(*n, cst->n);
1544 if (d)
1545 isl_int_set(*d, cst->d);
1546
1547 return 1;
1548 }
1549
1550 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1551 {
1552 int is_cst;
1553 struct isl_upoly_rec *rec;
1554
1555 if (!up)
1556 return -1;
1557
1558 if (up->var < 0)
1559 return 1;
1560
1561 rec = isl_upoly_as_rec(up);
1562 if (!rec)
1563 return -1;
1564
1565 if (rec->n > 2)
1566 return 0;
1567
1568 isl_assert(up->ctx, rec->n > 1, return -1);
1569
1570 is_cst = isl_upoly_is_cst(rec->p[1]);
1571 if (is_cst < 0)
1572 return -1;
1573 if (!is_cst)
1574 return 0;
1575
1576 return isl_upoly_is_affine(rec->p[0]);
1577 }
1578
1579 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1580 {
1581 if (!qp)
1582 return -1;
1583
1584 if (qp->div->n_row > 0)
1585 return 0;
1586
1587 return isl_upoly_is_affine(qp->upoly);
1588 }
1589
1590 static void update_coeff(__isl_keep isl_vec *aff,
1591 __isl_keep struct isl_upoly_cst *cst, int pos)
1592 {
1593 isl_int gcd;
1594 isl_int f;
1595
1596 if (isl_int_is_zero(cst->n))
1597 return;
1598
1599 isl_int_init(gcd);
1600 isl_int_init(f);
1601 isl_int_gcd(gcd, cst->d, aff->el[0]);
1602 isl_int_divexact(f, cst->d, gcd);
1603 isl_int_divexact(gcd, aff->el[0], gcd);
1604 isl_seq_scale(aff->el, aff->el, f, aff->size);
1605 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1606 isl_int_clear(gcd);
1607 isl_int_clear(f);
1608 }
1609
1610 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1611 __isl_keep isl_vec *aff)
1612 {
1613 struct isl_upoly_cst *cst;
1614 struct isl_upoly_rec *rec;
1615
1616 if (!up || !aff)
1617 return -1;
1618
1619 if (up->var < 0) {
1620 struct isl_upoly_cst *cst;
1621
1622 cst = isl_upoly_as_cst(up);
1623 if (!cst)
1624 return -1;
1625 update_coeff(aff, cst, 0);
1626 return 0;
1627 }
1628
1629 rec = isl_upoly_as_rec(up);
1630 if (!rec)
1631 return -1;
1632 isl_assert(up->ctx, rec->n == 2, return -1);
1633
1634 cst = isl_upoly_as_cst(rec->p[1]);
1635 if (!cst)
1636 return -1;
1637 update_coeff(aff, cst, 1 + up->var);
1638
1639 return isl_upoly_update_affine(rec->p[0], aff);
1640 }
1641
1642 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1643 __isl_keep isl_qpolynomial *qp)
1644 {
1645 isl_vec *aff;
1646 unsigned d;
1647
1648 if (!qp)
1649 return NULL;
1650
1651 d = isl_dim_total(qp->dim);
1652 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1653 if (!aff)
1654 return NULL;
1655
1656 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1657 isl_int_set_si(aff->el[0], 1);
1658
1659 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1660 goto error;
1661
1662 return aff;
1663 error:
1664 isl_vec_free(aff);
1665 return NULL;
1666 }
1667
1668 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1669 __isl_keep isl_qpolynomial *qp2)
1670 {
1671 int equal;
1672
1673 if (!qp1 || !qp2)
1674 return -1;
1675
1676 equal = isl_dim_equal(qp1->dim, qp2->dim);
1677 if (equal < 0 || !equal)
1678 return equal;
1679
1680 equal = isl_mat_is_equal(qp1->div, qp2->div);
1681 if (equal < 0 || !equal)
1682 return equal;
1683
1684 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1685 }
1686
1687 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1688 {
1689 int i;
1690 struct isl_upoly_rec *rec;
1691
1692 if (isl_upoly_is_cst(up)) {
1693 struct isl_upoly_cst *cst;
1694 cst = isl_upoly_as_cst(up);
1695 if (!cst)
1696 return;
1697 isl_int_lcm(*d, *d, cst->d);
1698 return;
1699 }
1700
1701 rec = isl_upoly_as_rec(up);
1702 if (!rec)
1703 return;
1704
1705 for (i = 0; i < rec->n; ++i)
1706 upoly_update_den(rec->p[i], d);
1707 }
1708
1709 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1710 {
1711 isl_int_set_si(*d, 1);
1712 if (!qp)
1713 return;
1714 upoly_update_den(qp->upoly, d);
1715 }
1716
1717 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1718 int pos, int power)
1719 {
1720 struct isl_ctx *ctx;
1721
1722 if (!dim)
1723 return NULL;
1724
1725 ctx = dim->ctx;
1726
1727 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1728 }
1729
1730 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1731 enum isl_dim_type type, unsigned pos)
1732 {
1733 if (!dim)
1734 return NULL;
1735
1736 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1737 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1738
1739 if (type == isl_dim_set)
1740 pos += isl_dim_size(dim, isl_dim_param);
1741
1742 return isl_qpolynomial_var_pow(dim, pos, 1);
1743 error:
1744 isl_dim_free(dim);
1745 return NULL;
1746 }
1747
1748 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1749 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1750 {
1751 int i;
1752 struct isl_upoly_rec *rec;
1753 struct isl_upoly *base, *res;
1754
1755 if (!up)
1756 return NULL;
1757
1758 if (isl_upoly_is_cst(up))
1759 return up;
1760
1761 if (up->var < first)
1762 return up;
1763
1764 rec = isl_upoly_as_rec(up);
1765 if (!rec)
1766 goto error;
1767
1768 isl_assert(up->ctx, rec->n >= 1, goto error);
1769
1770 if (up->var >= first + n)
1771 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1772 else
1773 base = isl_upoly_copy(subs[up->var - first]);
1774
1775 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1776 for (i = rec->n - 2; i >= 0; --i) {
1777 struct isl_upoly *t;
1778 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1779 res = isl_upoly_mul(res, isl_upoly_copy(base));
1780 res = isl_upoly_sum(res, t);
1781 }
1782
1783 isl_upoly_free(base);
1784 isl_upoly_free(up);
1785
1786 return res;
1787 error:
1788 isl_upoly_free(up);
1789 return NULL;
1790 }
1791
1792 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1793 isl_int denom, unsigned len)
1794 {
1795 int i;
1796 struct isl_upoly *up;
1797
1798 isl_assert(ctx, len >= 1, return NULL);
1799
1800 up = isl_upoly_rat_cst(ctx, f[0], denom);
1801 for (i = 0; i < len - 1; ++i) {
1802 struct isl_upoly *t;
1803 struct isl_upoly *c;
1804
1805 if (isl_int_is_zero(f[1 + i]))
1806 continue;
1807
1808 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1809 t = isl_upoly_var_pow(ctx, i, 1);
1810 t = isl_upoly_mul(c, t);
1811 up = isl_upoly_sum(up, t);
1812 }
1813
1814 return up;
1815 }
1816
1817 /* Remove common factor of non-constant terms and denominator.
1818 */
1819 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1820 {
1821 isl_ctx *ctx = qp->div->ctx;
1822 unsigned total = qp->div->n_col - 2;
1823
1824 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1825 isl_int_gcd(ctx->normalize_gcd,
1826 ctx->normalize_gcd, qp->div->row[div][0]);
1827 if (isl_int_is_one(ctx->normalize_gcd))
1828 return;
1829
1830 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1831 ctx->normalize_gcd, total);
1832 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1833 ctx->normalize_gcd);
1834 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1835 ctx->normalize_gcd);
1836 }
1837
1838 /* Replace the integer division identified by "div" by the polynomial "s".
1839 * The integer division is assumed not to appear in the definition
1840 * of any other integer divisions.
1841 */
1842 static __isl_give isl_qpolynomial *substitute_div(
1843 __isl_take isl_qpolynomial *qp,
1844 int div, __isl_take struct isl_upoly *s)
1845 {
1846 int i;
1847 int total;
1848 int *reordering;
1849
1850 if (!qp || !s)
1851 goto error;
1852
1853 qp = isl_qpolynomial_cow(qp);
1854 if (!qp)
1855 goto error;
1856
1857 total = isl_dim_total(qp->dim);
1858 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1859 if (!qp->upoly)
1860 goto error;
1861
1862 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1863 if (!reordering)
1864 goto error;
1865 for (i = 0; i < total + div; ++i)
1866 reordering[i] = i;
1867 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1868 reordering[i] = i - 1;
1869 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1870 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1871 qp->upoly = reorder(qp->upoly, reordering);
1872 free(reordering);
1873
1874 if (!qp->upoly || !qp->div)
1875 goto error;
1876
1877 isl_upoly_free(s);
1878 return qp;
1879 error:
1880 isl_qpolynomial_free(qp);
1881 isl_upoly_free(s);
1882 return NULL;
1883 }
1884
1885 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1886 * divisions because d is equal to 1 by their definition, i.e., e.
1887 */
1888 static __isl_give isl_qpolynomial *substitute_non_divs(
1889 __isl_take isl_qpolynomial *qp)
1890 {
1891 int i, j;
1892 int total;
1893 struct isl_upoly *s;
1894
1895 if (!qp)
1896 return NULL;
1897
1898 total = isl_dim_total(qp->dim);
1899 for (i = 0; qp && i < qp->div->n_row; ++i) {
1900 if (!isl_int_is_one(qp->div->row[i][0]))
1901 continue;
1902 for (j = i + 1; j < qp->div->n_row; ++j) {
1903 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1904 continue;
1905 isl_seq_combine(qp->div->row[j] + 1,
1906 qp->div->ctx->one, qp->div->row[j] + 1,
1907 qp->div->row[j][2 + total + i],
1908 qp->div->row[i] + 1, 1 + total + i);
1909 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1910 normalize_div(qp, j);
1911 }
1912 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1913 qp->div->row[i][0], qp->div->n_col - 1);
1914 qp = substitute_div(qp, i, s);
1915 --i;
1916 }
1917
1918 return qp;
1919 }
1920
1921 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1922 * with d the denominator. When replacing the coefficient e of x by
1923 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1924 * inside the division, so we need to add floor(e/d) * x outside.
1925 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1926 * to adjust the coefficient of x in each later div that depends on the
1927 * current div "div" and also in the affine expression "aff"
1928 * (if it too depends on "div").
1929 */
1930 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1931 __isl_keep isl_vec *aff)
1932 {
1933 int i, j;
1934 isl_int v;
1935 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1936
1937 isl_int_init(v);
1938 for (i = 0; i < 1 + total + div; ++i) {
1939 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1940 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1941 continue;
1942 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1943 isl_int_fdiv_r(qp->div->row[div][1 + i],
1944 qp->div->row[div][1 + i], qp->div->row[div][0]);
1945 if (!isl_int_is_zero(aff->el[1 + total + div]))
1946 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1947 for (j = div + 1; j < qp->div->n_row; ++j) {
1948 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1949 continue;
1950 isl_int_addmul(qp->div->row[j][1 + i],
1951 v, qp->div->row[j][2 + total + div]);
1952 }
1953 }
1954 isl_int_clear(v);
1955 }
1956
1957 /* Check if the last non-zero coefficient is bigger that half of the
1958 * denominator. If so, we will invert the div to further reduce the number
1959 * of distinct divs that may appear.
1960 * If the last non-zero coefficient is exactly half the denominator,
1961 * then we continue looking for earlier coefficients that are bigger
1962 * than half the denominator.
1963 */
1964 static int needs_invert(__isl_keep isl_mat *div, int row)
1965 {
1966 int i;
1967 int cmp;
1968
1969 for (i = div->n_col - 1; i >= 1; --i) {
1970 if (isl_int_is_zero(div->row[row][i]))
1971 continue;
1972 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1973 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1974 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1975 if (cmp)
1976 return cmp > 0;
1977 if (i == 1)
1978 return 1;
1979 }
1980
1981 return 0;
1982 }
1983
1984 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1985 * We only invert the coefficients of e (and the coefficient of q in
1986 * later divs and in "aff"). After calling this function, the
1987 * coefficients of e should be reduced again.
1988 */
1989 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1990 __isl_keep isl_vec *aff)
1991 {
1992 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1993
1994 isl_seq_neg(qp->div->row[div] + 1,
1995 qp->div->row[div] + 1, qp->div->n_col - 1);
1996 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
1997 isl_int_add(qp->div->row[div][1],
1998 qp->div->row[div][1], qp->div->row[div][0]);
1999 if (!isl_int_is_zero(aff->el[1 + total + div]))
2000 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2001 isl_mat_col_mul(qp->div, 2 + total + div,
2002 qp->div->ctx->negone, 2 + total + div);
2003 }
2004
2005 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2006 * in the interval [0, d-1], with d the denominator and such that the
2007 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2008 *
2009 * After the reduction, some divs may have become redundant or identical,
2010 * so we call substitute_non_divs and sort_divs. If these functions
2011 * eliminate divs or merge two or more divs into one, the coefficients
2012 * of the enclosing divs may have to be reduced again, so we call
2013 * ourselves recursively if the number of divs decreases.
2014 */
2015 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2016 {
2017 int i;
2018 isl_vec *aff = NULL;
2019 struct isl_upoly *s;
2020 unsigned n_div;
2021
2022 if (!qp)
2023 return NULL;
2024
2025 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2026 aff = isl_vec_clr(aff);
2027 if (!aff)
2028 goto error;
2029
2030 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2031
2032 for (i = 0; i < qp->div->n_row; ++i) {
2033 normalize_div(qp, i);
2034 reduce_div(qp, i, aff);
2035 if (needs_invert(qp->div, i)) {
2036 invert_div(qp, i, aff);
2037 reduce_div(qp, i, aff);
2038 }
2039 }
2040
2041 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2042 qp->div->ctx->one, aff->size);
2043 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2044 isl_upoly_free(s);
2045 if (!qp->upoly)
2046 goto error;
2047
2048 isl_vec_free(aff);
2049
2050 n_div = qp->div->n_row;
2051 qp = substitute_non_divs(qp);
2052 qp = sort_divs(qp);
2053 if (qp && qp->div->n_row < n_div)
2054 return reduce_divs(qp);
2055
2056 return qp;
2057 error:
2058 isl_qpolynomial_free(qp);
2059 isl_vec_free(aff);
2060 return NULL;
2061 }
2062
2063 /* Assumes each div only depends on earlier divs.
2064 */
2065 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2066 int power)
2067 {
2068 struct isl_qpolynomial *qp = NULL;
2069 struct isl_upoly_rec *rec;
2070 struct isl_upoly_cst *cst;
2071 int i, d;
2072 int pos;
2073
2074 if (!div)
2075 return NULL;
2076
2077 d = div->line - div->bmap->div;
2078
2079 pos = isl_dim_total(div->bmap->dim) + d;
2080 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2081 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2082 div->bmap->n_div, &rec->up);
2083 if (!qp)
2084 goto error;
2085
2086 for (i = 0; i < div->bmap->n_div; ++i)
2087 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2088
2089 for (i = 0; i < 1 + power; ++i) {
2090 rec->p[i] = isl_upoly_zero(div->ctx);
2091 if (!rec->p[i])
2092 goto error;
2093 rec->n++;
2094 }
2095 cst = isl_upoly_as_cst(rec->p[power]);
2096 isl_int_set_si(cst->n, 1);
2097
2098 isl_div_free(div);
2099
2100 qp = reduce_divs(qp);
2101
2102 return qp;
2103 error:
2104 isl_qpolynomial_free(qp);
2105 isl_div_free(div);
2106 return NULL;
2107 }
2108
2109 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2110 {
2111 return isl_qpolynomial_div_pow(div, 1);
2112 }
2113
2114 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2115 const isl_int n, const isl_int d)
2116 {
2117 struct isl_qpolynomial *qp;
2118 struct isl_upoly_cst *cst;
2119
2120 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2121 if (!qp)
2122 return NULL;
2123
2124 cst = isl_upoly_as_cst(qp->upoly);
2125 isl_int_set(cst->n, n);
2126 isl_int_set(cst->d, d);
2127
2128 return qp;
2129 }
2130
2131 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2132 {
2133 struct isl_upoly_rec *rec;
2134 int i;
2135
2136 if (!up)
2137 return -1;
2138
2139 if (isl_upoly_is_cst(up))
2140 return 0;
2141
2142 if (up->var < d)
2143 active[up->var] = 1;
2144
2145 rec = isl_upoly_as_rec(up);
2146 for (i = 0; i < rec->n; ++i)
2147 if (up_set_active(rec->p[i], active, d) < 0)
2148 return -1;
2149
2150 return 0;
2151 }
2152
2153 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2154 {
2155 int i, j;
2156 int d = isl_dim_total(qp->dim);
2157
2158 if (!qp || !active)
2159 return -1;
2160
2161 for (i = 0; i < d; ++i)
2162 for (j = 0; j < qp->div->n_row; ++j) {
2163 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2164 continue;
2165 active[i] = 1;
2166 break;
2167 }
2168
2169 return up_set_active(qp->upoly, active, d);
2170 }
2171
2172 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2173 enum isl_dim_type type, unsigned first, unsigned n)
2174 {
2175 int i;
2176 int *active = NULL;
2177 int involves = 0;
2178
2179 if (!qp)
2180 return -1;
2181 if (n == 0)
2182 return 0;
2183
2184 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2185 return -1);
2186 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2187 type == isl_dim_set, return -1);
2188
2189 active = isl_calloc_array(qp->dim->ctx, int, isl_dim_total(qp->dim));
2190 if (set_active(qp, active) < 0)
2191 goto error;
2192
2193 if (type == isl_dim_set)
2194 first += isl_dim_size(qp->dim, isl_dim_param);
2195 for (i = 0; i < n; ++i)
2196 if (active[first + i]) {
2197 involves = 1;
2198 break;
2199 }
2200
2201 free(active);
2202
2203 return involves;
2204 error:
2205 free(active);
2206 return -1;
2207 }
2208
2209 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2210 * of the divs that do appear in the quasi-polynomial.
2211 */
2212 static __isl_give isl_qpolynomial *remove_redundant_divs(
2213 __isl_take isl_qpolynomial *qp)
2214 {
2215 int i, j;
2216 int d;
2217 int len;
2218 int skip;
2219 int *active = NULL;
2220 int *reordering = NULL;
2221 int redundant = 0;
2222 int n_div;
2223 isl_ctx *ctx;
2224
2225 if (!qp)
2226 return NULL;
2227 if (qp->div->n_row == 0)
2228 return qp;
2229
2230 d = isl_dim_total(qp->dim);
2231 len = qp->div->n_col - 2;
2232 ctx = isl_qpolynomial_get_ctx(qp);
2233 active = isl_calloc_array(ctx, int, len);
2234 if (!active)
2235 goto error;
2236
2237 if (up_set_active(qp->upoly, active, len) < 0)
2238 goto error;
2239
2240 for (i = qp->div->n_row - 1; i >= 0; --i) {
2241 if (!active[d + i]) {
2242 redundant = 1;
2243 continue;
2244 }
2245 for (j = 0; j < i; ++j) {
2246 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2247 continue;
2248 active[d + j] = 1;
2249 break;
2250 }
2251 }
2252
2253 if (!redundant) {
2254 free(active);
2255 return qp;
2256 }
2257
2258 reordering = isl_alloc_array(qp->div->ctx, int, len);
2259 if (!reordering)
2260 goto error;
2261
2262 for (i = 0; i < d; ++i)
2263 reordering[i] = i;
2264
2265 skip = 0;
2266 n_div = qp->div->n_row;
2267 for (i = 0; i < n_div; ++i) {
2268 if (!active[d + i]) {
2269 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2270 qp->div = isl_mat_drop_cols(qp->div,
2271 2 + d + i - skip, 1);
2272 skip++;
2273 }
2274 reordering[d + i] = d + i - skip;
2275 }
2276
2277 qp->upoly = reorder(qp->upoly, reordering);
2278
2279 if (!qp->upoly || !qp->div)
2280 goto error;
2281
2282 free(active);
2283 free(reordering);
2284
2285 return qp;
2286 error:
2287 free(active);
2288 free(reordering);
2289 isl_qpolynomial_free(qp);
2290 return NULL;
2291 }
2292
2293 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2294 unsigned first, unsigned n)
2295 {
2296 int i;
2297 struct isl_upoly_rec *rec;
2298
2299 if (!up)
2300 return NULL;
2301 if (n == 0 || up->var < 0 || up->var < first)
2302 return up;
2303 if (up->var < first + n) {
2304 up = replace_by_constant_term(up);
2305 return isl_upoly_drop(up, first, n);
2306 }
2307 up = isl_upoly_cow(up);
2308 if (!up)
2309 return NULL;
2310 up->var -= n;
2311 rec = isl_upoly_as_rec(up);
2312 if (!rec)
2313 goto error;
2314
2315 for (i = 0; i < rec->n; ++i) {
2316 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2317 if (!rec->p[i])
2318 goto error;
2319 }
2320
2321 return up;
2322 error:
2323 isl_upoly_free(up);
2324 return NULL;
2325 }
2326
2327 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2328 __isl_take isl_qpolynomial *qp,
2329 enum isl_dim_type type, unsigned pos, const char *s)
2330 {
2331 qp = isl_qpolynomial_cow(qp);
2332 if (!qp)
2333 return NULL;
2334 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2335 if (!qp->dim)
2336 goto error;
2337 return qp;
2338 error:
2339 isl_qpolynomial_free(qp);
2340 return NULL;
2341 }
2342
2343 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2344 __isl_take isl_qpolynomial *qp,
2345 enum isl_dim_type type, unsigned first, unsigned n)
2346 {
2347 if (!qp)
2348 return NULL;
2349 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2350 return qp;
2351
2352 qp = isl_qpolynomial_cow(qp);
2353 if (!qp)
2354 return NULL;
2355
2356 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2357 goto error);
2358 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2359 type == isl_dim_set, goto error);
2360
2361 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2362 if (!qp->dim)
2363 goto error;
2364
2365 if (type == isl_dim_set)
2366 first += isl_dim_size(qp->dim, isl_dim_param);
2367
2368 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2369 if (!qp->div)
2370 goto error;
2371
2372 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2373 if (!qp->upoly)
2374 goto error;
2375
2376 return qp;
2377 error:
2378 isl_qpolynomial_free(qp);
2379 return NULL;
2380 }
2381
2382 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2383 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2384 {
2385 int i, j, k;
2386 isl_int denom;
2387 unsigned total;
2388 unsigned n_div;
2389 struct isl_upoly *up;
2390
2391 if (!eq)
2392 goto error;
2393 if (eq->n_eq == 0) {
2394 isl_basic_set_free(eq);
2395 return qp;
2396 }
2397
2398 qp = isl_qpolynomial_cow(qp);
2399 if (!qp)
2400 goto error;
2401 qp->div = isl_mat_cow(qp->div);
2402 if (!qp->div)
2403 goto error;
2404
2405 total = 1 + isl_dim_total(eq->dim);
2406 n_div = eq->n_div;
2407 isl_int_init(denom);
2408 for (i = 0; i < eq->n_eq; ++i) {
2409 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2410 if (j < 0 || j == 0 || j >= total)
2411 continue;
2412
2413 for (k = 0; k < qp->div->n_row; ++k) {
2414 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2415 continue;
2416 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2417 &qp->div->row[k][0]);
2418 normalize_div(qp, k);
2419 }
2420
2421 if (isl_int_is_pos(eq->eq[i][j]))
2422 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2423 isl_int_abs(denom, eq->eq[i][j]);
2424 isl_int_set_si(eq->eq[i][j], 0);
2425
2426 up = isl_upoly_from_affine(qp->dim->ctx,
2427 eq->eq[i], denom, total);
2428 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2429 isl_upoly_free(up);
2430 }
2431 isl_int_clear(denom);
2432
2433 if (!qp->upoly)
2434 goto error;
2435
2436 isl_basic_set_free(eq);
2437
2438 qp = substitute_non_divs(qp);
2439 qp = sort_divs(qp);
2440
2441 return qp;
2442 error:
2443 isl_basic_set_free(eq);
2444 isl_qpolynomial_free(qp);
2445 return NULL;
2446 }
2447
2448 static __isl_give isl_basic_set *add_div_constraints(
2449 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2450 {
2451 int i;
2452 unsigned total;
2453
2454 if (!bset || !div)
2455 goto error;
2456
2457 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2458 if (!bset)
2459 goto error;
2460 total = isl_basic_set_total_dim(bset);
2461 for (i = 0; i < div->n_row; ++i)
2462 if (isl_basic_set_add_div_constraints_var(bset,
2463 total - div->n_row + i, div->row[i]) < 0)
2464 goto error;
2465
2466 isl_mat_free(div);
2467 return bset;
2468 error:
2469 isl_mat_free(div);
2470 isl_basic_set_free(bset);
2471 return NULL;
2472 }
2473
2474 /* Look for equalities among the variables shared by context and qp
2475 * and the integer divisions of qp, if any.
2476 * The equalities are then used to eliminate variables and/or integer
2477 * divisions from qp.
2478 */
2479 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2480 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2481 {
2482 isl_basic_set *aff;
2483
2484 if (!qp)
2485 goto error;
2486 if (qp->div->n_row > 0) {
2487 isl_basic_set *bset;
2488 context = isl_set_add_dims(context, isl_dim_set,
2489 qp->div->n_row);
2490 bset = isl_basic_set_universe(isl_set_get_dim(context));
2491 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2492 context = isl_set_intersect(context,
2493 isl_set_from_basic_set(bset));
2494 }
2495
2496 aff = isl_set_affine_hull(context);
2497 return isl_qpolynomial_substitute_equalities(qp, aff);
2498 error:
2499 isl_qpolynomial_free(qp);
2500 isl_set_free(context);
2501 return NULL;
2502 }
2503
2504 #undef PW
2505 #define PW isl_pw_qpolynomial
2506 #undef EL
2507 #define EL isl_qpolynomial
2508 #undef EL_IS_ZERO
2509 #define EL_IS_ZERO is_zero
2510 #undef ZERO
2511 #define ZERO zero
2512 #undef IS_ZERO
2513 #define IS_ZERO is_zero
2514 #undef FIELD
2515 #define FIELD qp
2516
2517 #include <isl_pw_templ.c>
2518
2519 #undef UNION
2520 #define UNION isl_union_pw_qpolynomial
2521 #undef PART
2522 #define PART isl_pw_qpolynomial
2523 #undef PARTS
2524 #define PARTS pw_qpolynomial
2525
2526 #include <isl_union_templ.c>
2527
2528 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2529 {
2530 if (!pwqp)
2531 return -1;
2532
2533 if (pwqp->n != -1)
2534 return 0;
2535
2536 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2537 return 0;
2538
2539 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2540 }
2541
2542 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2543 __isl_take isl_pw_qpolynomial *pwqp1,
2544 __isl_take isl_pw_qpolynomial *pwqp2)
2545 {
2546 int i, j, n;
2547 struct isl_pw_qpolynomial *res;
2548
2549 if (!pwqp1 || !pwqp2)
2550 goto error;
2551
2552 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2553 goto error);
2554
2555 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2556 isl_pw_qpolynomial_free(pwqp2);
2557 return pwqp1;
2558 }
2559
2560 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2561 isl_pw_qpolynomial_free(pwqp1);
2562 return pwqp2;
2563 }
2564
2565 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2566 isl_pw_qpolynomial_free(pwqp1);
2567 return pwqp2;
2568 }
2569
2570 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2571 isl_pw_qpolynomial_free(pwqp2);
2572 return pwqp1;
2573 }
2574
2575 n = pwqp1->n * pwqp2->n;
2576 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2577
2578 for (i = 0; i < pwqp1->n; ++i) {
2579 for (j = 0; j < pwqp2->n; ++j) {
2580 struct isl_set *common;
2581 struct isl_qpolynomial *prod;
2582 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2583 isl_set_copy(pwqp2->p[j].set));
2584 if (isl_set_plain_is_empty(common)) {
2585 isl_set_free(common);
2586 continue;
2587 }
2588
2589 prod = isl_qpolynomial_mul(
2590 isl_qpolynomial_copy(pwqp1->p[i].qp),
2591 isl_qpolynomial_copy(pwqp2->p[j].qp));
2592
2593 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2594 }
2595 }
2596
2597 isl_pw_qpolynomial_free(pwqp1);
2598 isl_pw_qpolynomial_free(pwqp2);
2599
2600 return res;
2601 error:
2602 isl_pw_qpolynomial_free(pwqp1);
2603 isl_pw_qpolynomial_free(pwqp2);
2604 return NULL;
2605 }
2606
2607 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2608 __isl_take isl_pw_qpolynomial *pwqp)
2609 {
2610 int i;
2611
2612 if (!pwqp)
2613 return NULL;
2614
2615 if (isl_pw_qpolynomial_is_zero(pwqp))
2616 return pwqp;
2617
2618 pwqp = isl_pw_qpolynomial_cow(pwqp);
2619 if (!pwqp)
2620 return NULL;
2621
2622 for (i = 0; i < pwqp->n; ++i) {
2623 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2624 if (!pwqp->p[i].qp)
2625 goto error;
2626 }
2627
2628 return pwqp;
2629 error:
2630 isl_pw_qpolynomial_free(pwqp);
2631 return NULL;
2632 }
2633
2634 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2635 __isl_take isl_pw_qpolynomial *pwqp1,
2636 __isl_take isl_pw_qpolynomial *pwqp2)
2637 {
2638 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2639 }
2640
2641 __isl_give struct isl_upoly *isl_upoly_eval(
2642 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2643 {
2644 int i;
2645 struct isl_upoly_rec *rec;
2646 struct isl_upoly *res;
2647 struct isl_upoly *base;
2648
2649 if (isl_upoly_is_cst(up)) {
2650 isl_vec_free(vec);
2651 return up;
2652 }
2653
2654 rec = isl_upoly_as_rec(up);
2655 if (!rec)
2656 goto error;
2657
2658 isl_assert(up->ctx, rec->n >= 1, goto error);
2659
2660 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2661
2662 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2663 isl_vec_copy(vec));
2664
2665 for (i = rec->n - 2; i >= 0; --i) {
2666 res = isl_upoly_mul(res, isl_upoly_copy(base));
2667 res = isl_upoly_sum(res,
2668 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2669 isl_vec_copy(vec)));
2670 }
2671
2672 isl_upoly_free(base);
2673 isl_upoly_free(up);
2674 isl_vec_free(vec);
2675 return res;
2676 error:
2677 isl_upoly_free(up);
2678 isl_vec_free(vec);
2679 return NULL;
2680 }
2681
2682 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2683 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2684 {
2685 isl_vec *ext;
2686 struct isl_upoly *up;
2687 isl_dim *dim;
2688
2689 if (!qp || !pnt)
2690 goto error;
2691 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2692
2693 if (qp->div->n_row == 0)
2694 ext = isl_vec_copy(pnt->vec);
2695 else {
2696 int i;
2697 unsigned dim = isl_dim_total(qp->dim);
2698 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2699 if (!ext)
2700 goto error;
2701
2702 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2703 for (i = 0; i < qp->div->n_row; ++i) {
2704 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2705 1 + dim + i, &ext->el[1+dim+i]);
2706 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2707 qp->div->row[i][0]);
2708 }
2709 }
2710
2711 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2712 if (!up)
2713 goto error;
2714
2715 dim = isl_dim_copy(qp->dim);
2716 isl_qpolynomial_free(qp);
2717 isl_point_free(pnt);
2718
2719 return isl_qpolynomial_alloc(dim, 0, up);
2720 error:
2721 isl_qpolynomial_free(qp);
2722 isl_point_free(pnt);
2723 return NULL;
2724 }
2725
2726 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2727 __isl_keep struct isl_upoly_cst *cst2)
2728 {
2729 int cmp;
2730 isl_int t;
2731 isl_int_init(t);
2732 isl_int_mul(t, cst1->n, cst2->d);
2733 isl_int_submul(t, cst2->n, cst1->d);
2734 cmp = isl_int_sgn(t);
2735 isl_int_clear(t);
2736 return cmp;
2737 }
2738
2739 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2740 __isl_keep isl_qpolynomial *qp2)
2741 {
2742 struct isl_upoly_cst *cst1, *cst2;
2743
2744 if (!qp1 || !qp2)
2745 return -1;
2746 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2747 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2748 if (isl_qpolynomial_is_nan(qp1))
2749 return -1;
2750 if (isl_qpolynomial_is_nan(qp2))
2751 return -1;
2752 cst1 = isl_upoly_as_cst(qp1->upoly);
2753 cst2 = isl_upoly_as_cst(qp2->upoly);
2754
2755 return isl_upoly_cmp(cst1, cst2) <= 0;
2756 }
2757
2758 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2759 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2760 {
2761 struct isl_upoly_cst *cst1, *cst2;
2762 int cmp;
2763
2764 if (!qp1 || !qp2)
2765 goto error;
2766 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2767 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2768 cst1 = isl_upoly_as_cst(qp1->upoly);
2769 cst2 = isl_upoly_as_cst(qp2->upoly);
2770 cmp = isl_upoly_cmp(cst1, cst2);
2771
2772 if (cmp <= 0) {
2773 isl_qpolynomial_free(qp2);
2774 } else {
2775 isl_qpolynomial_free(qp1);
2776 qp1 = qp2;
2777 }
2778 return qp1;
2779 error:
2780 isl_qpolynomial_free(qp1);
2781 isl_qpolynomial_free(qp2);
2782 return NULL;
2783 }
2784
2785 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2786 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2787 {
2788 struct isl_upoly_cst *cst1, *cst2;
2789 int cmp;
2790
2791 if (!qp1 || !qp2)
2792 goto error;
2793 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2794 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2795 cst1 = isl_upoly_as_cst(qp1->upoly);
2796 cst2 = isl_upoly_as_cst(qp2->upoly);
2797 cmp = isl_upoly_cmp(cst1, cst2);
2798
2799 if (cmp >= 0) {
2800 isl_qpolynomial_free(qp2);
2801 } else {
2802 isl_qpolynomial_free(qp1);
2803 qp1 = qp2;
2804 }
2805 return qp1;
2806 error:
2807 isl_qpolynomial_free(qp1);
2808 isl_qpolynomial_free(qp2);
2809 return NULL;
2810 }
2811
2812 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2813 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2814 unsigned first, unsigned n)
2815 {
2816 unsigned total;
2817 unsigned g_pos;
2818 int *exp;
2819
2820 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2821 return qp;
2822
2823 qp = isl_qpolynomial_cow(qp);
2824 if (!qp)
2825 return NULL;
2826
2827 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2828 goto error);
2829
2830 g_pos = pos(qp->dim, type) + first;
2831
2832 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2833 if (!qp->div)
2834 goto error;
2835
2836 total = qp->div->n_col - 2;
2837 if (total > g_pos) {
2838 int i;
2839 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2840 if (!exp)
2841 goto error;
2842 for (i = 0; i < total - g_pos; ++i)
2843 exp[i] = i + n;
2844 qp->upoly = expand(qp->upoly, exp, g_pos);
2845 free(exp);
2846 if (!qp->upoly)
2847 goto error;
2848 }
2849
2850 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2851 if (!qp->dim)
2852 goto error;
2853
2854 return qp;
2855 error:
2856 isl_qpolynomial_free(qp);
2857 return NULL;
2858 }
2859
2860 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2861 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2862 {
2863 unsigned pos;
2864
2865 pos = isl_qpolynomial_dim(qp, type);
2866
2867 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2868 }
2869
2870 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2871 __isl_take isl_pw_qpolynomial *pwqp,
2872 enum isl_dim_type type, unsigned n)
2873 {
2874 unsigned pos;
2875
2876 pos = isl_pw_qpolynomial_dim(pwqp, type);
2877
2878 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2879 }
2880
2881 static int *reordering_move(isl_ctx *ctx,
2882 unsigned len, unsigned dst, unsigned src, unsigned n)
2883 {
2884 int i;
2885 int *reordering;
2886
2887 reordering = isl_alloc_array(ctx, int, len);
2888 if (!reordering)
2889 return NULL;
2890
2891 if (dst <= src) {
2892 for (i = 0; i < dst; ++i)
2893 reordering[i] = i;
2894 for (i = 0; i < n; ++i)
2895 reordering[src + i] = dst + i;
2896 for (i = 0; i < src - dst; ++i)
2897 reordering[dst + i] = dst + n + i;
2898 for (i = 0; i < len - src - n; ++i)
2899 reordering[src + n + i] = src + n + i;
2900 } else {
2901 for (i = 0; i < src; ++i)
2902 reordering[i] = i;
2903 for (i = 0; i < n; ++i)
2904 reordering[src + i] = dst + i;
2905 for (i = 0; i < dst - src; ++i)
2906 reordering[src + n + i] = src + i;
2907 for (i = 0; i < len - dst - n; ++i)
2908 reordering[dst + n + i] = dst + n + i;
2909 }
2910
2911 return reordering;
2912 }
2913
2914 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2915 __isl_take isl_qpolynomial *qp,
2916 enum isl_dim_type dst_type, unsigned dst_pos,
2917 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2918 {
2919 unsigned g_dst_pos;
2920 unsigned g_src_pos;
2921 int *reordering;
2922
2923 qp = isl_qpolynomial_cow(qp);
2924 if (!qp)
2925 return NULL;
2926
2927 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2928 goto error);
2929
2930 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2931 g_src_pos = pos(qp->dim, src_type) + src_pos;
2932 if (dst_type > src_type)
2933 g_dst_pos -= n;
2934
2935 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2936 if (!qp->div)
2937 goto error;
2938 qp = sort_divs(qp);
2939 if (!qp)
2940 goto error;
2941
2942 reordering = reordering_move(qp->dim->ctx,
2943 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2944 if (!reordering)
2945 goto error;
2946
2947 qp->upoly = reorder(qp->upoly, reordering);
2948 free(reordering);
2949 if (!qp->upoly)
2950 goto error;
2951
2952 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2953 if (!qp->dim)
2954 goto error;
2955
2956 return qp;
2957 error:
2958 isl_qpolynomial_free(qp);
2959 return NULL;
2960 }
2961
2962 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2963 isl_int *f, isl_int denom)
2964 {
2965 struct isl_upoly *up;
2966
2967 if (!dim)
2968 return NULL;
2969
2970 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2971
2972 return isl_qpolynomial_alloc(dim, 0, up);
2973 }
2974
2975 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
2976 {
2977 isl_ctx *ctx;
2978 struct isl_upoly *up;
2979 isl_qpolynomial *qp;
2980
2981 if (!aff)
2982 return NULL;
2983
2984 ctx = isl_aff_get_ctx(aff);
2985 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
2986 aff->v->size - 1);
2987
2988 qp = isl_qpolynomial_alloc(isl_aff_get_dim(aff),
2989 aff->ls->div->n_row, up);
2990 if (!qp)
2991 goto error;
2992
2993 isl_mat_free(qp->div);
2994 qp->div = isl_mat_copy(aff->ls->div);
2995 qp->div = isl_mat_cow(qp->div);
2996 if (!qp->div)
2997 goto error;
2998
2999 isl_aff_free(aff);
3000 qp = reduce_divs(qp);
3001 qp = remove_redundant_divs(qp);
3002 return qp;
3003 error:
3004 isl_aff_free(aff);
3005 return NULL;
3006 }
3007
3008 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
3009 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3010 {
3011 isl_int denom;
3012 isl_dim *dim;
3013 struct isl_upoly *up;
3014 isl_qpolynomial *qp;
3015 int sgn;
3016
3017 if (!c)
3018 return NULL;
3019
3020 isl_int_init(denom);
3021
3022 isl_constraint_get_coefficient(c, type, pos, &denom);
3023 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
3024 sgn = isl_int_sgn(denom);
3025 isl_int_abs(denom, denom);
3026 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
3027 1 + isl_constraint_dim(c, isl_dim_all));
3028 if (sgn < 0)
3029 isl_int_neg(denom, denom);
3030 isl_constraint_set_coefficient(c, type, pos, denom);
3031
3032 dim = isl_dim_copy(c->bmap->dim);
3033
3034 isl_int_clear(denom);
3035 isl_constraint_free(c);
3036
3037 qp = isl_qpolynomial_alloc(dim, 0, up);
3038 if (sgn > 0)
3039 qp = isl_qpolynomial_neg(qp);
3040 return qp;
3041 }
3042
3043 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3044 * in "qp" by subs[i].
3045 */
3046 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3047 __isl_take isl_qpolynomial *qp,
3048 enum isl_dim_type type, unsigned first, unsigned n,
3049 __isl_keep isl_qpolynomial **subs)
3050 {
3051 int i;
3052 struct isl_upoly **ups;
3053
3054 if (n == 0)
3055 return qp;
3056
3057 qp = isl_qpolynomial_cow(qp);
3058 if (!qp)
3059 return NULL;
3060 for (i = 0; i < n; ++i)
3061 if (!subs[i])
3062 goto error;
3063
3064 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
3065 goto error);
3066
3067 for (i = 0; i < n; ++i)
3068 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
3069 goto error);
3070
3071 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3072 for (i = 0; i < n; ++i)
3073 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3074
3075 first += pos(qp->dim, type);
3076
3077 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3078 if (!ups)
3079 goto error;
3080 for (i = 0; i < n; ++i)
3081 ups[i] = subs[i]->upoly;
3082
3083 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3084
3085 free(ups);
3086
3087 if (!qp->upoly)
3088 goto error;
3089
3090 return qp;
3091 error:
3092 isl_qpolynomial_free(qp);
3093 return NULL;
3094 }
3095
3096 /* Extend "bset" with extra set dimensions for each integer division
3097 * in "qp" and then call "fn" with the extended bset and the polynomial
3098 * that results from replacing each of the integer divisions by the
3099 * corresponding extra set dimension.
3100 */
3101 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3102 __isl_keep isl_basic_set *bset,
3103 int (*fn)(__isl_take isl_basic_set *bset,
3104 __isl_take isl_qpolynomial *poly, void *user), void *user)
3105 {
3106 isl_dim *dim;
3107 isl_mat *div;
3108 isl_qpolynomial *poly;
3109
3110 if (!qp || !bset)
3111 goto error;
3112 if (qp->div->n_row == 0)
3113 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3114 user);
3115
3116 div = isl_mat_copy(qp->div);
3117 dim = isl_dim_copy(qp->dim);
3118 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3119 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3120 bset = isl_basic_set_copy(bset);
3121 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3122 bset = add_div_constraints(bset, div);
3123
3124 return fn(bset, poly, user);
3125 error:
3126 return -1;
3127 }
3128
3129 /* Return total degree in variables first (inclusive) up to last (exclusive).
3130 */
3131 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3132 {
3133 int deg = -1;
3134 int i;
3135 struct isl_upoly_rec *rec;
3136
3137 if (!up)
3138 return -2;
3139 if (isl_upoly_is_zero(up))
3140 return -1;
3141 if (isl_upoly_is_cst(up) || up->var < first)
3142 return 0;
3143
3144 rec = isl_upoly_as_rec(up);
3145 if (!rec)
3146 return -2;
3147
3148 for (i = 0; i < rec->n; ++i) {
3149 int d;
3150
3151 if (isl_upoly_is_zero(rec->p[i]))
3152 continue;
3153 d = isl_upoly_degree(rec->p[i], first, last);
3154 if (up->var < last)
3155 d += i;
3156 if (d > deg)
3157 deg = d;
3158 }
3159
3160 return deg;
3161 }
3162
3163 /* Return total degree in set variables.
3164 */
3165 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3166 {
3167 unsigned ovar;
3168 unsigned nvar;
3169
3170 if (!poly)
3171 return -2;
3172
3173 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3174 nvar = isl_dim_size(poly->dim, isl_dim_set);
3175 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3176 }
3177
3178 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3179 unsigned pos, int deg)
3180 {
3181 int i;
3182 struct isl_upoly_rec *rec;
3183
3184 if (!up)
3185 return NULL;
3186
3187 if (isl_upoly_is_cst(up) || up->var < pos) {
3188 if (deg == 0)
3189 return isl_upoly_copy(up);
3190 else
3191 return isl_upoly_zero(up->ctx);
3192 }
3193
3194 rec = isl_upoly_as_rec(up);
3195 if (!rec)
3196 return NULL;
3197
3198 if (up->var == pos) {
3199 if (deg < rec->n)
3200 return isl_upoly_copy(rec->p[deg]);
3201 else
3202 return isl_upoly_zero(up->ctx);
3203 }
3204
3205 up = isl_upoly_copy(up);
3206 up = isl_upoly_cow(up);
3207 rec = isl_upoly_as_rec(up);
3208 if (!rec)
3209 goto error;
3210
3211 for (i = 0; i < rec->n; ++i) {
3212 struct isl_upoly *t;
3213 t = isl_upoly_coeff(rec->p[i], pos, deg);
3214 if (!t)
3215 goto error;
3216 isl_upoly_free(rec->p[i]);
3217 rec->p[i] = t;
3218 }
3219
3220 return up;
3221 error:
3222 isl_upoly_free(up);
3223 return NULL;
3224 }
3225
3226 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3227 */
3228 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3229 __isl_keep isl_qpolynomial *qp,
3230 enum isl_dim_type type, unsigned t_pos, int deg)
3231 {
3232 unsigned g_pos;
3233 struct isl_upoly *up;
3234 isl_qpolynomial *c;
3235
3236 if (!qp)
3237 return NULL;
3238
3239 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3240 return NULL);
3241
3242 g_pos = pos(qp->dim, type) + t_pos;
3243 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3244
3245 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3246 if (!c)
3247 return NULL;
3248 isl_mat_free(c->div);
3249 c->div = isl_mat_copy(qp->div);
3250 if (!c->div)
3251 goto error;
3252 return c;
3253 error:
3254 isl_qpolynomial_free(c);
3255 return NULL;
3256 }
3257
3258 /* Homogenize the polynomial in the variables first (inclusive) up to
3259 * last (exclusive) by inserting powers of variable first.
3260 * Variable first is assumed not to appear in the input.
3261 */
3262 __isl_give struct isl_upoly *isl_upoly_homogenize(
3263 __isl_take struct isl_upoly *up, int deg, int target,
3264 int first, int last)
3265 {
3266 int i;
3267 struct isl_upoly_rec *rec;
3268
3269 if (!up)
3270 return NULL;
3271 if (isl_upoly_is_zero(up))
3272 return up;
3273 if (deg == target)
3274 return up;
3275 if (isl_upoly_is_cst(up) || up->var < first) {
3276 struct isl_upoly *hom;
3277
3278 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3279 if (!hom)
3280 goto error;
3281 rec = isl_upoly_as_rec(hom);
3282 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3283
3284 return hom;
3285 }
3286
3287 up = isl_upoly_cow(up);
3288 rec = isl_upoly_as_rec(up);
3289 if (!rec)
3290 goto error;
3291
3292 for (i = 0; i < rec->n; ++i) {
3293 if (isl_upoly_is_zero(rec->p[i]))
3294 continue;
3295 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3296 up->var < last ? deg + i : i, target,
3297 first, last);
3298 if (!rec->p[i])
3299 goto error;
3300 }
3301
3302 return up;
3303 error:
3304 isl_upoly_free(up);
3305 return NULL;
3306 }
3307
3308 /* Homogenize the polynomial in the set variables by introducing
3309 * powers of an extra set variable at position 0.
3310 */
3311 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3312 __isl_take isl_qpolynomial *poly)
3313 {
3314 unsigned ovar;
3315 unsigned nvar;
3316 int deg = isl_qpolynomial_degree(poly);
3317
3318 if (deg < -1)
3319 goto error;
3320
3321 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3322 poly = isl_qpolynomial_cow(poly);
3323 if (!poly)
3324 goto error;
3325
3326 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3327 nvar = isl_dim_size(poly->dim, isl_dim_set);
3328 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3329 ovar, ovar + nvar);
3330 if (!poly->upoly)
3331 goto error;
3332
3333 return poly;
3334 error:
3335 isl_qpolynomial_free(poly);
3336 return NULL;
3337 }
3338
3339 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3340 __isl_take isl_mat *div)
3341 {
3342 isl_term *term;
3343 int n;
3344
3345 if (!dim || !div)
3346 goto error;
3347
3348 n = isl_dim_total(dim) + div->n_row;
3349
3350 term = isl_calloc(dim->ctx, struct isl_term,
3351 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3352 if (!term)
3353 goto error;
3354
3355 term->ref = 1;
3356 term->dim = dim;
3357 term->div = div;
3358 isl_int_init(term->n);
3359 isl_int_init(term->d);
3360
3361 return term;
3362 error:
3363 isl_dim_free(dim);
3364 isl_mat_free(div);
3365 return NULL;
3366 }
3367
3368 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3369 {
3370 if (!term)
3371 return NULL;
3372
3373 term->ref++;
3374 return term;
3375 }
3376
3377 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3378 {
3379 int i;
3380 isl_term *dup;
3381 unsigned total;
3382
3383 if (term)
3384 return NULL;
3385
3386 total = isl_dim_total(term->dim) + term->div->n_row;
3387
3388 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3389 if (!dup)
3390 return NULL;
3391
3392 isl_int_set(dup->n, term->n);
3393 isl_int_set(dup->d, term->d);
3394
3395 for (i = 0; i < total; ++i)
3396 dup->pow[i] = term->pow[i];
3397
3398 return dup;
3399 }
3400
3401 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3402 {
3403 if (!term)
3404 return NULL;
3405
3406 if (term->ref == 1)
3407 return term;
3408 term->ref--;
3409 return isl_term_dup(term);
3410 }
3411
3412 void isl_term_free(__isl_take isl_term *term)
3413 {
3414 if (!term)
3415 return;
3416
3417 if (--term->ref > 0)
3418 return;
3419
3420 isl_dim_free(term->dim);
3421 isl_mat_free(term->div);
3422 isl_int_clear(term->n);
3423 isl_int_clear(term->d);
3424 free(term);
3425 }
3426
3427 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3428 {
3429 if (!term)
3430 return 0;
3431
3432 switch (type) {
3433 case isl_dim_param:
3434 case isl_dim_in:
3435 case isl_dim_out: return isl_dim_size(term->dim, type);
3436 case isl_dim_div: return term->div->n_row;
3437 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3438 default: return 0;
3439 }
3440 }
3441
3442 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3443 {
3444 return term ? term->dim->ctx : NULL;
3445 }
3446
3447 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3448 {
3449 if (!term)
3450 return;
3451 isl_int_set(*n, term->n);
3452 }
3453
3454 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3455 {
3456 if (!term)
3457 return;
3458 isl_int_set(*d, term->d);
3459 }
3460
3461 int isl_term_get_exp(__isl_keep isl_term *term,
3462 enum isl_dim_type type, unsigned pos)
3463 {
3464 if (!term)
3465 return -1;
3466
3467 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3468
3469 if (type >= isl_dim_set)
3470 pos += isl_dim_size(term->dim, isl_dim_param);
3471 if (type >= isl_dim_div)
3472 pos += isl_dim_size(term->dim, isl_dim_set);
3473
3474 return term->pow[pos];
3475 }
3476
3477 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3478 {
3479 isl_basic_map *bmap;
3480 unsigned total;
3481 int k;
3482
3483 if (!term)
3484 return NULL;
3485
3486 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3487 return NULL);
3488
3489 total = term->div->n_col - term->div->n_row - 2;
3490 /* No nested divs for now */
3491 isl_assert(term->dim->ctx,
3492 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3493 term->div->n_row) == -1,
3494 return NULL);
3495
3496 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3497 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3498 goto error;
3499
3500 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3501
3502 return isl_basic_map_div(bmap, k);
3503 error:
3504 isl_basic_map_free(bmap);
3505 return NULL;
3506 }
3507
3508 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3509 int (*fn)(__isl_take isl_term *term, void *user),
3510 __isl_take isl_term *term, void *user)
3511 {
3512 int i;
3513 struct isl_upoly_rec *rec;
3514
3515 if (!up || !term)
3516 goto error;
3517
3518 if (isl_upoly_is_zero(up))
3519 return term;
3520
3521 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3522 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3523 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3524
3525 if (isl_upoly_is_cst(up)) {
3526 struct isl_upoly_cst *cst;
3527 cst = isl_upoly_as_cst(up);
3528 if (!cst)
3529 goto error;
3530 term = isl_term_cow(term);
3531 if (!term)
3532 goto error;
3533 isl_int_set(term->n, cst->n);
3534 isl_int_set(term->d, cst->d);
3535 if (fn(isl_term_copy(term), user) < 0)
3536 goto error;
3537 return term;
3538 }
3539
3540 rec = isl_upoly_as_rec(up);
3541 if (!rec)
3542 goto error;
3543
3544 for (i = 0; i < rec->n; ++i) {
3545 term = isl_term_cow(term);
3546 if (!term)
3547 goto error;
3548 term->pow[up->var] = i;
3549 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3550 if (!term)
3551 goto error;
3552 }
3553 term->pow[up->var] = 0;
3554
3555 return term;
3556 error:
3557 isl_term_free(term);
3558 return NULL;
3559 }
3560
3561 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3562 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3563 {
3564 isl_term *term;
3565
3566 if (!qp)
3567 return -1;
3568
3569 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3570 if (!term)
3571 return -1;
3572
3573 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3574
3575 isl_term_free(term);
3576
3577 return term ? 0 : -1;
3578 }
3579
3580 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3581 {
3582 struct isl_upoly *up;
3583 isl_qpolynomial *qp;
3584 int i, n;
3585
3586 if (!term)
3587 return NULL;
3588
3589 n = isl_dim_total(term->dim) + term->div->n_row;
3590
3591 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3592 for (i = 0; i < n; ++i) {
3593 if (!term->pow[i])
3594 continue;
3595 up = isl_upoly_mul(up,
3596 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3597 }
3598
3599 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3600 if (!qp)
3601 goto error;
3602 isl_mat_free(qp->div);
3603 qp->div = isl_mat_copy(term->div);
3604 if (!qp->div)
3605 goto error;
3606
3607 isl_term_free(term);
3608 return qp;
3609 error:
3610 isl_qpolynomial_free(qp);
3611 isl_term_free(term);
3612 return NULL;
3613 }
3614
3615 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3616 __isl_take isl_dim *dim)
3617 {
3618 int i;
3619 int extra;
3620 unsigned total;
3621
3622 if (!qp || !dim)
3623 goto error;
3624
3625 if (isl_dim_equal(qp->dim, dim)) {
3626 isl_dim_free(dim);
3627 return qp;
3628 }
3629
3630 qp = isl_qpolynomial_cow(qp);
3631 if (!qp)
3632 goto error;
3633
3634 extra = isl_dim_size(dim, isl_dim_set) -
3635 isl_dim_size(qp->dim, isl_dim_set);
3636 total = isl_dim_total(qp->dim);
3637 if (qp->div->n_row) {
3638 int *exp;
3639
3640 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3641 if (!exp)
3642 goto error;
3643 for (i = 0; i < qp->div->n_row; ++i)
3644 exp[i] = extra + i;
3645 qp->upoly = expand(qp->upoly, exp, total);
3646 free(exp);
3647 if (!qp->upoly)
3648 goto error;
3649 }
3650 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3651 if (!qp->div)
3652 goto error;
3653 for (i = 0; i < qp->div->n_row; ++i)
3654 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3655
3656 isl_dim_free(qp->dim);
3657 qp->dim = dim;
3658
3659 return qp;
3660 error:
3661 isl_dim_free(dim);
3662 isl_qpolynomial_free(qp);
3663 return NULL;
3664 }
3665
3666 /* For each parameter or variable that does not appear in qp,
3667 * first eliminate the variable from all constraints and then set it to zero.
3668 */
3669 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3670 __isl_keep isl_qpolynomial *qp)
3671 {
3672 int *active = NULL;
3673 int i;
3674 int d;
3675 unsigned nparam;
3676 unsigned nvar;
3677
3678 if (!set || !qp)
3679 goto error;
3680
3681 d = isl_dim_total(set->dim);
3682 active = isl_calloc_array(set->ctx, int, d);
3683 if (set_active(qp, active) < 0)
3684 goto error;
3685
3686 for (i = 0; i < d; ++i)
3687 if (!active[i])
3688 break;
3689
3690 if (i == d) {
3691 free(active);
3692 return set;
3693 }
3694
3695 nparam = isl_dim_size(set->dim, isl_dim_param);
3696 nvar = isl_dim_size(set->dim, isl_dim_set);
3697 for (i = 0; i < nparam; ++i) {
3698 if (active[i])
3699 continue;
3700 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3701 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3702 }
3703 for (i = 0; i < nvar; ++i) {
3704 if (active[nparam + i])
3705 continue;
3706 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3707 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3708 }
3709
3710 free(active);
3711
3712 return set;
3713 error:
3714 free(active);
3715 isl_set_free(set);
3716 return NULL;
3717 }
3718
3719 struct isl_opt_data {
3720 isl_qpolynomial *qp;
3721 int first;
3722 isl_qpolynomial *opt;
3723 int max;
3724 };
3725
3726 static int opt_fn(__isl_take isl_point *pnt, void *user)
3727 {
3728 struct isl_opt_data *data = (struct isl_opt_data *)user;
3729 isl_qpolynomial *val;
3730
3731 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3732 if (data->first) {
3733 data->first = 0;
3734 data->opt = val;
3735 } else if (data->max) {
3736 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3737 } else {
3738 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3739 }
3740
3741 return 0;
3742 }
3743
3744 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3745 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3746 {
3747 struct isl_opt_data data = { NULL, 1, NULL, max };
3748
3749 if (!set || !qp)
3750 goto error;
3751
3752 if (isl_upoly_is_cst(qp->upoly)) {
3753 isl_set_free(set);
3754 return qp;
3755 }
3756
3757 set = fix_inactive(set, qp);
3758
3759 data.qp = qp;
3760 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3761 goto error;
3762
3763 if (data.first)
3764 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3765
3766 isl_set_free(set);
3767 isl_qpolynomial_free(qp);
3768 return data.opt;
3769 error:
3770 isl_set_free(set);
3771 isl_qpolynomial_free(qp);
3772 isl_qpolynomial_free(data.opt);
3773 return NULL;
3774 }
3775
3776 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3777 __isl_take isl_morph *morph)
3778 {
3779 int i;
3780 int n_sub;
3781 isl_ctx *ctx;
3782 struct isl_upoly **subs;
3783 isl_mat *mat;
3784
3785 qp = isl_qpolynomial_cow(qp);
3786 if (!qp || !morph)
3787 goto error;
3788
3789 ctx = qp->dim->ctx;
3790 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3791
3792 n_sub = morph->inv->n_row - 1;
3793 if (morph->inv->n_row != morph->inv->n_col)
3794 n_sub += qp->div->n_row;
3795 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3796 if (!subs)
3797 goto error;
3798
3799 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3800 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3801 morph->inv->row[0][0], morph->inv->n_col);
3802 if (morph->inv->n_row != morph->inv->n_col)
3803 for (i = 0; i < qp->div->n_row; ++i)
3804 subs[morph->inv->n_row - 1 + i] =
3805 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3806
3807 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3808
3809 for (i = 0; i < n_sub; ++i)
3810 isl_upoly_free(subs[i]);
3811 free(subs);
3812
3813 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3814 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3815 qp->div = isl_mat_product(qp->div, mat);
3816 isl_dim_free(qp->dim);
3817 qp->dim = isl_dim_copy(morph->ran->dim);
3818
3819 if (!qp->upoly || !qp->div || !qp->dim)
3820 goto error;
3821
3822 isl_morph_free(morph);
3823
3824 return qp;
3825 error:
3826 isl_qpolynomial_free(qp);
3827 isl_morph_free(morph);
3828 return NULL;
3829 }
3830
3831 static int neg_entry(void **entry, void *user)
3832 {
3833 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3834
3835 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3836
3837 return *pwqp ? 0 : -1;
3838 }
3839
3840 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3841 __isl_take isl_union_pw_qpolynomial *upwqp)
3842 {
3843 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3844 if (!upwqp)
3845 return NULL;
3846
3847 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3848 &neg_entry, NULL) < 0)
3849 goto error;
3850
3851 return upwqp;
3852 error:
3853 isl_union_pw_qpolynomial_free(upwqp);
3854 return NULL;
3855 }
3856
3857 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3858 __isl_take isl_union_pw_qpolynomial *upwqp1,
3859 __isl_take isl_union_pw_qpolynomial *upwqp2)
3860 {
3861 return isl_union_pw_qpolynomial_add(upwqp1,
3862 isl_union_pw_qpolynomial_neg(upwqp2));
3863 }
3864
3865 static int mul_entry(void **entry, void *user)
3866 {
3867 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3868 uint32_t hash;
3869 struct isl_hash_table_entry *entry2;
3870 isl_pw_qpolynomial *pwpq = *entry;
3871 int empty;
3872
3873 hash = isl_dim_get_hash(pwpq->dim);
3874 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3875 hash, &has_dim, pwpq->dim, 0);
3876 if (!entry2)
3877 return 0;
3878
3879 pwpq = isl_pw_qpolynomial_copy(pwpq);
3880 pwpq = isl_pw_qpolynomial_mul(pwpq,
3881 isl_pw_qpolynomial_copy(entry2->data));
3882
3883 empty = isl_pw_qpolynomial_is_zero(pwpq);
3884 if (empty < 0) {
3885 isl_pw_qpolynomial_free(pwpq);
3886 return -1;
3887 }
3888 if (empty) {
3889 isl_pw_qpolynomial_free(pwpq);
3890 return 0;
3891 }
3892
3893 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3894
3895 return 0;
3896 }
3897
3898 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3899 __isl_take isl_union_pw_qpolynomial *upwqp1,
3900 __isl_take isl_union_pw_qpolynomial *upwqp2)
3901 {
3902 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3903 }
3904
3905 /* Reorder the columns of the given div definitions according to the
3906 * given reordering.
3907 */
3908 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3909 __isl_take isl_reordering *r)
3910 {
3911 int i, j;
3912 isl_mat *mat;
3913 int extra;
3914
3915 if (!div || !r)
3916 goto error;
3917
3918 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3919 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3920 if (!mat)
3921 goto error;
3922
3923 for (i = 0; i < div->n_row; ++i) {
3924 isl_seq_cpy(mat->row[i], div->row[i], 2);
3925 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3926 for (j = 0; j < r->len; ++j)
3927 isl_int_set(mat->row[i][2 + r->pos[j]],
3928 div->row[i][2 + j]);
3929 }
3930
3931 isl_reordering_free(r);
3932 isl_mat_free(div);
3933 return mat;
3934 error:
3935 isl_reordering_free(r);
3936 isl_mat_free(div);
3937 return NULL;
3938 }
3939
3940 /* Reorder the dimension of "qp" according to the given reordering.
3941 */
3942 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3943 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3944 {
3945 qp = isl_qpolynomial_cow(qp);
3946 if (!qp)
3947 goto error;
3948
3949 r = isl_reordering_extend(r, qp->div->n_row);
3950 if (!r)
3951 goto error;
3952
3953 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3954 if (!qp->div)
3955 goto error;
3956
3957 qp->upoly = reorder(qp->upoly, r->pos);
3958 if (!qp->upoly)
3959 goto error;
3960
3961 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3962
3963 isl_reordering_free(r);
3964 return qp;
3965 error:
3966 isl_qpolynomial_free(qp);
3967 isl_reordering_free(r);
3968 return NULL;
3969 }
3970
3971 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3972 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3973 {
3974 if (!qp || !model)
3975 goto error;
3976
3977 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
3978 isl_reordering *exp;
3979
3980 model = isl_dim_drop(model, isl_dim_in,
3981 0, isl_dim_size(model, isl_dim_in));
3982 model = isl_dim_drop(model, isl_dim_out,
3983 0, isl_dim_size(model, isl_dim_out));
3984 exp = isl_parameter_alignment_reordering(qp->dim, model);
3985 exp = isl_reordering_extend_dim(exp,
3986 isl_qpolynomial_get_dim(qp));
3987 qp = isl_qpolynomial_realign(qp, exp);
3988 }
3989
3990 isl_dim_free(model);
3991 return qp;
3992 error:
3993 isl_dim_free(model);
3994 isl_qpolynomial_free(qp);
3995 return NULL;
3996 }
3997
3998 struct isl_split_periods_data {
3999 int max_periods;
4000 isl_pw_qpolynomial *res;
4001 };
4002
4003 /* Create a slice where the integer division "div" has the fixed value "v".
4004 * In particular, if "div" refers to floor(f/m), then create a slice
4005 *
4006 * m v <= f <= m v + (m - 1)
4007 *
4008 * or
4009 *
4010 * f - m v >= 0
4011 * -f + m v + (m - 1) >= 0
4012 */
4013 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
4014 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4015 {
4016 int total;
4017 isl_basic_set *bset = NULL;
4018 int k;
4019
4020 if (!dim || !qp)
4021 goto error;
4022
4023 total = isl_dim_total(dim);
4024 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
4025
4026 k = isl_basic_set_alloc_inequality(bset);
4027 if (k < 0)
4028 goto error;
4029 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4030 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4031
4032 k = isl_basic_set_alloc_inequality(bset);
4033 if (k < 0)
4034 goto error;
4035 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4036 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4037 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4038 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4039
4040 isl_dim_free(dim);
4041 return isl_set_from_basic_set(bset);
4042 error:
4043 isl_basic_set_free(bset);
4044 isl_dim_free(dim);
4045 return NULL;
4046 }
4047
4048 static int split_periods(__isl_take isl_set *set,
4049 __isl_take isl_qpolynomial *qp, void *user);
4050
4051 /* Create a slice of the domain "set" such that integer division "div"
4052 * has the fixed value "v" and add the results to data->res,
4053 * replacing the integer division by "v" in "qp".
4054 */
4055 static int set_div(__isl_take isl_set *set,
4056 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4057 struct isl_split_periods_data *data)
4058 {
4059 int i;
4060 int total;
4061 isl_set *slice;
4062 struct isl_upoly *cst;
4063
4064 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
4065 set = isl_set_intersect(set, slice);
4066
4067 if (!qp)
4068 goto error;
4069
4070 total = isl_dim_total(qp->dim);
4071
4072 for (i = div + 1; i < qp->div->n_row; ++i) {
4073 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4074 continue;
4075 isl_int_addmul(qp->div->row[i][1],
4076 qp->div->row[i][2 + total + div], v);
4077 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4078 }
4079
4080 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4081 qp = substitute_div(qp, div, cst);
4082
4083 return split_periods(set, qp, data);
4084 error:
4085 isl_set_free(set);
4086 isl_qpolynomial_free(qp);
4087 return -1;
4088 }
4089
4090 /* Split the domain "set" such that integer division "div"
4091 * has a fixed value (ranging from "min" to "max") on each slice
4092 * and add the results to data->res.
4093 */
4094 static int split_div(__isl_take isl_set *set,
4095 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4096 struct isl_split_periods_data *data)
4097 {
4098 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4099 isl_set *set_i = isl_set_copy(set);
4100 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4101
4102 if (set_div(set_i, qp_i, div, min, data) < 0)
4103 goto error;
4104 }
4105 isl_set_free(set);
4106 isl_qpolynomial_free(qp);
4107 return 0;
4108 error:
4109 isl_set_free(set);
4110 isl_qpolynomial_free(qp);
4111 return -1;
4112 }
4113
4114 /* If "qp" refers to any integer division
4115 * that can only attain "max_periods" distinct values on "set"
4116 * then split the domain along those distinct values.
4117 * Add the results (or the original if no splitting occurs)
4118 * to data->res.
4119 */
4120 static int split_periods(__isl_take isl_set *set,
4121 __isl_take isl_qpolynomial *qp, void *user)
4122 {
4123 int i;
4124 isl_pw_qpolynomial *pwqp;
4125 struct isl_split_periods_data *data;
4126 isl_int min, max;
4127 int total;
4128 int r = 0;
4129
4130 data = (struct isl_split_periods_data *)user;
4131
4132 if (!set || !qp)
4133 goto error;
4134
4135 if (qp->div->n_row == 0) {
4136 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4137 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4138 return 0;
4139 }
4140
4141 isl_int_init(min);
4142 isl_int_init(max);
4143 total = isl_dim_total(qp->dim);
4144 for (i = 0; i < qp->div->n_row; ++i) {
4145 enum isl_lp_result lp_res;
4146
4147 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4148 qp->div->n_row) != -1)
4149 continue;
4150
4151 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4152 set->ctx->one, &min, NULL, NULL);
4153 if (lp_res == isl_lp_error)
4154 goto error2;
4155 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4156 continue;
4157 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4158
4159 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4160 set->ctx->one, &max, NULL, NULL);
4161 if (lp_res == isl_lp_error)
4162 goto error2;
4163 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4164 continue;
4165 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4166
4167 isl_int_sub(max, max, min);
4168 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4169 isl_int_add(max, max, min);
4170 break;
4171 }
4172 }
4173
4174 if (i < qp->div->n_row) {
4175 r = split_div(set, qp, i, min, max, data);
4176 } else {
4177 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4178 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4179 }
4180
4181 isl_int_clear(max);
4182 isl_int_clear(min);
4183
4184 return r;
4185 error2:
4186 isl_int_clear(max);
4187 isl_int_clear(min);
4188 error:
4189 isl_set_free(set);
4190 isl_qpolynomial_free(qp);
4191 return -1;
4192 }
4193
4194 /* If any quasi-polynomial in pwqp refers to any integer division
4195 * that can only attain "max_periods" distinct values on its domain
4196 * then split the domain along those distinct values.
4197 */
4198 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4199 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4200 {
4201 struct isl_split_periods_data data;
4202
4203 data.max_periods = max_periods;
4204 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4205
4206 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4207 goto error;
4208
4209 isl_pw_qpolynomial_free(pwqp);
4210
4211 return data.res;
4212 error:
4213 isl_pw_qpolynomial_free(data.res);
4214 isl_pw_qpolynomial_free(pwqp);
4215 return NULL;
4216 }
4217
4218 /* Construct a piecewise quasipolynomial that is constant on the given
4219 * domain. In particular, it is
4220 * 0 if cst == 0
4221 * 1 if cst == 1
4222 * infinity if cst == -1
4223 */
4224 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4225 __isl_take isl_basic_set *bset, int cst)
4226 {
4227 isl_dim *dim;
4228 isl_qpolynomial *qp;
4229
4230 if (!bset)
4231 return NULL;
4232
4233 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4234 dim = isl_basic_set_get_dim(bset);
4235 if (cst < 0)
4236 qp = isl_qpolynomial_infty(dim);
4237 else if (cst == 0)
4238 qp = isl_qpolynomial_zero(dim);
4239 else
4240 qp = isl_qpolynomial_one(dim);
4241 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4242 }
4243
4244 /* Factor bset, call fn on each of the factors and return the product.
4245 *
4246 * If no factors can be found, simply call fn on the input.
4247 * Otherwise, construct the factors based on the factorizer,
4248 * call fn on each factor and compute the product.
4249 */
4250 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4251 __isl_take isl_basic_set *bset,
4252 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4253 {
4254 int i, n;
4255 isl_dim *dim;
4256 isl_set *set;
4257 isl_factorizer *f;
4258 isl_qpolynomial *qp;
4259 isl_pw_qpolynomial *pwqp;
4260 unsigned nparam;
4261 unsigned nvar;
4262
4263 f = isl_basic_set_factorizer(bset);
4264 if (!f)
4265 goto error;
4266 if (f->n_group == 0) {
4267 isl_factorizer_free(f);
4268 return fn(bset);
4269 }
4270
4271 nparam = isl_basic_set_dim(bset, isl_dim_param);
4272 nvar = isl_basic_set_dim(bset, isl_dim_set);
4273
4274 dim = isl_basic_set_get_dim(bset);
4275 dim = isl_dim_domain(dim);
4276 set = isl_set_universe(isl_dim_copy(dim));
4277 qp = isl_qpolynomial_one(dim);
4278 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4279
4280 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4281
4282 for (i = 0, n = 0; i < f->n_group; ++i) {
4283 isl_basic_set *bset_i;
4284 isl_pw_qpolynomial *pwqp_i;
4285
4286 bset_i = isl_basic_set_copy(bset);
4287 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4288 nparam + n + f->len[i], nvar - n - f->len[i]);
4289 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4290 nparam, n);
4291 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4292 n + f->len[i], nvar - n - f->len[i]);
4293 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4294
4295 pwqp_i = fn(bset_i);
4296 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4297
4298 n += f->len[i];
4299 }
4300
4301 isl_basic_set_free(bset);
4302 isl_factorizer_free(f);
4303
4304 return pwqp;
4305 error:
4306 isl_basic_set_free(bset);
4307 return NULL;
4308 }
4309
4310 /* Factor bset, call fn on each of the factors and return the product.
4311 * The function is assumed to evaluate to zero on empty domains,
4312 * to one on zero-dimensional domains and to infinity on unbounded domains
4313 * and will not be called explicitly on zero-dimensional or unbounded domains.
4314 *
4315 * We first check for some special cases and remove all equalities.
4316 * Then we hand over control to compressed_multiplicative_call.
4317 */
4318 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4319 __isl_take isl_basic_set *bset,
4320 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4321 {
4322 int bounded;
4323 isl_morph *morph;
4324 isl_pw_qpolynomial *pwqp;
4325 unsigned orig_nvar, final_nvar;
4326
4327 if (!bset)
4328 return NULL;
4329
4330 if (isl_basic_set_plain_is_empty(bset))
4331 return constant_on_domain(bset, 0);
4332
4333 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4334
4335 if (orig_nvar == 0)
4336 return constant_on_domain(bset, 1);
4337
4338 bounded = isl_basic_set_is_bounded(bset);
4339 if (bounded < 0)
4340 goto error;
4341 if (!bounded)
4342 return constant_on_domain(bset, -1);
4343
4344 if (bset->n_eq == 0)
4345 return compressed_multiplicative_call(bset, fn);
4346
4347 morph = isl_basic_set_full_compression(bset);
4348 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4349
4350 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4351
4352 pwqp = compressed_multiplicative_call(bset, fn);
4353
4354 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4355 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4356 morph = isl_morph_inverse(morph);
4357
4358 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4359
4360 return pwqp;
4361 error:
4362 isl_basic_set_free(bset);
4363 return NULL;
4364 }
4365
4366 /* Drop all floors in "qp", turning each integer division [a/m] into
4367 * a rational division a/m. If "down" is set, then the integer division
4368 * is replaces by (a-(m-1))/m instead.
4369 */
4370 static __isl_give isl_qpolynomial *qp_drop_floors(
4371 __isl_take isl_qpolynomial *qp, int down)
4372 {
4373 int i;
4374 struct isl_upoly *s;
4375
4376 if (!qp)
4377 return NULL;
4378 if (qp->div->n_row == 0)
4379 return qp;
4380
4381 qp = isl_qpolynomial_cow(qp);
4382 if (!qp)
4383 return NULL;
4384
4385 for (i = qp->div->n_row - 1; i >= 0; --i) {
4386 if (down) {
4387 isl_int_sub(qp->div->row[i][1],
4388 qp->div->row[i][1], qp->div->row[i][0]);
4389 isl_int_add_ui(qp->div->row[i][1],
4390 qp->div->row[i][1], 1);
4391 }
4392 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4393 qp->div->row[i][0], qp->div->n_col - 1);
4394 qp = substitute_div(qp, i, s);
4395 if (!qp)
4396 return NULL;
4397 }
4398
4399 return qp;
4400 }
4401
4402 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4403 * a rational division a/m.
4404 */
4405 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4406 __isl_take isl_pw_qpolynomial *pwqp)
4407 {
4408 int i;
4409
4410 if (!pwqp)
4411 return NULL;
4412
4413 if (isl_pw_qpolynomial_is_zero(pwqp))
4414 return pwqp;
4415
4416 pwqp = isl_pw_qpolynomial_cow(pwqp);
4417 if (!pwqp)
4418 return NULL;
4419
4420 for (i = 0; i < pwqp->n; ++i) {
4421 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4422 if (!pwqp->p[i].qp)
4423 goto error;
4424 }
4425
4426 return pwqp;
4427 error:
4428 isl_pw_qpolynomial_free(pwqp);
4429 return NULL;
4430 }
4431
4432 /* Adjust all the integer divisions in "qp" such that they are at least
4433 * one over the given orthant (identified by "signs"). This ensures
4434 * that they will still be non-negative even after subtracting (m-1)/m.
4435 *
4436 * In particular, f is replaced by f' + v, changing f = [a/m]
4437 * to f' = [(a - m v)/m].
4438 * If the constant term k in a is smaller than m,
4439 * the constant term of v is set to floor(k/m) - 1.
4440 * For any other term, if the coefficient c and the variable x have
4441 * the same sign, then no changes are needed.
4442 * Otherwise, if the variable is positive (and c is negative),
4443 * then the coefficient of x in v is set to floor(c/m).
4444 * If the variable is negative (and c is positive),
4445 * then the coefficient of x in v is set to ceil(c/m).
4446 */
4447 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4448 int *signs)
4449 {
4450 int i, j;
4451 int total;
4452 isl_vec *v = NULL;
4453 struct isl_upoly *s;
4454
4455 qp = isl_qpolynomial_cow(qp);
4456 if (!qp)
4457 return NULL;
4458 qp->div = isl_mat_cow(qp->div);
4459 if (!qp->div)
4460 goto error;
4461
4462 total = isl_dim_total(qp->dim);
4463 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4464
4465 for (i = 0; i < qp->div->n_row; ++i) {
4466 isl_int *row = qp->div->row[i];
4467 v = isl_vec_clr(v);
4468 if (!v)
4469 goto error;
4470 if (isl_int_lt(row[1], row[0])) {
4471 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4472 isl_int_sub_ui(v->el[0], v->el[0], 1);
4473 isl_int_submul(row[1], row[0], v->el[0]);
4474 }
4475 for (j = 0; j < total; ++j) {
4476 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4477 continue;
4478 if (signs[j] < 0)
4479 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4480 else
4481 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4482 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4483 }
4484 for (j = 0; j < i; ++j) {
4485 if (isl_int_sgn(row[2 + total + j]) >= 0)
4486 continue;
4487 isl_int_fdiv_q(v->el[1 + total + j],
4488 row[2 + total + j], row[0]);
4489 isl_int_submul(row[2 + total + j],
4490 row[0], v->el[1 + total + j]);
4491 }
4492 for (j = i + 1; j < qp->div->n_row; ++j) {
4493 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4494 continue;
4495 isl_seq_combine(qp->div->row[j] + 1,
4496 qp->div->ctx->one, qp->div->row[j] + 1,
4497 qp->div->row[j][2 + total + i], v->el, v->size);
4498 }
4499 isl_int_set_si(v->el[1 + total + i], 1);
4500 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4501 qp->div->ctx->one, v->size);
4502 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4503 isl_upoly_free(s);
4504 if (!qp->upoly)
4505 goto error;
4506 }
4507
4508 isl_vec_free(v);
4509 return qp;
4510 error:
4511 isl_vec_free(v);
4512 isl_qpolynomial_free(qp);
4513 return NULL;
4514 }
4515
4516 struct isl_to_poly_data {
4517 int sign;
4518 isl_pw_qpolynomial *res;
4519 isl_qpolynomial *qp;
4520 };
4521
4522 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4523 * We first make all integer divisions positive and then split the
4524 * quasipolynomials into terms with sign data->sign (the direction
4525 * of the requested approximation) and terms with the opposite sign.
4526 * In the first set of terms, each integer division [a/m] is
4527 * overapproximated by a/m, while in the second it is underapproximated
4528 * by (a-(m-1))/m.
4529 */
4530 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4531 void *user)
4532 {
4533 struct isl_to_poly_data *data = user;
4534 isl_pw_qpolynomial *t;
4535 isl_qpolynomial *qp, *up, *down;
4536
4537 qp = isl_qpolynomial_copy(data->qp);
4538 qp = make_divs_pos(qp, signs);
4539
4540 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4541 up = qp_drop_floors(up, 0);
4542 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4543 down = qp_drop_floors(down, 1);
4544
4545 isl_qpolynomial_free(qp);
4546 qp = isl_qpolynomial_add(up, down);
4547
4548 t = isl_pw_qpolynomial_alloc(orthant, qp);
4549 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4550
4551 return 0;
4552 }
4553
4554 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4555 * the polynomial will be an overapproximation. If "sign" is negative,
4556 * it will be an underapproximation. If "sign" is zero, the approximation
4557 * will lie somewhere in between.
4558 *
4559 * In particular, is sign == 0, we simply drop the floors, turning
4560 * the integer divisions into rational divisions.
4561 * Otherwise, we split the domains into orthants, make all integer divisions
4562 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4563 * depending on the requested sign and the sign of the term in which
4564 * the integer division appears.
4565 */
4566 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4567 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4568 {
4569 int i;
4570 struct isl_to_poly_data data;
4571
4572 if (sign == 0)
4573 return pwqp_drop_floors(pwqp);
4574
4575 if (!pwqp)
4576 return NULL;
4577
4578 data.sign = sign;
4579 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4580
4581 for (i = 0; i < pwqp->n; ++i) {
4582 if (pwqp->p[i].qp->div->n_row == 0) {
4583 isl_pw_qpolynomial *t;
4584 t = isl_pw_qpolynomial_alloc(
4585 isl_set_copy(pwqp->p[i].set),
4586 isl_qpolynomial_copy(pwqp->p[i].qp));
4587 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4588 continue;
4589 }
4590 data.qp = pwqp->p[i].qp;
4591 if (isl_set_foreach_orthant(pwqp->p[i].set,
4592 &to_polynomial_on_orthant, &data) < 0)
4593 goto error;
4594 }
4595
4596 isl_pw_qpolynomial_free(pwqp);
4597
4598 return data.res;
4599 error:
4600 isl_pw_qpolynomial_free(pwqp);
4601 isl_pw_qpolynomial_free(data.res);
4602 return NULL;
4603 }
4604
4605 static int poly_entry(void **entry, void *user)
4606 {
4607 int *sign = user;
4608 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4609
4610 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4611
4612 return *pwqp ? 0 : -1;
4613 }
4614
4615 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4616 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4617 {
4618 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4619 if (!upwqp)
4620 return NULL;
4621
4622 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4623 &poly_entry, &sign) < 0)
4624 goto error;
4625
4626 return upwqp;
4627 error:
4628 isl_union_pw_qpolynomial_free(upwqp);
4629 return NULL;
4630 }
4631
4632 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4633 __isl_take isl_qpolynomial *qp)
4634 {
4635 int i, k;
4636 isl_dim *dim;
4637 isl_vec *aff = NULL;
4638 isl_basic_map *bmap = NULL;
4639 unsigned pos;
4640 unsigned n_div;
4641
4642 if (!qp)
4643 return NULL;
4644 if (!isl_upoly_is_affine(qp->upoly))
4645 isl_die(qp->dim->ctx, isl_error_invalid,
4646 "input quasi-polynomial not affine", goto error);
4647 aff = isl_qpolynomial_extract_affine(qp);
4648 if (!aff)
4649 goto error;
4650 dim = isl_qpolynomial_get_dim(qp);
4651 dim = isl_dim_from_domain(dim);
4652 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4653 dim = isl_dim_add(dim, isl_dim_out, 1);
4654 n_div = qp->div->n_row;
4655 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4656
4657 for (i = 0; i < n_div; ++i) {
4658 k = isl_basic_map_alloc_div(bmap);
4659 if (k < 0)
4660 goto error;
4661 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4662 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4663 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4664 goto error;
4665 }
4666 k = isl_basic_map_alloc_equality(bmap);
4667 if (k < 0)
4668 goto error;
4669 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4670 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4671 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4672
4673 isl_vec_free(aff);
4674 isl_qpolynomial_free(qp);
4675 bmap = isl_basic_map_finalize(bmap);
4676 return bmap;
4677 error:
4678 isl_vec_free(aff);
4679 isl_qpolynomial_free(qp);
4680 isl_basic_map_free(bmap);
4681 return NULL;
4682 }
Integer set library