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isl_qpolynomial_drop_dims: properly handle nested spaces
[isl.git] / isl_polynomial.c
blobec973cce3d44ca05dcb64e818de89dc517f9676d
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_mat_private.h>
22 #include <isl_range.h>
23
24 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
25 {
26 switch (type) {
27 case isl_dim_param: return 0;
28 case isl_dim_in: return dim->nparam;
29 case isl_dim_out: return dim->nparam + dim->n_in;
30 default: return 0;
31 }
32 }
33
34 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
35 {
36 if (!up)
37 return -1;
38
39 return up->var < 0;
40 }
41
42 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
43 {
44 if (!up)
45 return NULL;
46
47 isl_assert(up->ctx, up->var < 0, return NULL);
48
49 return (struct isl_upoly_cst *)up;
50 }
51
52 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
53 {
54 if (!up)
55 return NULL;
56
57 isl_assert(up->ctx, up->var >= 0, return NULL);
58
59 return (struct isl_upoly_rec *)up;
60 }
61
62 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
63 __isl_keep struct isl_upoly *up2)
64 {
65 int i;
66 struct isl_upoly_rec *rec1, *rec2;
67
68 if (!up1 || !up2)
69 return -1;
70 if (up1 == up2)
71 return 1;
72 if (up1->var != up2->var)
73 return 0;
74 if (isl_upoly_is_cst(up1)) {
75 struct isl_upoly_cst *cst1, *cst2;
76 cst1 = isl_upoly_as_cst(up1);
77 cst2 = isl_upoly_as_cst(up2);
78 if (!cst1 || !cst2)
79 return -1;
80 return isl_int_eq(cst1->n, cst2->n) &&
81 isl_int_eq(cst1->d, cst2->d);
82 }
83
84 rec1 = isl_upoly_as_rec(up1);
85 rec2 = isl_upoly_as_rec(up2);
86 if (!rec1 || !rec2)
87 return -1;
88
89 if (rec1->n != rec2->n)
90 return 0;
91
92 for (i = 0; i < rec1->n; ++i) {
93 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
94 if (eq < 0 || !eq)
95 return eq;
96 }
97
98 return 1;
99 }
100
101 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
102 {
103 struct isl_upoly_cst *cst;
104
105 if (!up)
106 return -1;
107 if (!isl_upoly_is_cst(up))
108 return 0;
109
110 cst = isl_upoly_as_cst(up);
111 if (!cst)
112 return -1;
113
114 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
115 }
116
117 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
118 {
119 struct isl_upoly_cst *cst;
120
121 if (!up)
122 return 0;
123 if (!isl_upoly_is_cst(up))
124 return 0;
125
126 cst = isl_upoly_as_cst(up);
127 if (!cst)
128 return 0;
129
130 return isl_int_sgn(cst->n);
131 }
132
133 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
134 {
135 struct isl_upoly_cst *cst;
136
137 if (!up)
138 return -1;
139 if (!isl_upoly_is_cst(up))
140 return 0;
141
142 cst = isl_upoly_as_cst(up);
143 if (!cst)
144 return -1;
145
146 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
147 }
148
149 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
150 {
151 struct isl_upoly_cst *cst;
152
153 if (!up)
154 return -1;
155 if (!isl_upoly_is_cst(up))
156 return 0;
157
158 cst = isl_upoly_as_cst(up);
159 if (!cst)
160 return -1;
161
162 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
163 }
164
165 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
166 {
167 struct isl_upoly_cst *cst;
168
169 if (!up)
170 return -1;
171 if (!isl_upoly_is_cst(up))
172 return 0;
173
174 cst = isl_upoly_as_cst(up);
175 if (!cst)
176 return -1;
177
178 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
179 }
180
181 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
182 {
183 struct isl_upoly_cst *cst;
184
185 if (!up)
186 return -1;
187 if (!isl_upoly_is_cst(up))
188 return 0;
189
190 cst = isl_upoly_as_cst(up);
191 if (!cst)
192 return -1;
193
194 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
195 }
196
197 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
198 {
199 struct isl_upoly_cst *cst;
200
201 if (!up)
202 return -1;
203 if (!isl_upoly_is_cst(up))
204 return 0;
205
206 cst = isl_upoly_as_cst(up);
207 if (!cst)
208 return -1;
209
210 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
211 }
212
213 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
214 {
215 struct isl_upoly_cst *cst;
216
217 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
218 if (!cst)
219 return NULL;
220
221 cst->up.ref = 1;
222 cst->up.ctx = ctx;
223 isl_ctx_ref(ctx);
224 cst->up.var = -1;
225
226 isl_int_init(cst->n);
227 isl_int_init(cst->d);
228
229 return cst;
230 }
231
232 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
233 {
234 struct isl_upoly_cst *cst;
235
236 cst = isl_upoly_cst_alloc(ctx);
237 if (!cst)
238 return NULL;
239
240 isl_int_set_si(cst->n, 0);
241 isl_int_set_si(cst->d, 1);
242
243 return &cst->up;
244 }
245
246 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
247 {
248 struct isl_upoly_cst *cst;
249
250 cst = isl_upoly_cst_alloc(ctx);
251 if (!cst)
252 return NULL;
253
254 isl_int_set_si(cst->n, 1);
255 isl_int_set_si(cst->d, 1);
256
257 return &cst->up;
258 }
259
260 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
261 {
262 struct isl_upoly_cst *cst;
263
264 cst = isl_upoly_cst_alloc(ctx);
265 if (!cst)
266 return NULL;
267
268 isl_int_set_si(cst->n, 1);
269 isl_int_set_si(cst->d, 0);
270
271 return &cst->up;
272 }
273
274 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
275 {
276 struct isl_upoly_cst *cst;
277
278 cst = isl_upoly_cst_alloc(ctx);
279 if (!cst)
280 return NULL;
281
282 isl_int_set_si(cst->n, -1);
283 isl_int_set_si(cst->d, 0);
284
285 return &cst->up;
286 }
287
288 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
289 {
290 struct isl_upoly_cst *cst;
291
292 cst = isl_upoly_cst_alloc(ctx);
293 if (!cst)
294 return NULL;
295
296 isl_int_set_si(cst->n, 0);
297 isl_int_set_si(cst->d, 0);
298
299 return &cst->up;
300 }
301
302 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
303 isl_int n, isl_int d)
304 {
305 struct isl_upoly_cst *cst;
306
307 cst = isl_upoly_cst_alloc(ctx);
308 if (!cst)
309 return NULL;
310
311 isl_int_set(cst->n, n);
312 isl_int_set(cst->d, d);
313
314 return &cst->up;
315 }
316
317 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
318 int var, int size)
319 {
320 struct isl_upoly_rec *rec;
321
322 isl_assert(ctx, var >= 0, return NULL);
323 isl_assert(ctx, size >= 0, return NULL);
324 rec = isl_calloc(ctx, struct isl_upoly_rec,
325 sizeof(struct isl_upoly_rec) +
326 (size - 1) * sizeof(struct isl_upoly *));
327 if (!rec)
328 return NULL;
329
330 rec->up.ref = 1;
331 rec->up.ctx = ctx;
332 isl_ctx_ref(ctx);
333 rec->up.var = var;
334
335 rec->n = 0;
336 rec->size = size;
337
338 return rec;
339 }
340
341 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
342 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
343 {
344 qp = isl_qpolynomial_cow(qp);
345 if (!qp || !dim)
346 goto error;
347
348 isl_dim_free(qp->dim);
349 qp->dim = dim;
350
351 return qp;
352 error:
353 isl_qpolynomial_free(qp);
354 isl_dim_free(dim);
355 return NULL;
356 }
357
358 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
359 {
360 return qp ? qp->dim->ctx : NULL;
361 }
362
363 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
364 {
365 return qp ? isl_dim_copy(qp->dim) : NULL;
366 }
367
368 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
369 enum isl_dim_type type)
370 {
371 return qp ? isl_dim_size(qp->dim, type) : 0;
372 }
373
374 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
375 {
376 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
377 }
378
379 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
380 {
381 return qp ? isl_upoly_is_one(qp->upoly) : -1;
382 }
383
384 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
385 {
386 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
387 }
388
389 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
390 {
391 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
392 }
393
394 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
395 {
396 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
397 }
398
399 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
400 {
401 return qp ? isl_upoly_sgn(qp->upoly) : 0;
402 }
403
404 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
405 {
406 isl_int_clear(cst->n);
407 isl_int_clear(cst->d);
408 }
409
410 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
411 {
412 int i;
413
414 for (i = 0; i < rec->n; ++i)
415 isl_upoly_free(rec->p[i]);
416 }
417
418 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
419 {
420 if (!up)
421 return NULL;
422
423 up->ref++;
424 return up;
425 }
426
427 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
428 {
429 struct isl_upoly_cst *cst;
430 struct isl_upoly_cst *dup;
431
432 cst = isl_upoly_as_cst(up);
433 if (!cst)
434 return NULL;
435
436 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
437 if (!dup)
438 return NULL;
439 isl_int_set(dup->n, cst->n);
440 isl_int_set(dup->d, cst->d);
441
442 return &dup->up;
443 }
444
445 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
446 {
447 int i;
448 struct isl_upoly_rec *rec;
449 struct isl_upoly_rec *dup;
450
451 rec = isl_upoly_as_rec(up);
452 if (!rec)
453 return NULL;
454
455 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
456 if (!dup)
457 return NULL;
458
459 for (i = 0; i < rec->n; ++i) {
460 dup->p[i] = isl_upoly_copy(rec->p[i]);
461 if (!dup->p[i])
462 goto error;
463 dup->n++;
464 }
465
466 return &dup->up;
467 error:
468 isl_upoly_free(&dup->up);
469 return NULL;
470 }
471
472 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
473 {
474 struct isl_upoly *dup;
475
476 if (!up)
477 return NULL;
478
479 if (isl_upoly_is_cst(up))
480 return isl_upoly_dup_cst(up);
481 else
482 return isl_upoly_dup_rec(up);
483 }
484
485 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
486 {
487 if (!up)
488 return NULL;
489
490 if (up->ref == 1)
491 return up;
492 up->ref--;
493 return isl_upoly_dup(up);
494 }
495
496 void isl_upoly_free(__isl_take struct isl_upoly *up)
497 {
498 if (!up)
499 return;
500
501 if (--up->ref > 0)
502 return;
503
504 if (up->var < 0)
505 upoly_free_cst((struct isl_upoly_cst *)up);
506 else
507 upoly_free_rec((struct isl_upoly_rec *)up);
508
509 isl_ctx_deref(up->ctx);
510 free(up);
511 }
512
513 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
514 {
515 isl_int gcd;
516
517 isl_int_init(gcd);
518 isl_int_gcd(gcd, cst->n, cst->d);
519 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
520 isl_int_divexact(cst->n, cst->n, gcd);
521 isl_int_divexact(cst->d, cst->d, gcd);
522 }
523 isl_int_clear(gcd);
524 }
525
526 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
527 __isl_take struct isl_upoly *up2)
528 {
529 struct isl_upoly_cst *cst1;
530 struct isl_upoly_cst *cst2;
531
532 up1 = isl_upoly_cow(up1);
533 if (!up1 || !up2)
534 goto error;
535
536 cst1 = isl_upoly_as_cst(up1);
537 cst2 = isl_upoly_as_cst(up2);
538
539 if (isl_int_eq(cst1->d, cst2->d))
540 isl_int_add(cst1->n, cst1->n, cst2->n);
541 else {
542 isl_int_mul(cst1->n, cst1->n, cst2->d);
543 isl_int_addmul(cst1->n, cst2->n, cst1->d);
544 isl_int_mul(cst1->d, cst1->d, cst2->d);
545 }
546
547 isl_upoly_cst_reduce(cst1);
548
549 isl_upoly_free(up2);
550 return up1;
551 error:
552 isl_upoly_free(up1);
553 isl_upoly_free(up2);
554 return NULL;
555 }
556
557 static __isl_give struct isl_upoly *replace_by_zero(
558 __isl_take struct isl_upoly *up)
559 {
560 struct isl_ctx *ctx;
561
562 if (!up)
563 return NULL;
564 ctx = up->ctx;
565 isl_upoly_free(up);
566 return isl_upoly_zero(ctx);
567 }
568
569 static __isl_give struct isl_upoly *replace_by_constant_term(
570 __isl_take struct isl_upoly *up)
571 {
572 struct isl_upoly_rec *rec;
573 struct isl_upoly *cst;
574
575 if (!up)
576 return NULL;
577
578 rec = isl_upoly_as_rec(up);
579 if (!rec)
580 goto error;
581 cst = isl_upoly_copy(rec->p[0]);
582 isl_upoly_free(up);
583 return cst;
584 error:
585 isl_upoly_free(up);
586 return NULL;
587 }
588
589 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
590 __isl_take struct isl_upoly *up2)
591 {
592 int i;
593 struct isl_upoly_rec *rec1, *rec2;
594
595 if (!up1 || !up2)
596 goto error;
597
598 if (isl_upoly_is_nan(up1)) {
599 isl_upoly_free(up2);
600 return up1;
601 }
602
603 if (isl_upoly_is_nan(up2)) {
604 isl_upoly_free(up1);
605 return up2;
606 }
607
608 if (isl_upoly_is_zero(up1)) {
609 isl_upoly_free(up1);
610 return up2;
611 }
612
613 if (isl_upoly_is_zero(up2)) {
614 isl_upoly_free(up2);
615 return up1;
616 }
617
618 if (up1->var < up2->var)
619 return isl_upoly_sum(up2, up1);
620
621 if (up2->var < up1->var) {
622 struct isl_upoly_rec *rec;
623 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
624 isl_upoly_free(up1);
625 return up2;
626 }
627 up1 = isl_upoly_cow(up1);
628 rec = isl_upoly_as_rec(up1);
629 if (!rec)
630 goto error;
631 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
632 if (rec->n == 1)
633 up1 = replace_by_constant_term(up1);
634 return up1;
635 }
636
637 if (isl_upoly_is_cst(up1))
638 return isl_upoly_sum_cst(up1, up2);
639
640 rec1 = isl_upoly_as_rec(up1);
641 rec2 = isl_upoly_as_rec(up2);
642 if (!rec1 || !rec2)
643 goto error;
644
645 if (rec1->n < rec2->n)
646 return isl_upoly_sum(up2, up1);
647
648 up1 = isl_upoly_cow(up1);
649 rec1 = isl_upoly_as_rec(up1);
650 if (!rec1)
651 goto error;
652
653 for (i = rec2->n - 1; i >= 0; --i) {
654 rec1->p[i] = isl_upoly_sum(rec1->p[i],
655 isl_upoly_copy(rec2->p[i]));
656 if (!rec1->p[i])
657 goto error;
658 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
659 isl_upoly_free(rec1->p[i]);
660 rec1->n--;
661 }
662 }
663
664 if (rec1->n == 0)
665 up1 = replace_by_zero(up1);
666 else if (rec1->n == 1)
667 up1 = replace_by_constant_term(up1);
668
669 isl_upoly_free(up2);
670
671 return up1;
672 error:
673 isl_upoly_free(up1);
674 isl_upoly_free(up2);
675 return NULL;
676 }
677
678 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
679 __isl_take struct isl_upoly *up, isl_int v)
680 {
681 struct isl_upoly_cst *cst;
682
683 up = isl_upoly_cow(up);
684 if (!up)
685 return NULL;
686
687 cst = isl_upoly_as_cst(up);
688
689 isl_int_addmul(cst->n, cst->d, v);
690
691 return up;
692 }
693
694 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
695 __isl_take struct isl_upoly *up, isl_int v)
696 {
697 struct isl_upoly_rec *rec;
698
699 if (!up)
700 return NULL;
701
702 if (isl_upoly_is_cst(up))
703 return isl_upoly_cst_add_isl_int(up, v);
704
705 up = isl_upoly_cow(up);
706 rec = isl_upoly_as_rec(up);
707 if (!rec)
708 goto error;
709
710 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
711 if (!rec->p[0])
712 goto error;
713
714 return up;
715 error:
716 isl_upoly_free(up);
717 return NULL;
718 }
719
720 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
721 __isl_take struct isl_upoly *up, isl_int v)
722 {
723 struct isl_upoly_cst *cst;
724
725 if (isl_upoly_is_zero(up))
726 return up;
727
728 up = isl_upoly_cow(up);
729 if (!up)
730 return NULL;
731
732 cst = isl_upoly_as_cst(up);
733
734 isl_int_mul(cst->n, cst->n, v);
735
736 return up;
737 }
738
739 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
740 __isl_take struct isl_upoly *up, isl_int v)
741 {
742 int i;
743 struct isl_upoly_rec *rec;
744
745 if (!up)
746 return NULL;
747
748 if (isl_upoly_is_cst(up))
749 return isl_upoly_cst_mul_isl_int(up, v);
750
751 up = isl_upoly_cow(up);
752 rec = isl_upoly_as_rec(up);
753 if (!rec)
754 goto error;
755
756 for (i = 0; i < rec->n; ++i) {
757 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
758 if (!rec->p[i])
759 goto error;
760 }
761
762 return up;
763 error:
764 isl_upoly_free(up);
765 return NULL;
766 }
767
768 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
769 __isl_take struct isl_upoly *up2)
770 {
771 struct isl_upoly_cst *cst1;
772 struct isl_upoly_cst *cst2;
773
774 up1 = isl_upoly_cow(up1);
775 if (!up1 || !up2)
776 goto error;
777
778 cst1 = isl_upoly_as_cst(up1);
779 cst2 = isl_upoly_as_cst(up2);
780
781 isl_int_mul(cst1->n, cst1->n, cst2->n);
782 isl_int_mul(cst1->d, cst1->d, cst2->d);
783
784 isl_upoly_cst_reduce(cst1);
785
786 isl_upoly_free(up2);
787 return up1;
788 error:
789 isl_upoly_free(up1);
790 isl_upoly_free(up2);
791 return NULL;
792 }
793
794 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
795 __isl_take struct isl_upoly *up2)
796 {
797 struct isl_upoly_rec *rec1;
798 struct isl_upoly_rec *rec2;
799 struct isl_upoly_rec *res;
800 int i, j;
801 int size;
802
803 rec1 = isl_upoly_as_rec(up1);
804 rec2 = isl_upoly_as_rec(up2);
805 if (!rec1 || !rec2)
806 goto error;
807 size = rec1->n + rec2->n - 1;
808 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
809 if (!res)
810 goto error;
811
812 for (i = 0; i < rec1->n; ++i) {
813 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
814 isl_upoly_copy(rec1->p[i]));
815 if (!res->p[i])
816 goto error;
817 res->n++;
818 }
819 for (; i < size; ++i) {
820 res->p[i] = isl_upoly_zero(up1->ctx);
821 if (!res->p[i])
822 goto error;
823 res->n++;
824 }
825 for (i = 0; i < rec1->n; ++i) {
826 for (j = 1; j < rec2->n; ++j) {
827 struct isl_upoly *up;
828 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
829 isl_upoly_copy(rec1->p[i]));
830 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
831 if (!res->p[i + j])
832 goto error;
833 }
834 }
835
836 isl_upoly_free(up1);
837 isl_upoly_free(up2);
838
839 return &res->up;
840 error:
841 isl_upoly_free(up1);
842 isl_upoly_free(up2);
843 isl_upoly_free(&res->up);
844 return NULL;
845 }
846
847 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
848 __isl_take struct isl_upoly *up2)
849 {
850 if (!up1 || !up2)
851 goto error;
852
853 if (isl_upoly_is_nan(up1)) {
854 isl_upoly_free(up2);
855 return up1;
856 }
857
858 if (isl_upoly_is_nan(up2)) {
859 isl_upoly_free(up1);
860 return up2;
861 }
862
863 if (isl_upoly_is_zero(up1)) {
864 isl_upoly_free(up2);
865 return up1;
866 }
867
868 if (isl_upoly_is_zero(up2)) {
869 isl_upoly_free(up1);
870 return up2;
871 }
872
873 if (isl_upoly_is_one(up1)) {
874 isl_upoly_free(up1);
875 return up2;
876 }
877
878 if (isl_upoly_is_one(up2)) {
879 isl_upoly_free(up2);
880 return up1;
881 }
882
883 if (up1->var < up2->var)
884 return isl_upoly_mul(up2, up1);
885
886 if (up2->var < up1->var) {
887 int i;
888 struct isl_upoly_rec *rec;
889 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
890 isl_ctx *ctx = up1->ctx;
891 isl_upoly_free(up1);
892 isl_upoly_free(up2);
893 return isl_upoly_nan(ctx);
894 }
895 up1 = isl_upoly_cow(up1);
896 rec = isl_upoly_as_rec(up1);
897 if (!rec)
898 goto error;
899
900 for (i = 0; i < rec->n; ++i) {
901 rec->p[i] = isl_upoly_mul(rec->p[i],
902 isl_upoly_copy(up2));
903 if (!rec->p[i])
904 goto error;
905 }
906 isl_upoly_free(up2);
907 return up1;
908 }
909
910 if (isl_upoly_is_cst(up1))
911 return isl_upoly_mul_cst(up1, up2);
912
913 return isl_upoly_mul_rec(up1, up2);
914 error:
915 isl_upoly_free(up1);
916 isl_upoly_free(up2);
917 return NULL;
918 }
919
920 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
921 unsigned power)
922 {
923 struct isl_upoly *res;
924
925 if (!up)
926 return NULL;
927 if (power == 1)
928 return up;
929
930 if (power % 2)
931 res = isl_upoly_copy(up);
932 else
933 res = isl_upoly_one(up->ctx);
934
935 while (power >>= 1) {
936 up = isl_upoly_mul(up, isl_upoly_copy(up));
937 if (power % 2)
938 res = isl_upoly_mul(res, isl_upoly_copy(up));
939 }
940
941 isl_upoly_free(up);
942 return res;
943 }
944
945 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
946 unsigned n_div, __isl_take struct isl_upoly *up)
947 {
948 struct isl_qpolynomial *qp = NULL;
949 unsigned total;
950
951 if (!dim || !up)
952 goto error;
953
954 total = isl_dim_total(dim);
955
956 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
957 if (!qp)
958 goto error;
959
960 qp->ref = 1;
961 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
962 if (!qp->div)
963 goto error;
964
965 qp->dim = dim;
966 qp->upoly = up;
967
968 return qp;
969 error:
970 isl_dim_free(dim);
971 isl_upoly_free(up);
972 isl_qpolynomial_free(qp);
973 return NULL;
974 }
975
976 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
977 {
978 if (!qp)
979 return NULL;
980
981 qp->ref++;
982 return qp;
983 }
984
985 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
986 {
987 struct isl_qpolynomial *dup;
988
989 if (!qp)
990 return NULL;
991
992 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
993 isl_upoly_copy(qp->upoly));
994 if (!dup)
995 return NULL;
996 isl_mat_free(dup->div);
997 dup->div = isl_mat_copy(qp->div);
998 if (!dup->div)
999 goto error;
1000
1001 return dup;
1002 error:
1003 isl_qpolynomial_free(dup);
1004 return NULL;
1005 }
1006
1007 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1008 {
1009 if (!qp)
1010 return NULL;
1011
1012 if (qp->ref == 1)
1013 return qp;
1014 qp->ref--;
1015 return isl_qpolynomial_dup(qp);
1016 }
1017
1018 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1019 {
1020 if (!qp)
1021 return;
1022
1023 if (--qp->ref > 0)
1024 return;
1025
1026 isl_dim_free(qp->dim);
1027 isl_mat_free(qp->div);
1028 isl_upoly_free(qp->upoly);
1029
1030 free(qp);
1031 }
1032
1033 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1034 {
1035 int i;
1036 struct isl_upoly *up;
1037 struct isl_upoly_rec *rec;
1038 struct isl_upoly_cst *cst;
1039
1040 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1041 if (!rec)
1042 return NULL;
1043 for (i = 0; i < 1 + power; ++i) {
1044 rec->p[i] = isl_upoly_zero(ctx);
1045 if (!rec->p[i])
1046 goto error;
1047 rec->n++;
1048 }
1049 cst = isl_upoly_as_cst(rec->p[power]);
1050 isl_int_set_si(cst->n, 1);
1051
1052 return &rec->up;
1053 error:
1054 isl_upoly_free(&rec->up);
1055 return NULL;
1056 }
1057
1058 /* r array maps original positions to new positions.
1059 */
1060 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1061 int *r)
1062 {
1063 int i;
1064 struct isl_upoly_rec *rec;
1065 struct isl_upoly *base;
1066 struct isl_upoly *res;
1067
1068 if (isl_upoly_is_cst(up))
1069 return up;
1070
1071 rec = isl_upoly_as_rec(up);
1072 if (!rec)
1073 goto error;
1074
1075 isl_assert(up->ctx, rec->n >= 1, goto error);
1076
1077 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1078 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1079
1080 for (i = rec->n - 2; i >= 0; --i) {
1081 res = isl_upoly_mul(res, isl_upoly_copy(base));
1082 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1083 }
1084
1085 isl_upoly_free(base);
1086 isl_upoly_free(up);
1087
1088 return res;
1089 error:
1090 isl_upoly_free(up);
1091 return NULL;
1092 }
1093
1094 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1095 {
1096 int n_row, n_col;
1097 int equal;
1098
1099 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1100 div1->n_col >= div2->n_col, return -1);
1101
1102 if (div1->n_row == div2->n_row)
1103 return isl_mat_is_equal(div1, div2);
1104
1105 n_row = div1->n_row;
1106 n_col = div1->n_col;
1107 div1->n_row = div2->n_row;
1108 div1->n_col = div2->n_col;
1109
1110 equal = isl_mat_is_equal(div1, div2);
1111
1112 div1->n_row = n_row;
1113 div1->n_col = n_col;
1114
1115 return equal;
1116 }
1117
1118 static void expand_row(__isl_keep isl_mat *dst, int d,
1119 __isl_keep isl_mat *src, int s, int *exp)
1120 {
1121 int i;
1122 unsigned c = src->n_col - src->n_row;
1123
1124 isl_seq_cpy(dst->row[d], src->row[s], c);
1125 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
1126
1127 for (i = 0; i < s; ++i)
1128 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
1129 }
1130
1131 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1132 {
1133 int li, lj;
1134
1135 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1136 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1137
1138 if (li != lj)
1139 return li - lj;
1140
1141 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1142 }
1143
1144 struct isl_div_sort_info {
1145 isl_mat *div;
1146 int row;
1147 };
1148
1149 static int div_sort_cmp(const void *p1, const void *p2)
1150 {
1151 const struct isl_div_sort_info *i1, *i2;
1152 i1 = (const struct isl_div_sort_info *) p1;
1153 i2 = (const struct isl_div_sort_info *) p2;
1154
1155 return cmp_row(i1->div, i1->row, i2->row);
1156 }
1157
1158 /* Sort divs and remove duplicates.
1159 */
1160 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1161 {
1162 int i;
1163 int skip;
1164 int len;
1165 struct isl_div_sort_info *array = NULL;
1166 int *pos = NULL, *at = NULL;
1167 int *reordering = NULL;
1168 unsigned div_pos;
1169
1170 if (!qp)
1171 return NULL;
1172 if (qp->div->n_row <= 1)
1173 return qp;
1174
1175 div_pos = isl_dim_total(qp->dim);
1176
1177 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1178 qp->div->n_row);
1179 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1180 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1181 len = qp->div->n_col - 2;
1182 reordering = isl_alloc_array(qp->div->ctx, int, len);
1183 if (!array || !pos || !at || !reordering)
1184 goto error;
1185
1186 for (i = 0; i < qp->div->n_row; ++i) {
1187 array[i].div = qp->div;
1188 array[i].row = i;
1189 pos[i] = i;
1190 at[i] = i;
1191 }
1192
1193 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1194 div_sort_cmp);
1195
1196 for (i = 0; i < div_pos; ++i)
1197 reordering[i] = i;
1198
1199 for (i = 0; i < qp->div->n_row; ++i) {
1200 if (pos[array[i].row] == i)
1201 continue;
1202 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1203 pos[at[i]] = pos[array[i].row];
1204 at[pos[array[i].row]] = at[i];
1205 at[i] = array[i].row;
1206 pos[array[i].row] = i;
1207 }
1208
1209 skip = 0;
1210 for (i = 0; i < len - div_pos; ++i) {
1211 if (i > 0 &&
1212 isl_seq_eq(qp->div->row[i - skip - 1],
1213 qp->div->row[i - skip], qp->div->n_col)) {
1214 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1215 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1216 2 + div_pos + i - skip);
1217 qp->div = isl_mat_drop_cols(qp->div,
1218 2 + div_pos + i - skip, 1);
1219 skip++;
1220 }
1221 reordering[div_pos + array[i].row] = div_pos + i - skip;
1222 }
1223
1224 qp->upoly = reorder(qp->upoly, reordering);
1225
1226 if (!qp->upoly || !qp->div)
1227 goto error;
1228
1229 free(at);
1230 free(pos);
1231 free(array);
1232 free(reordering);
1233
1234 return qp;
1235 error:
1236 free(at);
1237 free(pos);
1238 free(array);
1239 free(reordering);
1240 isl_qpolynomial_free(qp);
1241 return NULL;
1242 }
1243
1244 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1245 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1246 {
1247 int i, j, k;
1248 isl_mat *div = NULL;
1249 unsigned d = div1->n_col - div1->n_row;
1250
1251 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1252 d + div1->n_row + div2->n_row);
1253 if (!div)
1254 return NULL;
1255
1256 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1257 int cmp;
1258
1259 expand_row(div, k, div1, i, exp1);
1260 expand_row(div, k + 1, div2, j, exp2);
1261
1262 cmp = cmp_row(div, k, k + 1);
1263 if (cmp == 0) {
1264 exp1[i++] = k;
1265 exp2[j++] = k;
1266 } else if (cmp < 0) {
1267 exp1[i++] = k;
1268 } else {
1269 exp2[j++] = k;
1270 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1271 }
1272 }
1273 for (; i < div1->n_row; ++i, ++k) {
1274 expand_row(div, k, div1, i, exp1);
1275 exp1[i] = k;
1276 }
1277 for (; j < div2->n_row; ++j, ++k) {
1278 expand_row(div, k, div2, j, exp2);
1279 exp2[j] = k;
1280 }
1281
1282 div->n_row = k;
1283 div->n_col = d + k;
1284
1285 return div;
1286 }
1287
1288 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1289 int *exp, int first)
1290 {
1291 int i;
1292 struct isl_upoly_rec *rec;
1293
1294 if (isl_upoly_is_cst(up))
1295 return up;
1296
1297 if (up->var < first)
1298 return up;
1299
1300 if (exp[up->var - first] == up->var - first)
1301 return up;
1302
1303 up = isl_upoly_cow(up);
1304 if (!up)
1305 goto error;
1306
1307 up->var = exp[up->var - first] + first;
1308
1309 rec = isl_upoly_as_rec(up);
1310 if (!rec)
1311 goto error;
1312
1313 for (i = 0; i < rec->n; ++i) {
1314 rec->p[i] = expand(rec->p[i], exp, first);
1315 if (!rec->p[i])
1316 goto error;
1317 }
1318
1319 return up;
1320 error:
1321 isl_upoly_free(up);
1322 return NULL;
1323 }
1324
1325 static __isl_give isl_qpolynomial *with_merged_divs(
1326 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1327 __isl_take isl_qpolynomial *qp2),
1328 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1329 {
1330 int *exp1 = NULL;
1331 int *exp2 = NULL;
1332 isl_mat *div = NULL;
1333
1334 qp1 = isl_qpolynomial_cow(qp1);
1335 qp2 = isl_qpolynomial_cow(qp2);
1336
1337 if (!qp1 || !qp2)
1338 goto error;
1339
1340 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1341 qp1->div->n_col >= qp2->div->n_col, goto error);
1342
1343 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1344 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1345 if (!exp1 || !exp2)
1346 goto error;
1347
1348 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1349 if (!div)
1350 goto error;
1351
1352 isl_mat_free(qp1->div);
1353 qp1->div = isl_mat_copy(div);
1354 isl_mat_free(qp2->div);
1355 qp2->div = isl_mat_copy(div);
1356
1357 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1358 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1359
1360 if (!qp1->upoly || !qp2->upoly)
1361 goto error;
1362
1363 isl_mat_free(div);
1364 free(exp1);
1365 free(exp2);
1366
1367 return fn(qp1, qp2);
1368 error:
1369 isl_mat_free(div);
1370 free(exp1);
1371 free(exp2);
1372 isl_qpolynomial_free(qp1);
1373 isl_qpolynomial_free(qp2);
1374 return NULL;
1375 }
1376
1377 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1378 __isl_take isl_qpolynomial *qp2)
1379 {
1380 qp1 = isl_qpolynomial_cow(qp1);
1381
1382 if (!qp1 || !qp2)
1383 goto error;
1384
1385 if (qp1->div->n_row < qp2->div->n_row)
1386 return isl_qpolynomial_add(qp2, qp1);
1387
1388 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1389 if (!compatible_divs(qp1->div, qp2->div))
1390 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1391
1392 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1393 if (!qp1->upoly)
1394 goto error;
1395
1396 isl_qpolynomial_free(qp2);
1397
1398 return qp1;
1399 error:
1400 isl_qpolynomial_free(qp1);
1401 isl_qpolynomial_free(qp2);
1402 return NULL;
1403 }
1404
1405 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1406 __isl_keep isl_set *dom,
1407 __isl_take isl_qpolynomial *qp1,
1408 __isl_take isl_qpolynomial *qp2)
1409 {
1410 qp1 = isl_qpolynomial_add(qp1, qp2);
1411 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1412 return qp1;
1413 }
1414
1415 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1416 __isl_take isl_qpolynomial *qp2)
1417 {
1418 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1419 }
1420
1421 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1422 __isl_take isl_qpolynomial *qp, isl_int v)
1423 {
1424 if (isl_int_is_zero(v))
1425 return qp;
1426
1427 qp = isl_qpolynomial_cow(qp);
1428 if (!qp)
1429 return NULL;
1430
1431 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1432 if (!qp->upoly)
1433 goto error;
1434
1435 return qp;
1436 error:
1437 isl_qpolynomial_free(qp);
1438 return NULL;
1439
1440 }
1441
1442 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1443 {
1444 if (!qp)
1445 return NULL;
1446
1447 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1448 }
1449
1450 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1451 __isl_take isl_qpolynomial *qp, isl_int v)
1452 {
1453 if (isl_int_is_one(v))
1454 return qp;
1455
1456 if (qp && isl_int_is_zero(v)) {
1457 isl_qpolynomial *zero;
1458 zero = isl_qpolynomial_zero(isl_dim_copy(qp->dim));
1459 isl_qpolynomial_free(qp);
1460 return zero;
1461 }
1462
1463 qp = isl_qpolynomial_cow(qp);
1464 if (!qp)
1465 return NULL;
1466
1467 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1468 if (!qp->upoly)
1469 goto error;
1470
1471 return qp;
1472 error:
1473 isl_qpolynomial_free(qp);
1474 return NULL;
1475 }
1476
1477 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1478 __isl_take isl_qpolynomial *qp2)
1479 {
1480 qp1 = isl_qpolynomial_cow(qp1);
1481
1482 if (!qp1 || !qp2)
1483 goto error;
1484
1485 if (qp1->div->n_row < qp2->div->n_row)
1486 return isl_qpolynomial_mul(qp2, qp1);
1487
1488 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1489 if (!compatible_divs(qp1->div, qp2->div))
1490 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1491
1492 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1493 if (!qp1->upoly)
1494 goto error;
1495
1496 isl_qpolynomial_free(qp2);
1497
1498 return qp1;
1499 error:
1500 isl_qpolynomial_free(qp1);
1501 isl_qpolynomial_free(qp2);
1502 return NULL;
1503 }
1504
1505 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1506 unsigned power)
1507 {
1508 qp = isl_qpolynomial_cow(qp);
1509
1510 if (!qp)
1511 return NULL;
1512
1513 qp->upoly = isl_upoly_pow(qp->upoly, power);
1514 if (!qp->upoly)
1515 goto error;
1516
1517 return qp;
1518 error:
1519 isl_qpolynomial_free(qp);
1520 return NULL;
1521 }
1522
1523 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1524 {
1525 if (!dim)
1526 return NULL;
1527 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1528 }
1529
1530 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1531 {
1532 if (!dim)
1533 return NULL;
1534 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1535 }
1536
1537 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1538 {
1539 if (!dim)
1540 return NULL;
1541 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1542 }
1543
1544 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1545 {
1546 if (!dim)
1547 return NULL;
1548 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1549 }
1550
1551 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1552 {
1553 if (!dim)
1554 return NULL;
1555 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1556 }
1557
1558 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1559 isl_int v)
1560 {
1561 struct isl_qpolynomial *qp;
1562 struct isl_upoly_cst *cst;
1563
1564 if (!dim)
1565 return NULL;
1566
1567 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1568 if (!qp)
1569 return NULL;
1570
1571 cst = isl_upoly_as_cst(qp->upoly);
1572 isl_int_set(cst->n, v);
1573
1574 return qp;
1575 }
1576
1577 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1578 isl_int *n, isl_int *d)
1579 {
1580 struct isl_upoly_cst *cst;
1581
1582 if (!qp)
1583 return -1;
1584
1585 if (!isl_upoly_is_cst(qp->upoly))
1586 return 0;
1587
1588 cst = isl_upoly_as_cst(qp->upoly);
1589 if (!cst)
1590 return -1;
1591
1592 if (n)
1593 isl_int_set(*n, cst->n);
1594 if (d)
1595 isl_int_set(*d, cst->d);
1596
1597 return 1;
1598 }
1599
1600 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1601 {
1602 int is_cst;
1603 struct isl_upoly_rec *rec;
1604
1605 if (!up)
1606 return -1;
1607
1608 if (up->var < 0)
1609 return 1;
1610
1611 rec = isl_upoly_as_rec(up);
1612 if (!rec)
1613 return -1;
1614
1615 if (rec->n > 2)
1616 return 0;
1617
1618 isl_assert(up->ctx, rec->n > 1, return -1);
1619
1620 is_cst = isl_upoly_is_cst(rec->p[1]);
1621 if (is_cst < 0)
1622 return -1;
1623 if (!is_cst)
1624 return 0;
1625
1626 return isl_upoly_is_affine(rec->p[0]);
1627 }
1628
1629 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1630 {
1631 if (!qp)
1632 return -1;
1633
1634 if (qp->div->n_row > 0)
1635 return 0;
1636
1637 return isl_upoly_is_affine(qp->upoly);
1638 }
1639
1640 static void update_coeff(__isl_keep isl_vec *aff,
1641 __isl_keep struct isl_upoly_cst *cst, int pos)
1642 {
1643 isl_int gcd;
1644 isl_int f;
1645
1646 if (isl_int_is_zero(cst->n))
1647 return;
1648
1649 isl_int_init(gcd);
1650 isl_int_init(f);
1651 isl_int_gcd(gcd, cst->d, aff->el[0]);
1652 isl_int_divexact(f, cst->d, gcd);
1653 isl_int_divexact(gcd, aff->el[0], gcd);
1654 isl_seq_scale(aff->el, aff->el, f, aff->size);
1655 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1656 isl_int_clear(gcd);
1657 isl_int_clear(f);
1658 }
1659
1660 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1661 __isl_keep isl_vec *aff)
1662 {
1663 struct isl_upoly_cst *cst;
1664 struct isl_upoly_rec *rec;
1665
1666 if (!up || !aff)
1667 return -1;
1668
1669 if (up->var < 0) {
1670 struct isl_upoly_cst *cst;
1671
1672 cst = isl_upoly_as_cst(up);
1673 if (!cst)
1674 return -1;
1675 update_coeff(aff, cst, 0);
1676 return 0;
1677 }
1678
1679 rec = isl_upoly_as_rec(up);
1680 if (!rec)
1681 return -1;
1682 isl_assert(up->ctx, rec->n == 2, return -1);
1683
1684 cst = isl_upoly_as_cst(rec->p[1]);
1685 if (!cst)
1686 return -1;
1687 update_coeff(aff, cst, 1 + up->var);
1688
1689 return isl_upoly_update_affine(rec->p[0], aff);
1690 }
1691
1692 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1693 __isl_keep isl_qpolynomial *qp)
1694 {
1695 isl_vec *aff;
1696 unsigned d;
1697
1698 if (!qp)
1699 return NULL;
1700
1701 d = isl_dim_total(qp->dim);
1702 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1703 if (!aff)
1704 return NULL;
1705
1706 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1707 isl_int_set_si(aff->el[0], 1);
1708
1709 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1710 goto error;
1711
1712 return aff;
1713 error:
1714 isl_vec_free(aff);
1715 return NULL;
1716 }
1717
1718 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1719 __isl_keep isl_qpolynomial *qp2)
1720 {
1721 int equal;
1722
1723 if (!qp1 || !qp2)
1724 return -1;
1725
1726 equal = isl_dim_equal(qp1->dim, qp2->dim);
1727 if (equal < 0 || !equal)
1728 return equal;
1729
1730 equal = isl_mat_is_equal(qp1->div, qp2->div);
1731 if (equal < 0 || !equal)
1732 return equal;
1733
1734 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1735 }
1736
1737 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1738 {
1739 int i;
1740 struct isl_upoly_rec *rec;
1741
1742 if (isl_upoly_is_cst(up)) {
1743 struct isl_upoly_cst *cst;
1744 cst = isl_upoly_as_cst(up);
1745 if (!cst)
1746 return;
1747 isl_int_lcm(*d, *d, cst->d);
1748 return;
1749 }
1750
1751 rec = isl_upoly_as_rec(up);
1752 if (!rec)
1753 return;
1754
1755 for (i = 0; i < rec->n; ++i)
1756 upoly_update_den(rec->p[i], d);
1757 }
1758
1759 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1760 {
1761 isl_int_set_si(*d, 1);
1762 if (!qp)
1763 return;
1764 upoly_update_den(qp->upoly, d);
1765 }
1766
1767 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1768 int pos, int power)
1769 {
1770 struct isl_ctx *ctx;
1771
1772 if (!dim)
1773 return NULL;
1774
1775 ctx = dim->ctx;
1776
1777 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1778 }
1779
1780 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1781 enum isl_dim_type type, unsigned pos)
1782 {
1783 if (!dim)
1784 return NULL;
1785
1786 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1787 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1788
1789 if (type == isl_dim_set)
1790 pos += isl_dim_size(dim, isl_dim_param);
1791
1792 return isl_qpolynomial_var_pow(dim, pos, 1);
1793 error:
1794 isl_dim_free(dim);
1795 return NULL;
1796 }
1797
1798 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1799 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1800 {
1801 int i;
1802 struct isl_upoly_rec *rec;
1803 struct isl_upoly *base, *res;
1804
1805 if (!up)
1806 return NULL;
1807
1808 if (isl_upoly_is_cst(up))
1809 return up;
1810
1811 if (up->var < first)
1812 return up;
1813
1814 rec = isl_upoly_as_rec(up);
1815 if (!rec)
1816 goto error;
1817
1818 isl_assert(up->ctx, rec->n >= 1, goto error);
1819
1820 if (up->var >= first + n)
1821 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1822 else
1823 base = isl_upoly_copy(subs[up->var - first]);
1824
1825 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1826 for (i = rec->n - 2; i >= 0; --i) {
1827 struct isl_upoly *t;
1828 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1829 res = isl_upoly_mul(res, isl_upoly_copy(base));
1830 res = isl_upoly_sum(res, t);
1831 }
1832
1833 isl_upoly_free(base);
1834 isl_upoly_free(up);
1835
1836 return res;
1837 error:
1838 isl_upoly_free(up);
1839 return NULL;
1840 }
1841
1842 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1843 isl_int denom, unsigned len)
1844 {
1845 int i;
1846 struct isl_upoly *up;
1847
1848 isl_assert(ctx, len >= 1, return NULL);
1849
1850 up = isl_upoly_rat_cst(ctx, f[0], denom);
1851 for (i = 0; i < len - 1; ++i) {
1852 struct isl_upoly *t;
1853 struct isl_upoly *c;
1854
1855 if (isl_int_is_zero(f[1 + i]))
1856 continue;
1857
1858 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1859 t = isl_upoly_var_pow(ctx, i, 1);
1860 t = isl_upoly_mul(c, t);
1861 up = isl_upoly_sum(up, t);
1862 }
1863
1864 return up;
1865 }
1866
1867 /* Remove common factor of non-constant terms and denominator.
1868 */
1869 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1870 {
1871 isl_ctx *ctx = qp->div->ctx;
1872 unsigned total = qp->div->n_col - 2;
1873
1874 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1875 isl_int_gcd(ctx->normalize_gcd,
1876 ctx->normalize_gcd, qp->div->row[div][0]);
1877 if (isl_int_is_one(ctx->normalize_gcd))
1878 return;
1879
1880 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1881 ctx->normalize_gcd, total);
1882 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1883 ctx->normalize_gcd);
1884 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1885 ctx->normalize_gcd);
1886 }
1887
1888 /* Replace the integer division identified by "div" by the polynomial "s".
1889 * The integer division is assumed not to appear in the definition
1890 * of any other integer divisions.
1891 */
1892 static __isl_give isl_qpolynomial *substitute_div(
1893 __isl_take isl_qpolynomial *qp,
1894 int div, __isl_take struct isl_upoly *s)
1895 {
1896 int i;
1897 int total;
1898 int *reordering;
1899
1900 if (!qp || !s)
1901 goto error;
1902
1903 qp = isl_qpolynomial_cow(qp);
1904 if (!qp)
1905 goto error;
1906
1907 total = isl_dim_total(qp->dim);
1908 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1909 if (!qp->upoly)
1910 goto error;
1911
1912 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1913 if (!reordering)
1914 goto error;
1915 for (i = 0; i < total + div; ++i)
1916 reordering[i] = i;
1917 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1918 reordering[i] = i - 1;
1919 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1920 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1921 qp->upoly = reorder(qp->upoly, reordering);
1922 free(reordering);
1923
1924 if (!qp->upoly || !qp->div)
1925 goto error;
1926
1927 isl_upoly_free(s);
1928 return qp;
1929 error:
1930 isl_qpolynomial_free(qp);
1931 isl_upoly_free(s);
1932 return NULL;
1933 }
1934
1935 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1936 * divisions because d is equal to 1 by their definition, i.e., e.
1937 */
1938 static __isl_give isl_qpolynomial *substitute_non_divs(
1939 __isl_take isl_qpolynomial *qp)
1940 {
1941 int i, j;
1942 int total;
1943 struct isl_upoly *s;
1944
1945 if (!qp)
1946 return NULL;
1947
1948 total = isl_dim_total(qp->dim);
1949 for (i = 0; qp && i < qp->div->n_row; ++i) {
1950 if (!isl_int_is_one(qp->div->row[i][0]))
1951 continue;
1952 for (j = i + 1; j < qp->div->n_row; ++j) {
1953 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1954 continue;
1955 isl_seq_combine(qp->div->row[j] + 1,
1956 qp->div->ctx->one, qp->div->row[j] + 1,
1957 qp->div->row[j][2 + total + i],
1958 qp->div->row[i] + 1, 1 + total + i);
1959 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1960 normalize_div(qp, j);
1961 }
1962 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1963 qp->div->row[i][0], qp->div->n_col - 1);
1964 qp = substitute_div(qp, i, s);
1965 --i;
1966 }
1967
1968 return qp;
1969 }
1970
1971 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1972 * with d the denominator. When replacing the coefficient e of x by
1973 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1974 * inside the division, so we need to add floor(e/d) * x outside.
1975 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1976 * to adjust the coefficient of x in each later div that depends on the
1977 * current div "div" and also in the affine expression "aff"
1978 * (if it too depends on "div").
1979 */
1980 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1981 __isl_keep isl_vec *aff)
1982 {
1983 int i, j;
1984 isl_int v;
1985 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1986
1987 isl_int_init(v);
1988 for (i = 0; i < 1 + total + div; ++i) {
1989 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1990 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1991 continue;
1992 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1993 isl_int_fdiv_r(qp->div->row[div][1 + i],
1994 qp->div->row[div][1 + i], qp->div->row[div][0]);
1995 if (!isl_int_is_zero(aff->el[1 + total + div]))
1996 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1997 for (j = div + 1; j < qp->div->n_row; ++j) {
1998 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1999 continue;
2000 isl_int_addmul(qp->div->row[j][1 + i],
2001 v, qp->div->row[j][2 + total + div]);
2002 }
2003 }
2004 isl_int_clear(v);
2005 }
2006
2007 /* Check if the last non-zero coefficient is bigger that half of the
2008 * denominator. If so, we will invert the div to further reduce the number
2009 * of distinct divs that may appear.
2010 * If the last non-zero coefficient is exactly half the denominator,
2011 * then we continue looking for earlier coefficients that are bigger
2012 * than half the denominator.
2013 */
2014 static int needs_invert(__isl_keep isl_mat *div, int row)
2015 {
2016 int i;
2017 int cmp;
2018
2019 for (i = div->n_col - 1; i >= 1; --i) {
2020 if (isl_int_is_zero(div->row[row][i]))
2021 continue;
2022 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
2023 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
2024 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
2025 if (cmp)
2026 return cmp > 0;
2027 if (i == 1)
2028 return 1;
2029 }
2030
2031 return 0;
2032 }
2033
2034 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2035 * We only invert the coefficients of e (and the coefficient of q in
2036 * later divs and in "aff"). After calling this function, the
2037 * coefficients of e should be reduced again.
2038 */
2039 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
2040 __isl_keep isl_vec *aff)
2041 {
2042 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2043
2044 isl_seq_neg(qp->div->row[div] + 1,
2045 qp->div->row[div] + 1, qp->div->n_col - 1);
2046 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2047 isl_int_add(qp->div->row[div][1],
2048 qp->div->row[div][1], qp->div->row[div][0]);
2049 if (!isl_int_is_zero(aff->el[1 + total + div]))
2050 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2051 isl_mat_col_mul(qp->div, 2 + total + div,
2052 qp->div->ctx->negone, 2 + total + div);
2053 }
2054
2055 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2056 * in the interval [0, d-1], with d the denominator and such that the
2057 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2058 *
2059 * After the reduction, some divs may have become redundant or identical,
2060 * so we call substitute_non_divs and sort_divs. If these functions
2061 * eliminate divs of merge * two or more divs into one, the coefficients
2062 * of the enclosing divs may have to be reduced again, so we call
2063 * ourselves recursively if the number of divs decreases.
2064 */
2065 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2066 {
2067 int i, j;
2068 isl_vec *aff = NULL;
2069 struct isl_upoly *s;
2070 unsigned n_div;
2071
2072 if (!qp)
2073 return NULL;
2074
2075 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2076 aff = isl_vec_clr(aff);
2077 if (!aff)
2078 goto error;
2079
2080 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2081
2082 for (i = 0; i < qp->div->n_row; ++i) {
2083 normalize_div(qp, i);
2084 reduce_div(qp, i, aff);
2085 if (needs_invert(qp->div, i)) {
2086 invert_div(qp, i, aff);
2087 reduce_div(qp, i, aff);
2088 }
2089 }
2090
2091 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2092 qp->div->ctx->one, aff->size);
2093 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2094 isl_upoly_free(s);
2095 if (!qp->upoly)
2096 goto error;
2097
2098 isl_vec_free(aff);
2099
2100 n_div = qp->div->n_row;
2101 qp = substitute_non_divs(qp);
2102 qp = sort_divs(qp);
2103 if (qp && qp->div->n_row < n_div)
2104 return reduce_divs(qp);
2105
2106 return qp;
2107 error:
2108 isl_qpolynomial_free(qp);
2109 isl_vec_free(aff);
2110 return NULL;
2111 }
2112
2113 /* Assumes each div only depends on earlier divs.
2114 */
2115 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2116 int power)
2117 {
2118 struct isl_qpolynomial *qp = NULL;
2119 struct isl_upoly_rec *rec;
2120 struct isl_upoly_cst *cst;
2121 int i, d;
2122 int pos;
2123
2124 if (!div)
2125 return NULL;
2126
2127 d = div->line - div->bmap->div;
2128
2129 pos = isl_dim_total(div->bmap->dim) + d;
2130 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2131 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2132 div->bmap->n_div, &rec->up);
2133 if (!qp)
2134 goto error;
2135
2136 for (i = 0; i < div->bmap->n_div; ++i)
2137 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2138
2139 for (i = 0; i < 1 + power; ++i) {
2140 rec->p[i] = isl_upoly_zero(div->ctx);
2141 if (!rec->p[i])
2142 goto error;
2143 rec->n++;
2144 }
2145 cst = isl_upoly_as_cst(rec->p[power]);
2146 isl_int_set_si(cst->n, 1);
2147
2148 isl_div_free(div);
2149
2150 qp = reduce_divs(qp);
2151
2152 return qp;
2153 error:
2154 isl_qpolynomial_free(qp);
2155 isl_div_free(div);
2156 return NULL;
2157 }
2158
2159 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2160 {
2161 return isl_qpolynomial_div_pow(div, 1);
2162 }
2163
2164 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2165 const isl_int n, const isl_int d)
2166 {
2167 struct isl_qpolynomial *qp;
2168 struct isl_upoly_cst *cst;
2169
2170 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2171 if (!qp)
2172 return NULL;
2173
2174 cst = isl_upoly_as_cst(qp->upoly);
2175 isl_int_set(cst->n, n);
2176 isl_int_set(cst->d, d);
2177
2178 return qp;
2179 }
2180
2181 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2182 {
2183 struct isl_upoly_rec *rec;
2184 int i;
2185
2186 if (!up)
2187 return -1;
2188
2189 if (isl_upoly_is_cst(up))
2190 return 0;
2191
2192 if (up->var < d)
2193 active[up->var] = 1;
2194
2195 rec = isl_upoly_as_rec(up);
2196 for (i = 0; i < rec->n; ++i)
2197 if (up_set_active(rec->p[i], active, d) < 0)
2198 return -1;
2199
2200 return 0;
2201 }
2202
2203 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2204 {
2205 int i, j;
2206 int d = isl_dim_total(qp->dim);
2207
2208 if (!qp || !active)
2209 return -1;
2210
2211 for (i = 0; i < d; ++i)
2212 for (j = 0; j < qp->div->n_row; ++j) {
2213 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2214 continue;
2215 active[i] = 1;
2216 break;
2217 }
2218
2219 return up_set_active(qp->upoly, active, d);
2220 }
2221
2222 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2223 enum isl_dim_type type, unsigned first, unsigned n)
2224 {
2225 int i;
2226 int *active = NULL;
2227 int involves = 0;
2228
2229 if (!qp)
2230 return -1;
2231 if (n == 0)
2232 return 0;
2233
2234 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2235 return -1);
2236 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2237 type == isl_dim_set, return -1);
2238
2239 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
2240 if (set_active(qp, active) < 0)
2241 goto error;
2242
2243 if (type == isl_dim_set)
2244 first += isl_dim_size(qp->dim, isl_dim_param);
2245 for (i = 0; i < n; ++i)
2246 if (active[first + i]) {
2247 involves = 1;
2248 break;
2249 }
2250
2251 free(active);
2252
2253 return involves;
2254 error:
2255 free(active);
2256 return -1;
2257 }
2258
2259 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2260 unsigned first, unsigned n)
2261 {
2262 int i;
2263 struct isl_upoly_rec *rec;
2264
2265 if (!up)
2266 return NULL;
2267 if (n == 0 || up->var < 0 || up->var < first)
2268 return up;
2269 if (up->var < first + n) {
2270 up = replace_by_constant_term(up);
2271 return isl_upoly_drop(up, first, n);
2272 }
2273 up = isl_upoly_cow(up);
2274 if (!up)
2275 return NULL;
2276 up->var -= n;
2277 rec = isl_upoly_as_rec(up);
2278 if (!rec)
2279 goto error;
2280
2281 for (i = 0; i < rec->n; ++i) {
2282 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2283 if (!rec->p[i])
2284 goto error;
2285 }
2286
2287 return up;
2288 error:
2289 isl_upoly_free(up);
2290 return NULL;
2291 }
2292
2293 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2294 __isl_take isl_qpolynomial *qp,
2295 enum isl_dim_type type, unsigned pos, const char *s)
2296 {
2297 qp = isl_qpolynomial_cow(qp);
2298 if (!qp)
2299 return NULL;
2300 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2301 if (!qp->dim)
2302 goto error;
2303 return qp;
2304 error:
2305 isl_qpolynomial_free(qp);
2306 return NULL;
2307 }
2308
2309 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2310 __isl_take isl_qpolynomial *qp,
2311 enum isl_dim_type type, unsigned first, unsigned n)
2312 {
2313 if (!qp)
2314 return NULL;
2315 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2316 return qp;
2317
2318 qp = isl_qpolynomial_cow(qp);
2319 if (!qp)
2320 return NULL;
2321
2322 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2323 goto error);
2324 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2325 type == isl_dim_set, goto error);
2326
2327 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2328 if (!qp->dim)
2329 goto error;
2330
2331 if (type == isl_dim_set)
2332 first += isl_dim_size(qp->dim, isl_dim_param);
2333
2334 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2335 if (!qp->div)
2336 goto error;
2337
2338 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2339 if (!qp->upoly)
2340 goto error;
2341
2342 return qp;
2343 error:
2344 isl_qpolynomial_free(qp);
2345 return NULL;
2346 }
2347
2348 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2349 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2350 {
2351 int i, j, k;
2352 isl_int denom;
2353 unsigned total;
2354 unsigned n_div;
2355 struct isl_upoly *up;
2356
2357 if (!eq)
2358 goto error;
2359 if (eq->n_eq == 0) {
2360 isl_basic_set_free(eq);
2361 return qp;
2362 }
2363
2364 qp = isl_qpolynomial_cow(qp);
2365 if (!qp)
2366 goto error;
2367 qp->div = isl_mat_cow(qp->div);
2368 if (!qp->div)
2369 goto error;
2370
2371 total = 1 + isl_dim_total(eq->dim);
2372 n_div = eq->n_div;
2373 isl_int_init(denom);
2374 for (i = 0; i < eq->n_eq; ++i) {
2375 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2376 if (j < 0 || j == 0 || j >= total)
2377 continue;
2378
2379 for (k = 0; k < qp->div->n_row; ++k) {
2380 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2381 continue;
2382 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2383 &qp->div->row[k][0]);
2384 normalize_div(qp, k);
2385 }
2386
2387 if (isl_int_is_pos(eq->eq[i][j]))
2388 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2389 isl_int_abs(denom, eq->eq[i][j]);
2390 isl_int_set_si(eq->eq[i][j], 0);
2391
2392 up = isl_upoly_from_affine(qp->dim->ctx,
2393 eq->eq[i], denom, total);
2394 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2395 isl_upoly_free(up);
2396 }
2397 isl_int_clear(denom);
2398
2399 if (!qp->upoly)
2400 goto error;
2401
2402 isl_basic_set_free(eq);
2403
2404 qp = substitute_non_divs(qp);
2405 qp = sort_divs(qp);
2406
2407 return qp;
2408 error:
2409 isl_basic_set_free(eq);
2410 isl_qpolynomial_free(qp);
2411 return NULL;
2412 }
2413
2414 static __isl_give isl_basic_set *add_div_constraints(
2415 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2416 {
2417 int i;
2418 unsigned total;
2419
2420 if (!bset || !div)
2421 goto error;
2422
2423 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2424 if (!bset)
2425 goto error;
2426 total = isl_basic_set_total_dim(bset);
2427 for (i = 0; i < div->n_row; ++i)
2428 if (isl_basic_set_add_div_constraints_var(bset,
2429 total - div->n_row + i, div->row[i]) < 0)
2430 goto error;
2431
2432 isl_mat_free(div);
2433 return bset;
2434 error:
2435 isl_mat_free(div);
2436 isl_basic_set_free(bset);
2437 return NULL;
2438 }
2439
2440 /* Look for equalities among the variables shared by context and qp
2441 * and the integer divisions of qp, if any.
2442 * The equalities are then used to eliminate variables and/or integer
2443 * divisions from qp.
2444 */
2445 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2446 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2447 {
2448 isl_basic_set *aff;
2449
2450 if (!qp)
2451 goto error;
2452 if (qp->div->n_row > 0) {
2453 isl_basic_set *bset;
2454 context = isl_set_add_dims(context, isl_dim_set,
2455 qp->div->n_row);
2456 bset = isl_basic_set_universe(isl_set_get_dim(context));
2457 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2458 context = isl_set_intersect(context,
2459 isl_set_from_basic_set(bset));
2460 }
2461
2462 aff = isl_set_affine_hull(context);
2463 return isl_qpolynomial_substitute_equalities(qp, aff);
2464 error:
2465 isl_qpolynomial_free(qp);
2466 isl_set_free(context);
2467 return NULL;
2468 }
2469
2470 #undef PW
2471 #define PW isl_pw_qpolynomial
2472 #undef EL
2473 #define EL isl_qpolynomial
2474 #undef IS_ZERO
2475 #define IS_ZERO is_zero
2476 #undef FIELD
2477 #define FIELD qp
2478
2479 #include <isl_pw_templ.c>
2480
2481 #undef UNION
2482 #define UNION isl_union_pw_qpolynomial
2483 #undef PART
2484 #define PART isl_pw_qpolynomial
2485 #undef PARTS
2486 #define PARTS pw_qpolynomial
2487
2488 #include <isl_union_templ.c>
2489
2490 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2491 {
2492 if (!pwqp)
2493 return -1;
2494
2495 if (pwqp->n != -1)
2496 return 0;
2497
2498 if (!isl_set_fast_is_universe(pwqp->p[0].set))
2499 return 0;
2500
2501 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2502 }
2503
2504 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2505 __isl_take isl_pw_qpolynomial *pwqp1,
2506 __isl_take isl_pw_qpolynomial *pwqp2)
2507 {
2508 int i, j, n;
2509 struct isl_pw_qpolynomial *res;
2510 isl_set *set;
2511
2512 if (!pwqp1 || !pwqp2)
2513 goto error;
2514
2515 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2516 goto error);
2517
2518 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2519 isl_pw_qpolynomial_free(pwqp2);
2520 return pwqp1;
2521 }
2522
2523 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2524 isl_pw_qpolynomial_free(pwqp1);
2525 return pwqp2;
2526 }
2527
2528 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2529 isl_pw_qpolynomial_free(pwqp1);
2530 return pwqp2;
2531 }
2532
2533 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2534 isl_pw_qpolynomial_free(pwqp2);
2535 return pwqp1;
2536 }
2537
2538 n = pwqp1->n * pwqp2->n;
2539 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2540
2541 for (i = 0; i < pwqp1->n; ++i) {
2542 for (j = 0; j < pwqp2->n; ++j) {
2543 struct isl_set *common;
2544 struct isl_qpolynomial *prod;
2545 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2546 isl_set_copy(pwqp2->p[j].set));
2547 if (isl_set_fast_is_empty(common)) {
2548 isl_set_free(common);
2549 continue;
2550 }
2551
2552 prod = isl_qpolynomial_mul(
2553 isl_qpolynomial_copy(pwqp1->p[i].qp),
2554 isl_qpolynomial_copy(pwqp2->p[j].qp));
2555
2556 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2557 }
2558 }
2559
2560 isl_pw_qpolynomial_free(pwqp1);
2561 isl_pw_qpolynomial_free(pwqp2);
2562
2563 return res;
2564 error:
2565 isl_pw_qpolynomial_free(pwqp1);
2566 isl_pw_qpolynomial_free(pwqp2);
2567 return NULL;
2568 }
2569
2570 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2571 __isl_take isl_pw_qpolynomial *pwqp)
2572 {
2573 int i;
2574
2575 if (!pwqp)
2576 return NULL;
2577
2578 if (isl_pw_qpolynomial_is_zero(pwqp))
2579 return pwqp;
2580
2581 pwqp = isl_pw_qpolynomial_cow(pwqp);
2582 if (!pwqp)
2583 return NULL;
2584
2585 for (i = 0; i < pwqp->n; ++i) {
2586 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2587 if (!pwqp->p[i].qp)
2588 goto error;
2589 }
2590
2591 return pwqp;
2592 error:
2593 isl_pw_qpolynomial_free(pwqp);
2594 return NULL;
2595 }
2596
2597 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2598 __isl_take isl_pw_qpolynomial *pwqp1,
2599 __isl_take isl_pw_qpolynomial *pwqp2)
2600 {
2601 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2602 }
2603
2604 __isl_give struct isl_upoly *isl_upoly_eval(
2605 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2606 {
2607 int i;
2608 struct isl_upoly_rec *rec;
2609 struct isl_upoly *res;
2610 struct isl_upoly *base;
2611
2612 if (isl_upoly_is_cst(up)) {
2613 isl_vec_free(vec);
2614 return up;
2615 }
2616
2617 rec = isl_upoly_as_rec(up);
2618 if (!rec)
2619 goto error;
2620
2621 isl_assert(up->ctx, rec->n >= 1, goto error);
2622
2623 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2624
2625 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2626 isl_vec_copy(vec));
2627
2628 for (i = rec->n - 2; i >= 0; --i) {
2629 res = isl_upoly_mul(res, isl_upoly_copy(base));
2630 res = isl_upoly_sum(res,
2631 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2632 isl_vec_copy(vec)));
2633 }
2634
2635 isl_upoly_free(base);
2636 isl_upoly_free(up);
2637 isl_vec_free(vec);
2638 return res;
2639 error:
2640 isl_upoly_free(up);
2641 isl_vec_free(vec);
2642 return NULL;
2643 }
2644
2645 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2646 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2647 {
2648 isl_vec *ext;
2649 struct isl_upoly *up;
2650 isl_dim *dim;
2651
2652 if (!qp || !pnt)
2653 goto error;
2654 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2655
2656 if (qp->div->n_row == 0)
2657 ext = isl_vec_copy(pnt->vec);
2658 else {
2659 int i;
2660 unsigned dim = isl_dim_total(qp->dim);
2661 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2662 if (!ext)
2663 goto error;
2664
2665 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2666 for (i = 0; i < qp->div->n_row; ++i) {
2667 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2668 1 + dim + i, &ext->el[1+dim+i]);
2669 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2670 qp->div->row[i][0]);
2671 }
2672 }
2673
2674 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2675 if (!up)
2676 goto error;
2677
2678 dim = isl_dim_copy(qp->dim);
2679 isl_qpolynomial_free(qp);
2680 isl_point_free(pnt);
2681
2682 return isl_qpolynomial_alloc(dim, 0, up);
2683 error:
2684 isl_qpolynomial_free(qp);
2685 isl_point_free(pnt);
2686 return NULL;
2687 }
2688
2689 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2690 __isl_keep struct isl_upoly_cst *cst2)
2691 {
2692 int cmp;
2693 isl_int t;
2694 isl_int_init(t);
2695 isl_int_mul(t, cst1->n, cst2->d);
2696 isl_int_submul(t, cst2->n, cst1->d);
2697 cmp = isl_int_sgn(t);
2698 isl_int_clear(t);
2699 return cmp;
2700 }
2701
2702 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2703 __isl_keep isl_qpolynomial *qp2)
2704 {
2705 struct isl_upoly_cst *cst1, *cst2;
2706
2707 if (!qp1 || !qp2)
2708 return -1;
2709 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2710 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2711 if (isl_qpolynomial_is_nan(qp1))
2712 return -1;
2713 if (isl_qpolynomial_is_nan(qp2))
2714 return -1;
2715 cst1 = isl_upoly_as_cst(qp1->upoly);
2716 cst2 = isl_upoly_as_cst(qp2->upoly);
2717
2718 return isl_upoly_cmp(cst1, cst2) <= 0;
2719 }
2720
2721 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2722 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2723 {
2724 struct isl_upoly_cst *cst1, *cst2;
2725 int cmp;
2726
2727 if (!qp1 || !qp2)
2728 goto error;
2729 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2730 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2731 cst1 = isl_upoly_as_cst(qp1->upoly);
2732 cst2 = isl_upoly_as_cst(qp2->upoly);
2733 cmp = isl_upoly_cmp(cst1, cst2);
2734
2735 if (cmp <= 0) {
2736 isl_qpolynomial_free(qp2);
2737 } else {
2738 isl_qpolynomial_free(qp1);
2739 qp1 = qp2;
2740 }
2741 return qp1;
2742 error:
2743 isl_qpolynomial_free(qp1);
2744 isl_qpolynomial_free(qp2);
2745 return NULL;
2746 }
2747
2748 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2749 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2750 {
2751 struct isl_upoly_cst *cst1, *cst2;
2752 int cmp;
2753
2754 if (!qp1 || !qp2)
2755 goto error;
2756 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2757 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2758 cst1 = isl_upoly_as_cst(qp1->upoly);
2759 cst2 = isl_upoly_as_cst(qp2->upoly);
2760 cmp = isl_upoly_cmp(cst1, cst2);
2761
2762 if (cmp >= 0) {
2763 isl_qpolynomial_free(qp2);
2764 } else {
2765 isl_qpolynomial_free(qp1);
2766 qp1 = qp2;
2767 }
2768 return qp1;
2769 error:
2770 isl_qpolynomial_free(qp1);
2771 isl_qpolynomial_free(qp2);
2772 return NULL;
2773 }
2774
2775 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2776 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2777 unsigned first, unsigned n)
2778 {
2779 unsigned total;
2780 unsigned g_pos;
2781 int *exp;
2782
2783 if (n == 0)
2784 return qp;
2785
2786 qp = isl_qpolynomial_cow(qp);
2787 if (!qp)
2788 return NULL;
2789
2790 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2791 goto error);
2792
2793 g_pos = pos(qp->dim, type) + first;
2794
2795 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2796 if (!qp->div)
2797 goto error;
2798
2799 total = qp->div->n_col - 2;
2800 if (total > g_pos) {
2801 int i;
2802 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2803 if (!exp)
2804 goto error;
2805 for (i = 0; i < total - g_pos; ++i)
2806 exp[i] = i + n;
2807 qp->upoly = expand(qp->upoly, exp, g_pos);
2808 free(exp);
2809 if (!qp->upoly)
2810 goto error;
2811 }
2812
2813 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2814 if (!qp->dim)
2815 goto error;
2816
2817 return qp;
2818 error:
2819 isl_qpolynomial_free(qp);
2820 return NULL;
2821 }
2822
2823 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2824 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2825 {
2826 unsigned pos;
2827
2828 pos = isl_qpolynomial_dim(qp, type);
2829
2830 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2831 }
2832
2833 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2834 __isl_take isl_pw_qpolynomial *pwqp,
2835 enum isl_dim_type type, unsigned n)
2836 {
2837 unsigned pos;
2838
2839 pos = isl_pw_qpolynomial_dim(pwqp, type);
2840
2841 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2842 }
2843
2844 static int *reordering_move(isl_ctx *ctx,
2845 unsigned len, unsigned dst, unsigned src, unsigned n)
2846 {
2847 int i;
2848 int *reordering;
2849
2850 reordering = isl_alloc_array(ctx, int, len);
2851 if (!reordering)
2852 return NULL;
2853
2854 if (dst <= src) {
2855 for (i = 0; i < dst; ++i)
2856 reordering[i] = i;
2857 for (i = 0; i < n; ++i)
2858 reordering[src + i] = dst + i;
2859 for (i = 0; i < src - dst; ++i)
2860 reordering[dst + i] = dst + n + i;
2861 for (i = 0; i < len - src - n; ++i)
2862 reordering[src + n + i] = src + n + i;
2863 } else {
2864 for (i = 0; i < src; ++i)
2865 reordering[i] = i;
2866 for (i = 0; i < n; ++i)
2867 reordering[src + i] = dst + i;
2868 for (i = 0; i < dst - src; ++i)
2869 reordering[src + n + i] = src + i;
2870 for (i = 0; i < len - dst - n; ++i)
2871 reordering[dst + n + i] = dst + n + i;
2872 }
2873
2874 return reordering;
2875 }
2876
2877 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2878 __isl_take isl_qpolynomial *qp,
2879 enum isl_dim_type dst_type, unsigned dst_pos,
2880 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2881 {
2882 unsigned g_dst_pos;
2883 unsigned g_src_pos;
2884 int *reordering;
2885
2886 qp = isl_qpolynomial_cow(qp);
2887 if (!qp)
2888 return NULL;
2889
2890 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2891 goto error);
2892
2893 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2894 g_src_pos = pos(qp->dim, src_type) + src_pos;
2895 if (dst_type > src_type)
2896 g_dst_pos -= n;
2897
2898 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2899 if (!qp->div)
2900 goto error;
2901 qp = sort_divs(qp);
2902 if (!qp)
2903 goto error;
2904
2905 reordering = reordering_move(qp->dim->ctx,
2906 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2907 if (!reordering)
2908 goto error;
2909
2910 qp->upoly = reorder(qp->upoly, reordering);
2911 free(reordering);
2912 if (!qp->upoly)
2913 goto error;
2914
2915 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2916 if (!qp->dim)
2917 goto error;
2918
2919 return qp;
2920 error:
2921 isl_qpolynomial_free(qp);
2922 return NULL;
2923 }
2924
2925 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2926 isl_int *f, isl_int denom)
2927 {
2928 struct isl_upoly *up;
2929
2930 if (!dim)
2931 return NULL;
2932
2933 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2934
2935 return isl_qpolynomial_alloc(dim, 0, up);
2936 }
2937
2938 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2939 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2940 {
2941 isl_int denom;
2942 isl_dim *dim;
2943 struct isl_upoly *up;
2944 isl_qpolynomial *qp;
2945 int sgn;
2946
2947 if (!c)
2948 return NULL;
2949
2950 isl_int_init(denom);
2951
2952 isl_constraint_get_coefficient(c, type, pos, &denom);
2953 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2954 sgn = isl_int_sgn(denom);
2955 isl_int_abs(denom, denom);
2956 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2957 1 + isl_constraint_dim(c, isl_dim_all));
2958 if (sgn < 0)
2959 isl_int_neg(denom, denom);
2960 isl_constraint_set_coefficient(c, type, pos, denom);
2961
2962 dim = isl_dim_copy(c->bmap->dim);
2963
2964 isl_int_clear(denom);
2965 isl_constraint_free(c);
2966
2967 qp = isl_qpolynomial_alloc(dim, 0, up);
2968 if (sgn > 0)
2969 qp = isl_qpolynomial_neg(qp);
2970 return qp;
2971 }
2972
2973 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2974 * in "qp" by subs[i].
2975 */
2976 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2977 __isl_take isl_qpolynomial *qp,
2978 enum isl_dim_type type, unsigned first, unsigned n,
2979 __isl_keep isl_qpolynomial **subs)
2980 {
2981 int i;
2982 struct isl_upoly **ups;
2983
2984 if (n == 0)
2985 return qp;
2986
2987 qp = isl_qpolynomial_cow(qp);
2988 if (!qp)
2989 return NULL;
2990 for (i = 0; i < n; ++i)
2991 if (!subs[i])
2992 goto error;
2993
2994 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2995 goto error);
2996
2997 for (i = 0; i < n; ++i)
2998 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2999 goto error);
3000
3001 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3002 for (i = 0; i < n; ++i)
3003 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3004
3005 first += pos(qp->dim, type);
3006
3007 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3008 if (!ups)
3009 goto error;
3010 for (i = 0; i < n; ++i)
3011 ups[i] = subs[i]->upoly;
3012
3013 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3014
3015 free(ups);
3016
3017 if (!qp->upoly)
3018 goto error;
3019
3020 return qp;
3021 error:
3022 isl_qpolynomial_free(qp);
3023 return NULL;
3024 }
3025
3026 /* Extend "bset" with extra set dimensions for each integer division
3027 * in "qp" and then call "fn" with the extended bset and the polynomial
3028 * that results from replacing each of the integer divisions by the
3029 * corresponding extra set dimension.
3030 */
3031 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3032 __isl_keep isl_basic_set *bset,
3033 int (*fn)(__isl_take isl_basic_set *bset,
3034 __isl_take isl_qpolynomial *poly, void *user), void *user)
3035 {
3036 isl_dim *dim;
3037 isl_mat *div;
3038 isl_qpolynomial *poly;
3039
3040 if (!qp || !bset)
3041 goto error;
3042 if (qp->div->n_row == 0)
3043 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3044 user);
3045
3046 div = isl_mat_copy(qp->div);
3047 dim = isl_dim_copy(qp->dim);
3048 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3049 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3050 bset = isl_basic_set_copy(bset);
3051 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3052 bset = add_div_constraints(bset, div);
3053
3054 return fn(bset, poly, user);
3055 error:
3056 return -1;
3057 }
3058
3059 /* Return total degree in variables first (inclusive) up to last (exclusive).
3060 */
3061 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3062 {
3063 int deg = -1;
3064 int i;
3065 struct isl_upoly_rec *rec;
3066
3067 if (!up)
3068 return -2;
3069 if (isl_upoly_is_zero(up))
3070 return -1;
3071 if (isl_upoly_is_cst(up) || up->var < first)
3072 return 0;
3073
3074 rec = isl_upoly_as_rec(up);
3075 if (!rec)
3076 return -2;
3077
3078 for (i = 0; i < rec->n; ++i) {
3079 int d;
3080
3081 if (isl_upoly_is_zero(rec->p[i]))
3082 continue;
3083 d = isl_upoly_degree(rec->p[i], first, last);
3084 if (up->var < last)
3085 d += i;
3086 if (d > deg)
3087 deg = d;
3088 }
3089
3090 return deg;
3091 }
3092
3093 /* Return total degree in set variables.
3094 */
3095 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3096 {
3097 unsigned ovar;
3098 unsigned nvar;
3099
3100 if (!poly)
3101 return -2;
3102
3103 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3104 nvar = isl_dim_size(poly->dim, isl_dim_set);
3105 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3106 }
3107
3108 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3109 unsigned pos, int deg)
3110 {
3111 int i;
3112 struct isl_upoly_rec *rec;
3113
3114 if (!up)
3115 return NULL;
3116
3117 if (isl_upoly_is_cst(up) || up->var < pos) {
3118 if (deg == 0)
3119 return isl_upoly_copy(up);
3120 else
3121 return isl_upoly_zero(up->ctx);
3122 }
3123
3124 rec = isl_upoly_as_rec(up);
3125 if (!rec)
3126 return NULL;
3127
3128 if (up->var == pos) {
3129 if (deg < rec->n)
3130 return isl_upoly_copy(rec->p[deg]);
3131 else
3132 return isl_upoly_zero(up->ctx);
3133 }
3134
3135 up = isl_upoly_copy(up);
3136 up = isl_upoly_cow(up);
3137 rec = isl_upoly_as_rec(up);
3138 if (!rec)
3139 goto error;
3140
3141 for (i = 0; i < rec->n; ++i) {
3142 struct isl_upoly *t;
3143 t = isl_upoly_coeff(rec->p[i], pos, deg);
3144 if (!t)
3145 goto error;
3146 isl_upoly_free(rec->p[i]);
3147 rec->p[i] = t;
3148 }
3149
3150 return up;
3151 error:
3152 isl_upoly_free(up);
3153 return NULL;
3154 }
3155
3156 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3157 */
3158 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3159 __isl_keep isl_qpolynomial *qp,
3160 enum isl_dim_type type, unsigned t_pos, int deg)
3161 {
3162 unsigned g_pos;
3163 struct isl_upoly *up;
3164 isl_qpolynomial *c;
3165
3166 if (!qp)
3167 return NULL;
3168
3169 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3170 return NULL);
3171
3172 g_pos = pos(qp->dim, type) + t_pos;
3173 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3174
3175 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3176 if (!c)
3177 return NULL;
3178 isl_mat_free(c->div);
3179 c->div = isl_mat_copy(qp->div);
3180 if (!c->div)
3181 goto error;
3182 return c;
3183 error:
3184 isl_qpolynomial_free(c);
3185 return NULL;
3186 }
3187
3188 /* Homogenize the polynomial in the variables first (inclusive) up to
3189 * last (exclusive) by inserting powers of variable first.
3190 * Variable first is assumed not to appear in the input.
3191 */
3192 __isl_give struct isl_upoly *isl_upoly_homogenize(
3193 __isl_take struct isl_upoly *up, int deg, int target,
3194 int first, int last)
3195 {
3196 int i;
3197 struct isl_upoly_rec *rec;
3198
3199 if (!up)
3200 return NULL;
3201 if (isl_upoly_is_zero(up))
3202 return up;
3203 if (deg == target)
3204 return up;
3205 if (isl_upoly_is_cst(up) || up->var < first) {
3206 struct isl_upoly *hom;
3207
3208 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3209 if (!hom)
3210 goto error;
3211 rec = isl_upoly_as_rec(hom);
3212 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3213
3214 return hom;
3215 }
3216
3217 up = isl_upoly_cow(up);
3218 rec = isl_upoly_as_rec(up);
3219 if (!rec)
3220 goto error;
3221
3222 for (i = 0; i < rec->n; ++i) {
3223 if (isl_upoly_is_zero(rec->p[i]))
3224 continue;
3225 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3226 up->var < last ? deg + i : i, target,
3227 first, last);
3228 if (!rec->p[i])
3229 goto error;
3230 }
3231
3232 return up;
3233 error:
3234 isl_upoly_free(up);
3235 return NULL;
3236 }
3237
3238 /* Homogenize the polynomial in the set variables by introducing
3239 * powers of an extra set variable at position 0.
3240 */
3241 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3242 __isl_take isl_qpolynomial *poly)
3243 {
3244 unsigned ovar;
3245 unsigned nvar;
3246 int deg = isl_qpolynomial_degree(poly);
3247
3248 if (deg < -1)
3249 goto error;
3250
3251 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3252 poly = isl_qpolynomial_cow(poly);
3253 if (!poly)
3254 goto error;
3255
3256 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3257 nvar = isl_dim_size(poly->dim, isl_dim_set);
3258 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3259 ovar, ovar + nvar);
3260 if (!poly->upoly)
3261 goto error;
3262
3263 return poly;
3264 error:
3265 isl_qpolynomial_free(poly);
3266 return NULL;
3267 }
3268
3269 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3270 __isl_take isl_mat *div)
3271 {
3272 isl_term *term;
3273 int n;
3274
3275 if (!dim || !div)
3276 goto error;
3277
3278 n = isl_dim_total(dim) + div->n_row;
3279
3280 term = isl_calloc(dim->ctx, struct isl_term,
3281 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3282 if (!term)
3283 goto error;
3284
3285 term->ref = 1;
3286 term->dim = dim;
3287 term->div = div;
3288 isl_int_init(term->n);
3289 isl_int_init(term->d);
3290
3291 return term;
3292 error:
3293 isl_dim_free(dim);
3294 isl_mat_free(div);
3295 return NULL;
3296 }
3297
3298 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3299 {
3300 if (!term)
3301 return NULL;
3302
3303 term->ref++;
3304 return term;
3305 }
3306
3307 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3308 {
3309 int i;
3310 isl_term *dup;
3311 unsigned total;
3312
3313 if (term)
3314 return NULL;
3315
3316 total = isl_dim_total(term->dim) + term->div->n_row;
3317
3318 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3319 if (!dup)
3320 return NULL;
3321
3322 isl_int_set(dup->n, term->n);
3323 isl_int_set(dup->d, term->d);
3324
3325 for (i = 0; i < total; ++i)
3326 dup->pow[i] = term->pow[i];
3327
3328 return dup;
3329 }
3330
3331 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3332 {
3333 if (!term)
3334 return NULL;
3335
3336 if (term->ref == 1)
3337 return term;
3338 term->ref--;
3339 return isl_term_dup(term);
3340 }
3341
3342 void isl_term_free(__isl_take isl_term *term)
3343 {
3344 if (!term)
3345 return;
3346
3347 if (--term->ref > 0)
3348 return;
3349
3350 isl_dim_free(term->dim);
3351 isl_mat_free(term->div);
3352 isl_int_clear(term->n);
3353 isl_int_clear(term->d);
3354 free(term);
3355 }
3356
3357 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3358 {
3359 if (!term)
3360 return 0;
3361
3362 switch (type) {
3363 case isl_dim_param:
3364 case isl_dim_in:
3365 case isl_dim_out: return isl_dim_size(term->dim, type);
3366 case isl_dim_div: return term->div->n_row;
3367 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3368 default: return 0;
3369 }
3370 }
3371
3372 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3373 {
3374 return term ? term->dim->ctx : NULL;
3375 }
3376
3377 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3378 {
3379 if (!term)
3380 return;
3381 isl_int_set(*n, term->n);
3382 }
3383
3384 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3385 {
3386 if (!term)
3387 return;
3388 isl_int_set(*d, term->d);
3389 }
3390
3391 int isl_term_get_exp(__isl_keep isl_term *term,
3392 enum isl_dim_type type, unsigned pos)
3393 {
3394 if (!term)
3395 return -1;
3396
3397 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3398
3399 if (type >= isl_dim_set)
3400 pos += isl_dim_size(term->dim, isl_dim_param);
3401 if (type >= isl_dim_div)
3402 pos += isl_dim_size(term->dim, isl_dim_set);
3403
3404 return term->pow[pos];
3405 }
3406
3407 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3408 {
3409 isl_basic_map *bmap;
3410 unsigned total;
3411 int k;
3412
3413 if (!term)
3414 return NULL;
3415
3416 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3417 return NULL);
3418
3419 total = term->div->n_col - term->div->n_row - 2;
3420 /* No nested divs for now */
3421 isl_assert(term->dim->ctx,
3422 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3423 term->div->n_row) == -1,
3424 return NULL);
3425
3426 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3427 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3428 goto error;
3429
3430 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3431
3432 return isl_basic_map_div(bmap, k);
3433 error:
3434 isl_basic_map_free(bmap);
3435 return NULL;
3436 }
3437
3438 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3439 int (*fn)(__isl_take isl_term *term, void *user),
3440 __isl_take isl_term *term, void *user)
3441 {
3442 int i;
3443 struct isl_upoly_rec *rec;
3444
3445 if (!up || !term)
3446 goto error;
3447
3448 if (isl_upoly_is_zero(up))
3449 return term;
3450
3451 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3452 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3453 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3454
3455 if (isl_upoly_is_cst(up)) {
3456 struct isl_upoly_cst *cst;
3457 cst = isl_upoly_as_cst(up);
3458 if (!cst)
3459 goto error;
3460 term = isl_term_cow(term);
3461 if (!term)
3462 goto error;
3463 isl_int_set(term->n, cst->n);
3464 isl_int_set(term->d, cst->d);
3465 if (fn(isl_term_copy(term), user) < 0)
3466 goto error;
3467 return term;
3468 }
3469
3470 rec = isl_upoly_as_rec(up);
3471 if (!rec)
3472 goto error;
3473
3474 for (i = 0; i < rec->n; ++i) {
3475 term = isl_term_cow(term);
3476 if (!term)
3477 goto error;
3478 term->pow[up->var] = i;
3479 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3480 if (!term)
3481 goto error;
3482 }
3483 term->pow[up->var] = 0;
3484
3485 return term;
3486 error:
3487 isl_term_free(term);
3488 return NULL;
3489 }
3490
3491 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3492 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3493 {
3494 isl_term *term;
3495
3496 if (!qp)
3497 return -1;
3498
3499 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3500 if (!term)
3501 return -1;
3502
3503 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3504
3505 isl_term_free(term);
3506
3507 return term ? 0 : -1;
3508 }
3509
3510 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3511 {
3512 struct isl_upoly *up;
3513 isl_qpolynomial *qp;
3514 int i, n;
3515
3516 if (!term)
3517 return NULL;
3518
3519 n = isl_dim_total(term->dim) + term->div->n_row;
3520
3521 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3522 for (i = 0; i < n; ++i) {
3523 if (!term->pow[i])
3524 continue;
3525 up = isl_upoly_mul(up,
3526 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3527 }
3528
3529 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3530 if (!qp)
3531 goto error;
3532 isl_mat_free(qp->div);
3533 qp->div = isl_mat_copy(term->div);
3534 if (!qp->div)
3535 goto error;
3536
3537 isl_term_free(term);
3538 return qp;
3539 error:
3540 isl_qpolynomial_free(qp);
3541 isl_term_free(term);
3542 return NULL;
3543 }
3544
3545 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3546 __isl_take isl_dim *dim)
3547 {
3548 int i;
3549 int extra;
3550 unsigned total;
3551
3552 if (!qp || !dim)
3553 goto error;
3554
3555 if (isl_dim_equal(qp->dim, dim)) {
3556 isl_dim_free(dim);
3557 return qp;
3558 }
3559
3560 qp = isl_qpolynomial_cow(qp);
3561 if (!qp)
3562 goto error;
3563
3564 extra = isl_dim_size(dim, isl_dim_set) -
3565 isl_dim_size(qp->dim, isl_dim_set);
3566 total = isl_dim_total(qp->dim);
3567 if (qp->div->n_row) {
3568 int *exp;
3569
3570 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3571 if (!exp)
3572 goto error;
3573 for (i = 0; i < qp->div->n_row; ++i)
3574 exp[i] = extra + i;
3575 qp->upoly = expand(qp->upoly, exp, total);
3576 free(exp);
3577 if (!qp->upoly)
3578 goto error;
3579 }
3580 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3581 if (!qp->div)
3582 goto error;
3583 for (i = 0; i < qp->div->n_row; ++i)
3584 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3585
3586 isl_dim_free(qp->dim);
3587 qp->dim = dim;
3588
3589 return qp;
3590 error:
3591 isl_dim_free(dim);
3592 isl_qpolynomial_free(qp);
3593 return NULL;
3594 }
3595
3596 /* For each parameter or variable that does not appear in qp,
3597 * first eliminate the variable from all constraints and then set it to zero.
3598 */
3599 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3600 __isl_keep isl_qpolynomial *qp)
3601 {
3602 int *active = NULL;
3603 int i;
3604 int d;
3605 unsigned nparam;
3606 unsigned nvar;
3607
3608 if (!set || !qp)
3609 goto error;
3610
3611 d = isl_dim_total(set->dim);
3612 active = isl_calloc_array(set->ctx, int, d);
3613 if (set_active(qp, active) < 0)
3614 goto error;
3615
3616 for (i = 0; i < d; ++i)
3617 if (!active[i])
3618 break;
3619
3620 if (i == d) {
3621 free(active);
3622 return set;
3623 }
3624
3625 nparam = isl_dim_size(set->dim, isl_dim_param);
3626 nvar = isl_dim_size(set->dim, isl_dim_set);
3627 for (i = 0; i < nparam; ++i) {
3628 if (active[i])
3629 continue;
3630 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3631 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3632 }
3633 for (i = 0; i < nvar; ++i) {
3634 if (active[nparam + i])
3635 continue;
3636 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3637 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3638 }
3639
3640 free(active);
3641
3642 return set;
3643 error:
3644 free(active);
3645 isl_set_free(set);
3646 return NULL;
3647 }
3648
3649 struct isl_opt_data {
3650 isl_qpolynomial *qp;
3651 int first;
3652 isl_qpolynomial *opt;
3653 int max;
3654 };
3655
3656 static int opt_fn(__isl_take isl_point *pnt, void *user)
3657 {
3658 struct isl_opt_data *data = (struct isl_opt_data *)user;
3659 isl_qpolynomial *val;
3660
3661 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3662 if (data->first) {
3663 data->first = 0;
3664 data->opt = val;
3665 } else if (data->max) {
3666 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3667 } else {
3668 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3669 }
3670
3671 return 0;
3672 }
3673
3674 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3675 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3676 {
3677 struct isl_opt_data data = { NULL, 1, NULL, max };
3678
3679 if (!set || !qp)
3680 goto error;
3681
3682 if (isl_upoly_is_cst(qp->upoly)) {
3683 isl_set_free(set);
3684 return qp;
3685 }
3686
3687 set = fix_inactive(set, qp);
3688
3689 data.qp = qp;
3690 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3691 goto error;
3692
3693 if (data.first)
3694 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3695
3696 isl_set_free(set);
3697 isl_qpolynomial_free(qp);
3698 return data.opt;
3699 error:
3700 isl_set_free(set);
3701 isl_qpolynomial_free(qp);
3702 isl_qpolynomial_free(data.opt);
3703 return NULL;
3704 }
3705
3706 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3707 __isl_take isl_morph *morph)
3708 {
3709 int i;
3710 int n_sub;
3711 isl_ctx *ctx;
3712 struct isl_upoly *up;
3713 unsigned n_div;
3714 struct isl_upoly **subs;
3715 isl_mat *mat;
3716
3717 qp = isl_qpolynomial_cow(qp);
3718 if (!qp || !morph)
3719 goto error;
3720
3721 ctx = qp->dim->ctx;
3722 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3723
3724 n_sub = morph->inv->n_row - 1;
3725 if (morph->inv->n_row != morph->inv->n_col)
3726 n_sub += qp->div->n_row;
3727 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3728 if (!subs)
3729 goto error;
3730
3731 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3732 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3733 morph->inv->row[0][0], morph->inv->n_col);
3734 if (morph->inv->n_row != morph->inv->n_col)
3735 for (i = 0; i < qp->div->n_row; ++i)
3736 subs[morph->inv->n_row - 1 + i] =
3737 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3738
3739 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3740
3741 for (i = 0; i < n_sub; ++i)
3742 isl_upoly_free(subs[i]);
3743 free(subs);
3744
3745 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3746 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3747 qp->div = isl_mat_product(qp->div, mat);
3748 isl_dim_free(qp->dim);
3749 qp->dim = isl_dim_copy(morph->ran->dim);
3750
3751 if (!qp->upoly || !qp->div || !qp->dim)
3752 goto error;
3753
3754 isl_morph_free(morph);
3755
3756 return qp;
3757 error:
3758 isl_qpolynomial_free(qp);
3759 isl_morph_free(morph);
3760 return NULL;
3761 }
3762
3763 static int neg_entry(void **entry, void *user)
3764 {
3765 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3766
3767 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3768
3769 return *pwqp ? 0 : -1;
3770 }
3771
3772 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3773 __isl_take isl_union_pw_qpolynomial *upwqp)
3774 {
3775 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3776 if (!upwqp)
3777 return NULL;
3778
3779 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3780 &neg_entry, NULL) < 0)
3781 goto error;
3782
3783 return upwqp;
3784 error:
3785 isl_union_pw_qpolynomial_free(upwqp);
3786 return NULL;
3787 }
3788
3789 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3790 __isl_take isl_union_pw_qpolynomial *upwqp1,
3791 __isl_take isl_union_pw_qpolynomial *upwqp2)
3792 {
3793 return isl_union_pw_qpolynomial_add(upwqp1,
3794 isl_union_pw_qpolynomial_neg(upwqp2));
3795 }
3796
3797 static int mul_entry(void **entry, void *user)
3798 {
3799 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3800 uint32_t hash;
3801 struct isl_hash_table_entry *entry2;
3802 isl_pw_qpolynomial *pwpq = *entry;
3803 int empty;
3804
3805 hash = isl_dim_get_hash(pwpq->dim);
3806 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3807 hash, &has_dim, pwpq->dim, 0);
3808 if (!entry2)
3809 return 0;
3810
3811 pwpq = isl_pw_qpolynomial_copy(pwpq);
3812 pwpq = isl_pw_qpolynomial_mul(pwpq,
3813 isl_pw_qpolynomial_copy(entry2->data));
3814
3815 empty = isl_pw_qpolynomial_is_zero(pwpq);
3816 if (empty < 0) {
3817 isl_pw_qpolynomial_free(pwpq);
3818 return -1;
3819 }
3820 if (empty) {
3821 isl_pw_qpolynomial_free(pwpq);
3822 return 0;
3823 }
3824
3825 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3826
3827 return 0;
3828 }
3829
3830 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3831 __isl_take isl_union_pw_qpolynomial *upwqp1,
3832 __isl_take isl_union_pw_qpolynomial *upwqp2)
3833 {
3834 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3835 }
3836
3837 /* Reorder the columns of the given div definitions according to the
3838 * given reordering.
3839 */
3840 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3841 __isl_take isl_reordering *r)
3842 {
3843 int i, j;
3844 isl_mat *mat;
3845 int extra;
3846
3847 if (!div || !r)
3848 goto error;
3849
3850 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3851 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3852 if (!mat)
3853 goto error;
3854
3855 for (i = 0; i < div->n_row; ++i) {
3856 isl_seq_cpy(mat->row[i], div->row[i], 2);
3857 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3858 for (j = 0; j < r->len; ++j)
3859 isl_int_set(mat->row[i][2 + r->pos[j]],
3860 div->row[i][2 + j]);
3861 }
3862
3863 isl_reordering_free(r);
3864 isl_mat_free(div);
3865 return mat;
3866 error:
3867 isl_reordering_free(r);
3868 isl_mat_free(div);
3869 return NULL;
3870 }
3871
3872 /* Reorder the dimension of "qp" according to the given reordering.
3873 */
3874 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3875 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3876 {
3877 qp = isl_qpolynomial_cow(qp);
3878 if (!qp)
3879 goto error;
3880
3881 r = isl_reordering_extend(r, qp->div->n_row);
3882 if (!r)
3883 goto error;
3884
3885 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3886 if (!qp->div)
3887 goto error;
3888
3889 qp->upoly = reorder(qp->upoly, r->pos);
3890 if (!qp->upoly)
3891 goto error;
3892
3893 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3894
3895 isl_reordering_free(r);
3896 return qp;
3897 error:
3898 isl_qpolynomial_free(qp);
3899 isl_reordering_free(r);
3900 return NULL;
3901 }
3902
3903 struct isl_split_periods_data {
3904 int max_periods;
3905 isl_pw_qpolynomial *res;
3906 };
3907
3908 /* Create a slice where the integer division "div" has the fixed value "v".
3909 * In particular, if "div" refers to floor(f/m), then create a slice
3910 *
3911 * m v <= f <= m v + (m - 1)
3912 *
3913 * or
3914 *
3915 * f - m v >= 0
3916 * -f + m v + (m - 1) >= 0
3917 */
3918 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3919 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3920 {
3921 int total;
3922 isl_basic_set *bset = NULL;
3923 int k;
3924
3925 if (!dim || !qp)
3926 goto error;
3927
3928 total = isl_dim_total(dim);
3929 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3930
3931 k = isl_basic_set_alloc_inequality(bset);
3932 if (k < 0)
3933 goto error;
3934 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3935 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3936
3937 k = isl_basic_set_alloc_inequality(bset);
3938 if (k < 0)
3939 goto error;
3940 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3941 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3942 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3943 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3944
3945 isl_dim_free(dim);
3946 return isl_set_from_basic_set(bset);
3947 error:
3948 isl_basic_set_free(bset);
3949 isl_dim_free(dim);
3950 return NULL;
3951 }
3952
3953 static int split_periods(__isl_take isl_set *set,
3954 __isl_take isl_qpolynomial *qp, void *user);
3955
3956 /* Create a slice of the domain "set" such that integer division "div"
3957 * has the fixed value "v" and add the results to data->res,
3958 * replacing the integer division by "v" in "qp".
3959 */
3960 static int set_div(__isl_take isl_set *set,
3961 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3962 struct isl_split_periods_data *data)
3963 {
3964 int i;
3965 int total;
3966 isl_set *slice;
3967 struct isl_upoly *cst;
3968
3969 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3970 set = isl_set_intersect(set, slice);
3971
3972 if (!qp)
3973 goto error;
3974
3975 total = isl_dim_total(qp->dim);
3976
3977 for (i = div + 1; i < qp->div->n_row; ++i) {
3978 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
3979 continue;
3980 isl_int_addmul(qp->div->row[i][1],
3981 qp->div->row[i][2 + total + div], v);
3982 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
3983 }
3984
3985 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3986 qp = substitute_div(qp, div, cst);
3987
3988 return split_periods(set, qp, data);
3989 error:
3990 isl_set_free(set);
3991 isl_qpolynomial_free(qp);
3992 return -1;
3993 }
3994
3995 /* Split the domain "set" such that integer division "div"
3996 * has a fixed value (ranging from "min" to "max") on each slice
3997 * and add the results to data->res.
3998 */
3999 static int split_div(__isl_take isl_set *set,
4000 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4001 struct isl_split_periods_data *data)
4002 {
4003 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4004 isl_set *set_i = isl_set_copy(set);
4005 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4006
4007 if (set_div(set_i, qp_i, div, min, data) < 0)
4008 goto error;
4009 }
4010 isl_set_free(set);
4011 isl_qpolynomial_free(qp);
4012 return 0;
4013 error:
4014 isl_set_free(set);
4015 isl_qpolynomial_free(qp);
4016 return -1;
4017 }
4018
4019 /* If "qp" refers to any integer division
4020 * that can only attain "max_periods" distinct values on "set"
4021 * then split the domain along those distinct values.
4022 * Add the results (or the original if no splitting occurs)
4023 * to data->res.
4024 */
4025 static int split_periods(__isl_take isl_set *set,
4026 __isl_take isl_qpolynomial *qp, void *user)
4027 {
4028 int i;
4029 isl_pw_qpolynomial *pwqp;
4030 struct isl_split_periods_data *data;
4031 isl_int min, max;
4032 int total;
4033 int r = 0;
4034
4035 data = (struct isl_split_periods_data *)user;
4036
4037 if (!set || !qp)
4038 goto error;
4039
4040 if (qp->div->n_row == 0) {
4041 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4042 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4043 return 0;
4044 }
4045
4046 isl_int_init(min);
4047 isl_int_init(max);
4048 total = isl_dim_total(qp->dim);
4049 for (i = 0; i < qp->div->n_row; ++i) {
4050 enum isl_lp_result lp_res;
4051
4052 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4053 qp->div->n_row) != -1)
4054 continue;
4055
4056 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4057 set->ctx->one, &min, NULL, NULL);
4058 if (lp_res == isl_lp_error)
4059 goto error2;
4060 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4061 continue;
4062 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4063
4064 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4065 set->ctx->one, &max, NULL, NULL);
4066 if (lp_res == isl_lp_error)
4067 goto error2;
4068 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4069 continue;
4070 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4071
4072 isl_int_sub(max, max, min);
4073 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4074 isl_int_add(max, max, min);
4075 break;
4076 }
4077 }
4078
4079 if (i < qp->div->n_row) {
4080 r = split_div(set, qp, i, min, max, data);
4081 } else {
4082 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4083 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4084 }
4085
4086 isl_int_clear(max);
4087 isl_int_clear(min);
4088
4089 return r;
4090 error2:
4091 isl_int_clear(max);
4092 isl_int_clear(min);
4093 error:
4094 isl_set_free(set);
4095 isl_qpolynomial_free(qp);
4096 return -1;
4097 }
4098
4099 /* If any quasi-polynomial in pwqp refers to any integer division
4100 * that can only attain "max_periods" distinct values on its domain
4101 * then split the domain along those distinct values.
4102 */
4103 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4104 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4105 {
4106 struct isl_split_periods_data data;
4107
4108 data.max_periods = max_periods;
4109 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4110
4111 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4112 goto error;
4113
4114 isl_pw_qpolynomial_free(pwqp);
4115
4116 return data.res;
4117 error:
4118 isl_pw_qpolynomial_free(data.res);
4119 isl_pw_qpolynomial_free(pwqp);
4120 return NULL;
4121 }
4122
4123 /* Construct a piecewise quasipolynomial that is constant on the given
4124 * domain. In particular, it is
4125 * 0 if cst == 0
4126 * 1 if cst == 1
4127 * infinity if cst == -1
4128 */
4129 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4130 __isl_take isl_basic_set *bset, int cst)
4131 {
4132 isl_dim *dim;
4133 isl_qpolynomial *qp;
4134
4135 if (!bset)
4136 return NULL;
4137
4138 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4139 dim = isl_basic_set_get_dim(bset);
4140 if (cst < 0)
4141 qp = isl_qpolynomial_infty(dim);
4142 else if (cst == 0)
4143 qp = isl_qpolynomial_zero(dim);
4144 else
4145 qp = isl_qpolynomial_one(dim);
4146 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4147 }
4148
4149 /* Factor bset, call fn on each of the factors and return the product.
4150 *
4151 * If no factors can be found, simply call fn on the input.
4152 * Otherwise, construct the factors based on the factorizer,
4153 * call fn on each factor and compute the product.
4154 */
4155 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4156 __isl_take isl_basic_set *bset,
4157 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4158 {
4159 int i, n;
4160 isl_dim *dim;
4161 isl_set *set;
4162 isl_factorizer *f;
4163 isl_qpolynomial *qp;
4164 isl_pw_qpolynomial *pwqp;
4165 unsigned nparam;
4166 unsigned nvar;
4167
4168 f = isl_basic_set_factorizer(bset);
4169 if (!f)
4170 goto error;
4171 if (f->n_group == 0) {
4172 isl_factorizer_free(f);
4173 return fn(bset);
4174 }
4175
4176 nparam = isl_basic_set_dim(bset, isl_dim_param);
4177 nvar = isl_basic_set_dim(bset, isl_dim_set);
4178
4179 dim = isl_basic_set_get_dim(bset);
4180 dim = isl_dim_domain(dim);
4181 set = isl_set_universe(isl_dim_copy(dim));
4182 qp = isl_qpolynomial_one(dim);
4183 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4184
4185 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4186
4187 for (i = 0, n = 0; i < f->n_group; ++i) {
4188 isl_basic_set *bset_i;
4189 isl_pw_qpolynomial *pwqp_i;
4190
4191 bset_i = isl_basic_set_copy(bset);
4192 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4193 nparam + n + f->len[i], nvar - n - f->len[i]);
4194 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4195 nparam, n);
4196 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4197 n + f->len[i], nvar - n - f->len[i]);
4198 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4199
4200 pwqp_i = fn(bset_i);
4201 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4202
4203 n += f->len[i];
4204 }
4205
4206 isl_basic_set_free(bset);
4207 isl_factorizer_free(f);
4208
4209 return pwqp;
4210 error:
4211 isl_basic_set_free(bset);
4212 return NULL;
4213 }
4214
4215 /* Factor bset, call fn on each of the factors and return the product.
4216 * The function is assumed to evaluate to zero on empty domains,
4217 * to one on zero-dimensional domains and to infinity on unbounded domains
4218 * and will not be called explicitly on zero-dimensional or unbounded domains.
4219 *
4220 * We first check for some special cases and remove all equalities.
4221 * Then we hand over control to compressed_multiplicative_call.
4222 */
4223 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4224 __isl_take isl_basic_set *bset,
4225 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4226 {
4227 int bounded;
4228 isl_morph *morph;
4229 isl_pw_qpolynomial *pwqp;
4230 unsigned orig_nvar, final_nvar;
4231
4232 if (!bset)
4233 return NULL;
4234
4235 if (isl_basic_set_fast_is_empty(bset))
4236 return constant_on_domain(bset, 0);
4237
4238 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4239
4240 if (orig_nvar == 0)
4241 return constant_on_domain(bset, 1);
4242
4243 bounded = isl_basic_set_is_bounded(bset);
4244 if (bounded < 0)
4245 goto error;
4246 if (!bounded)
4247 return constant_on_domain(bset, -1);
4248
4249 if (bset->n_eq == 0)
4250 return compressed_multiplicative_call(bset, fn);
4251
4252 morph = isl_basic_set_full_compression(bset);
4253 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4254
4255 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4256
4257 pwqp = compressed_multiplicative_call(bset, fn);
4258
4259 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4260 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4261 morph = isl_morph_inverse(morph);
4262
4263 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4264
4265 return pwqp;
4266 error:
4267 isl_basic_set_free(bset);
4268 return NULL;
4269 }
4270
4271 /* Drop all floors in "qp", turning each integer division [a/m] into
4272 * a rational division a/m. If "down" is set, then the integer division
4273 * is replaces by (a-(m-1))/m instead.
4274 */
4275 static __isl_give isl_qpolynomial *qp_drop_floors(
4276 __isl_take isl_qpolynomial *qp, int down)
4277 {
4278 int i;
4279 struct isl_upoly *s;
4280
4281 if (!qp)
4282 return NULL;
4283 if (qp->div->n_row == 0)
4284 return qp;
4285
4286 qp = isl_qpolynomial_cow(qp);
4287 if (!qp)
4288 return NULL;
4289
4290 for (i = qp->div->n_row - 1; i >= 0; --i) {
4291 if (down) {
4292 isl_int_sub(qp->div->row[i][1],
4293 qp->div->row[i][1], qp->div->row[i][0]);
4294 isl_int_add_ui(qp->div->row[i][1],
4295 qp->div->row[i][1], 1);
4296 }
4297 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4298 qp->div->row[i][0], qp->div->n_col - 1);
4299 qp = substitute_div(qp, i, s);
4300 if (!qp)
4301 return NULL;
4302 }
4303
4304 return qp;
4305 }
4306
4307 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4308 * a rational division a/m.
4309 */
4310 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4311 __isl_take isl_pw_qpolynomial *pwqp)
4312 {
4313 int i;
4314
4315 if (!pwqp)
4316 return NULL;
4317
4318 if (isl_pw_qpolynomial_is_zero(pwqp))
4319 return pwqp;
4320
4321 pwqp = isl_pw_qpolynomial_cow(pwqp);
4322 if (!pwqp)
4323 return NULL;
4324
4325 for (i = 0; i < pwqp->n; ++i) {
4326 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4327 if (!pwqp->p[i].qp)
4328 goto error;
4329 }
4330
4331 return pwqp;
4332 error:
4333 isl_pw_qpolynomial_free(pwqp);
4334 return NULL;
4335 }
4336
4337 /* Adjust all the integer divisions in "qp" such that they are at least
4338 * one over the given orthant (identified by "signs"). This ensures
4339 * that they will still be non-negative even after subtracting (m-1)/m.
4340 *
4341 * In particular, f is replaced by f' + v, changing f = [a/m]
4342 * to f' = [(a - m v)/m].
4343 * If the constant term k in a is smaller than m,
4344 * the constant term of v is set to floor(k/m) - 1.
4345 * For any other term, if the coefficient c and the variable x have
4346 * the same sign, then no changes are needed.
4347 * Otherwise, if the variable is positive (and c is negative),
4348 * then the coefficient of x in v is set to floor(c/m).
4349 * If the variable is negative (and c is positive),
4350 * then the coefficient of x in v is set to ceil(c/m).
4351 */
4352 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4353 int *signs)
4354 {
4355 int i, j;
4356 int total;
4357 isl_vec *v = NULL;
4358 struct isl_upoly *s;
4359
4360 qp = isl_qpolynomial_cow(qp);
4361 if (!qp)
4362 return NULL;
4363 qp->div = isl_mat_cow(qp->div);
4364 if (!qp->div)
4365 goto error;
4366
4367 total = isl_dim_total(qp->dim);
4368 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4369
4370 for (i = 0; i < qp->div->n_row; ++i) {
4371 isl_int *row = qp->div->row[i];
4372 v = isl_vec_clr(v);
4373 if (!v)
4374 goto error;
4375 if (isl_int_lt(row[1], row[0])) {
4376 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4377 isl_int_sub_ui(v->el[0], v->el[0], 1);
4378 isl_int_submul(row[1], row[0], v->el[0]);
4379 }
4380 for (j = 0; j < total; ++j) {
4381 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4382 continue;
4383 if (signs[j] < 0)
4384 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4385 else
4386 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4387 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4388 }
4389 for (j = 0; j < i; ++j) {
4390 if (isl_int_sgn(row[2 + total + j]) >= 0)
4391 continue;
4392 isl_int_fdiv_q(v->el[1 + total + j],
4393 row[2 + total + j], row[0]);
4394 isl_int_submul(row[2 + total + j],
4395 row[0], v->el[1 + total + j]);
4396 }
4397 for (j = i + 1; j < qp->div->n_row; ++j) {
4398 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4399 continue;
4400 isl_seq_combine(qp->div->row[j] + 1,
4401 qp->div->ctx->one, qp->div->row[j] + 1,
4402 qp->div->row[j][2 + total + i], v->el, v->size);
4403 }
4404 isl_int_set_si(v->el[1 + total + i], 1);
4405 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4406 qp->div->ctx->one, v->size);
4407 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4408 isl_upoly_free(s);
4409 if (!qp->upoly)
4410 goto error;
4411 }
4412
4413 isl_vec_free(v);
4414 return qp;
4415 error:
4416 isl_vec_free(v);
4417 isl_qpolynomial_free(qp);
4418 return NULL;
4419 }
4420
4421 struct isl_to_poly_data {
4422 int sign;
4423 isl_pw_qpolynomial *res;
4424 isl_qpolynomial *qp;
4425 };
4426
4427 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4428 * We first make all integer divisions positive and then split the
4429 * quasipolynomials into terms with sign data->sign (the direction
4430 * of the requested approximation) and terms with the opposite sign.
4431 * In the first set of terms, each integer division [a/m] is
4432 * overapproximated by a/m, while in the second it is underapproximated
4433 * by (a-(m-1))/m.
4434 */
4435 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4436 void *user)
4437 {
4438 struct isl_to_poly_data *data = user;
4439 isl_pw_qpolynomial *t;
4440 isl_qpolynomial *qp, *up, *down;
4441
4442 qp = isl_qpolynomial_copy(data->qp);
4443 qp = make_divs_pos(qp, signs);
4444
4445 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4446 up = qp_drop_floors(up, 0);
4447 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4448 down = qp_drop_floors(down, 1);
4449
4450 isl_qpolynomial_free(qp);
4451 qp = isl_qpolynomial_add(up, down);
4452
4453 t = isl_pw_qpolynomial_alloc(orthant, qp);
4454 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4455
4456 return 0;
4457 }
4458
4459 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4460 * the polynomial will be an overapproximation. If "sign" is negative,
4461 * it will be an underapproximation. If "sign" is zero, the approximation
4462 * will lie somewhere in between.
4463 *
4464 * In particular, is sign == 0, we simply drop the floors, turning
4465 * the integer divisions into rational divisions.
4466 * Otherwise, we split the domains into orthants, make all integer divisions
4467 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4468 * depending on the requested sign and the sign of the term in which
4469 * the integer division appears.
4470 */
4471 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4472 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4473 {
4474 int i;
4475 struct isl_to_poly_data data;
4476
4477 if (sign == 0)
4478 return pwqp_drop_floors(pwqp);
4479
4480 if (!pwqp)
4481 return NULL;
4482
4483 data.sign = sign;
4484 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4485
4486 for (i = 0; i < pwqp->n; ++i) {
4487 if (pwqp->p[i].qp->div->n_row == 0) {
4488 isl_pw_qpolynomial *t;
4489 t = isl_pw_qpolynomial_alloc(
4490 isl_set_copy(pwqp->p[i].set),
4491 isl_qpolynomial_copy(pwqp->p[i].qp));
4492 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4493 continue;
4494 }
4495 data.qp = pwqp->p[i].qp;
4496 if (isl_set_foreach_orthant(pwqp->p[i].set,
4497 &to_polynomial_on_orthant, &data) < 0)
4498 goto error;
4499 }
4500
4501 isl_pw_qpolynomial_free(pwqp);
4502
4503 return data.res;
4504 error:
4505 isl_pw_qpolynomial_free(pwqp);
4506 isl_pw_qpolynomial_free(data.res);
4507 return NULL;
4508 }
4509
4510 static int poly_entry(void **entry, void *user)
4511 {
4512 int *sign = user;
4513 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4514
4515 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4516
4517 return *pwqp ? 0 : -1;
4518 }
4519
4520 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4521 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4522 {
4523 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4524 if (!upwqp)
4525 return NULL;
4526
4527 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4528 &poly_entry, &sign) < 0)
4529 goto error;
4530
4531 return upwqp;
4532 error:
4533 isl_union_pw_qpolynomial_free(upwqp);
4534 return NULL;
4535 }
4536
4537 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4538 __isl_take isl_qpolynomial *qp)
4539 {
4540 int i, k;
4541 isl_dim *dim;
4542 isl_vec *aff = NULL;
4543 isl_basic_map *bmap = NULL;
4544 unsigned pos;
4545 unsigned n_div;
4546
4547 if (!qp)
4548 return NULL;
4549 if (!isl_upoly_is_affine(qp->upoly))
4550 isl_die(qp->dim->ctx, isl_error_invalid,
4551 "input quasi-polynomial not affine", goto error);
4552 aff = isl_qpolynomial_extract_affine(qp);
4553 if (!aff)
4554 goto error;
4555 dim = isl_qpolynomial_get_dim(qp);
4556 dim = isl_dim_from_domain(dim);
4557 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4558 dim = isl_dim_add(dim, isl_dim_out, 1);
4559 n_div = qp->div->n_row;
4560 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4561
4562 for (i = 0; i < n_div; ++i) {
4563 k = isl_basic_map_alloc_div(bmap);
4564 if (k < 0)
4565 goto error;
4566 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4567 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4568 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4569 goto error;
4570 }
4571 k = isl_basic_map_alloc_equality(bmap);
4572 if (k < 0)
4573 goto error;
4574 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4575 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4576 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4577
4578 isl_vec_free(aff);
4579 isl_qpolynomial_free(qp);
4580 bmap = isl_basic_map_finalize(bmap);
4581 return bmap;
4582 error:
4583 isl_vec_free(aff);
4584 isl_qpolynomial_free(qp);
4585 isl_basic_map_free(bmap);
4586 return NULL;
4587 }
Integer set library