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add isl_mat_diag
[isl.git] / isl_polynomial.c
blob7e486a6f4f5668838d8988ae9f295cf9fb5e40ce
1 /*
2 * Copyright 2010 INRIA Saclay
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
8 * 91893 Orsay, France
9 */
10
11 #include <stdlib.h>
12 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl_factorization.h>
15 #include <isl/lp.h>
16 #include <isl/seq.h>
17 #include <isl_union_map_private.h>
18 #include <isl_constraint_private.h>
19 #include <isl_polynomial_private.h>
20 #include <isl_point_private.h>
21 #include <isl_dim_private.h>
22 #include <isl_div_private.h>
23 #include <isl_mat_private.h>
24 #include <isl_range.h>
25 #include <isl_local_space_private.h>
26 #include <isl_aff_private.h>
27 #include <isl_config.h>
28
29 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
30 {
31 switch (type) {
32 case isl_dim_param: return 0;
33 case isl_dim_in: return dim->nparam;
34 case isl_dim_out: return dim->nparam + dim->n_in;
35 default: return 0;
36 }
37 }
38
39 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
40 {
41 if (!up)
42 return -1;
43
44 return up->var < 0;
45 }
46
47 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
48 {
49 if (!up)
50 return NULL;
51
52 isl_assert(up->ctx, up->var < 0, return NULL);
53
54 return (struct isl_upoly_cst *)up;
55 }
56
57 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
58 {
59 if (!up)
60 return NULL;
61
62 isl_assert(up->ctx, up->var >= 0, return NULL);
63
64 return (struct isl_upoly_rec *)up;
65 }
66
67 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
68 __isl_keep struct isl_upoly *up2)
69 {
70 int i;
71 struct isl_upoly_rec *rec1, *rec2;
72
73 if (!up1 || !up2)
74 return -1;
75 if (up1 == up2)
76 return 1;
77 if (up1->var != up2->var)
78 return 0;
79 if (isl_upoly_is_cst(up1)) {
80 struct isl_upoly_cst *cst1, *cst2;
81 cst1 = isl_upoly_as_cst(up1);
82 cst2 = isl_upoly_as_cst(up2);
83 if (!cst1 || !cst2)
84 return -1;
85 return isl_int_eq(cst1->n, cst2->n) &&
86 isl_int_eq(cst1->d, cst2->d);
87 }
88
89 rec1 = isl_upoly_as_rec(up1);
90 rec2 = isl_upoly_as_rec(up2);
91 if (!rec1 || !rec2)
92 return -1;
93
94 if (rec1->n != rec2->n)
95 return 0;
96
97 for (i = 0; i < rec1->n; ++i) {
98 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
99 if (eq < 0 || !eq)
100 return eq;
101 }
102
103 return 1;
104 }
105
106 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
107 {
108 struct isl_upoly_cst *cst;
109
110 if (!up)
111 return -1;
112 if (!isl_upoly_is_cst(up))
113 return 0;
114
115 cst = isl_upoly_as_cst(up);
116 if (!cst)
117 return -1;
118
119 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
120 }
121
122 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
123 {
124 struct isl_upoly_cst *cst;
125
126 if (!up)
127 return 0;
128 if (!isl_upoly_is_cst(up))
129 return 0;
130
131 cst = isl_upoly_as_cst(up);
132 if (!cst)
133 return 0;
134
135 return isl_int_sgn(cst->n);
136 }
137
138 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
139 {
140 struct isl_upoly_cst *cst;
141
142 if (!up)
143 return -1;
144 if (!isl_upoly_is_cst(up))
145 return 0;
146
147 cst = isl_upoly_as_cst(up);
148 if (!cst)
149 return -1;
150
151 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
152 }
153
154 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
155 {
156 struct isl_upoly_cst *cst;
157
158 if (!up)
159 return -1;
160 if (!isl_upoly_is_cst(up))
161 return 0;
162
163 cst = isl_upoly_as_cst(up);
164 if (!cst)
165 return -1;
166
167 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
168 }
169
170 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
171 {
172 struct isl_upoly_cst *cst;
173
174 if (!up)
175 return -1;
176 if (!isl_upoly_is_cst(up))
177 return 0;
178
179 cst = isl_upoly_as_cst(up);
180 if (!cst)
181 return -1;
182
183 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
184 }
185
186 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
187 {
188 struct isl_upoly_cst *cst;
189
190 if (!up)
191 return -1;
192 if (!isl_upoly_is_cst(up))
193 return 0;
194
195 cst = isl_upoly_as_cst(up);
196 if (!cst)
197 return -1;
198
199 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
200 }
201
202 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
203 {
204 struct isl_upoly_cst *cst;
205
206 if (!up)
207 return -1;
208 if (!isl_upoly_is_cst(up))
209 return 0;
210
211 cst = isl_upoly_as_cst(up);
212 if (!cst)
213 return -1;
214
215 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
216 }
217
218 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
219 {
220 struct isl_upoly_cst *cst;
221
222 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
223 if (!cst)
224 return NULL;
225
226 cst->up.ref = 1;
227 cst->up.ctx = ctx;
228 isl_ctx_ref(ctx);
229 cst->up.var = -1;
230
231 isl_int_init(cst->n);
232 isl_int_init(cst->d);
233
234 return cst;
235 }
236
237 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
238 {
239 struct isl_upoly_cst *cst;
240
241 cst = isl_upoly_cst_alloc(ctx);
242 if (!cst)
243 return NULL;
244
245 isl_int_set_si(cst->n, 0);
246 isl_int_set_si(cst->d, 1);
247
248 return &cst->up;
249 }
250
251 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
252 {
253 struct isl_upoly_cst *cst;
254
255 cst = isl_upoly_cst_alloc(ctx);
256 if (!cst)
257 return NULL;
258
259 isl_int_set_si(cst->n, 1);
260 isl_int_set_si(cst->d, 1);
261
262 return &cst->up;
263 }
264
265 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
266 {
267 struct isl_upoly_cst *cst;
268
269 cst = isl_upoly_cst_alloc(ctx);
270 if (!cst)
271 return NULL;
272
273 isl_int_set_si(cst->n, 1);
274 isl_int_set_si(cst->d, 0);
275
276 return &cst->up;
277 }
278
279 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
280 {
281 struct isl_upoly_cst *cst;
282
283 cst = isl_upoly_cst_alloc(ctx);
284 if (!cst)
285 return NULL;
286
287 isl_int_set_si(cst->n, -1);
288 isl_int_set_si(cst->d, 0);
289
290 return &cst->up;
291 }
292
293 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
294 {
295 struct isl_upoly_cst *cst;
296
297 cst = isl_upoly_cst_alloc(ctx);
298 if (!cst)
299 return NULL;
300
301 isl_int_set_si(cst->n, 0);
302 isl_int_set_si(cst->d, 0);
303
304 return &cst->up;
305 }
306
307 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
308 isl_int n, isl_int d)
309 {
310 struct isl_upoly_cst *cst;
311
312 cst = isl_upoly_cst_alloc(ctx);
313 if (!cst)
314 return NULL;
315
316 isl_int_set(cst->n, n);
317 isl_int_set(cst->d, d);
318
319 return &cst->up;
320 }
321
322 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
323 int var, int size)
324 {
325 struct isl_upoly_rec *rec;
326
327 isl_assert(ctx, var >= 0, return NULL);
328 isl_assert(ctx, size >= 0, return NULL);
329 rec = isl_calloc(ctx, struct isl_upoly_rec,
330 sizeof(struct isl_upoly_rec) +
331 size * sizeof(struct isl_upoly *));
332 if (!rec)
333 return NULL;
334
335 rec->up.ref = 1;
336 rec->up.ctx = ctx;
337 isl_ctx_ref(ctx);
338 rec->up.var = var;
339
340 rec->n = 0;
341 rec->size = size;
342
343 return rec;
344 }
345
346 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
347 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
348 {
349 qp = isl_qpolynomial_cow(qp);
350 if (!qp || !dim)
351 goto error;
352
353 isl_dim_free(qp->dim);
354 qp->dim = dim;
355
356 return qp;
357 error:
358 isl_qpolynomial_free(qp);
359 isl_dim_free(dim);
360 return NULL;
361 }
362
363 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
364 {
365 return qp ? qp->dim->ctx : NULL;
366 }
367
368 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
369 {
370 return qp ? isl_dim_copy(qp->dim) : NULL;
371 }
372
373 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
374 enum isl_dim_type type)
375 {
376 return qp ? isl_dim_size(qp->dim, type) : 0;
377 }
378
379 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
380 {
381 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
382 }
383
384 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
385 {
386 return qp ? isl_upoly_is_one(qp->upoly) : -1;
387 }
388
389 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
390 {
391 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
392 }
393
394 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
395 {
396 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
397 }
398
399 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
400 {
401 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
402 }
403
404 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
405 {
406 return qp ? isl_upoly_sgn(qp->upoly) : 0;
407 }
408
409 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
410 {
411 isl_int_clear(cst->n);
412 isl_int_clear(cst->d);
413 }
414
415 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
416 {
417 int i;
418
419 for (i = 0; i < rec->n; ++i)
420 isl_upoly_free(rec->p[i]);
421 }
422
423 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
424 {
425 if (!up)
426 return NULL;
427
428 up->ref++;
429 return up;
430 }
431
432 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
433 {
434 struct isl_upoly_cst *cst;
435 struct isl_upoly_cst *dup;
436
437 cst = isl_upoly_as_cst(up);
438 if (!cst)
439 return NULL;
440
441 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
442 if (!dup)
443 return NULL;
444 isl_int_set(dup->n, cst->n);
445 isl_int_set(dup->d, cst->d);
446
447 return &dup->up;
448 }
449
450 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
451 {
452 int i;
453 struct isl_upoly_rec *rec;
454 struct isl_upoly_rec *dup;
455
456 rec = isl_upoly_as_rec(up);
457 if (!rec)
458 return NULL;
459
460 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
461 if (!dup)
462 return NULL;
463
464 for (i = 0; i < rec->n; ++i) {
465 dup->p[i] = isl_upoly_copy(rec->p[i]);
466 if (!dup->p[i])
467 goto error;
468 dup->n++;
469 }
470
471 return &dup->up;
472 error:
473 isl_upoly_free(&dup->up);
474 return NULL;
475 }
476
477 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
478 {
479 if (!up)
480 return NULL;
481
482 if (isl_upoly_is_cst(up))
483 return isl_upoly_dup_cst(up);
484 else
485 return isl_upoly_dup_rec(up);
486 }
487
488 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
489 {
490 if (!up)
491 return NULL;
492
493 if (up->ref == 1)
494 return up;
495 up->ref--;
496 return isl_upoly_dup(up);
497 }
498
499 void isl_upoly_free(__isl_take struct isl_upoly *up)
500 {
501 if (!up)
502 return;
503
504 if (--up->ref > 0)
505 return;
506
507 if (up->var < 0)
508 upoly_free_cst((struct isl_upoly_cst *)up);
509 else
510 upoly_free_rec((struct isl_upoly_rec *)up);
511
512 isl_ctx_deref(up->ctx);
513 free(up);
514 }
515
516 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
517 {
518 isl_int gcd;
519
520 isl_int_init(gcd);
521 isl_int_gcd(gcd, cst->n, cst->d);
522 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
523 isl_int_divexact(cst->n, cst->n, gcd);
524 isl_int_divexact(cst->d, cst->d, gcd);
525 }
526 isl_int_clear(gcd);
527 }
528
529 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
530 __isl_take struct isl_upoly *up2)
531 {
532 struct isl_upoly_cst *cst1;
533 struct isl_upoly_cst *cst2;
534
535 up1 = isl_upoly_cow(up1);
536 if (!up1 || !up2)
537 goto error;
538
539 cst1 = isl_upoly_as_cst(up1);
540 cst2 = isl_upoly_as_cst(up2);
541
542 if (isl_int_eq(cst1->d, cst2->d))
543 isl_int_add(cst1->n, cst1->n, cst2->n);
544 else {
545 isl_int_mul(cst1->n, cst1->n, cst2->d);
546 isl_int_addmul(cst1->n, cst2->n, cst1->d);
547 isl_int_mul(cst1->d, cst1->d, cst2->d);
548 }
549
550 isl_upoly_cst_reduce(cst1);
551
552 isl_upoly_free(up2);
553 return up1;
554 error:
555 isl_upoly_free(up1);
556 isl_upoly_free(up2);
557 return NULL;
558 }
559
560 static __isl_give struct isl_upoly *replace_by_zero(
561 __isl_take struct isl_upoly *up)
562 {
563 struct isl_ctx *ctx;
564
565 if (!up)
566 return NULL;
567 ctx = up->ctx;
568 isl_upoly_free(up);
569 return isl_upoly_zero(ctx);
570 }
571
572 static __isl_give struct isl_upoly *replace_by_constant_term(
573 __isl_take struct isl_upoly *up)
574 {
575 struct isl_upoly_rec *rec;
576 struct isl_upoly *cst;
577
578 if (!up)
579 return NULL;
580
581 rec = isl_upoly_as_rec(up);
582 if (!rec)
583 goto error;
584 cst = isl_upoly_copy(rec->p[0]);
585 isl_upoly_free(up);
586 return cst;
587 error:
588 isl_upoly_free(up);
589 return NULL;
590 }
591
592 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
593 __isl_take struct isl_upoly *up2)
594 {
595 int i;
596 struct isl_upoly_rec *rec1, *rec2;
597
598 if (!up1 || !up2)
599 goto error;
600
601 if (isl_upoly_is_nan(up1)) {
602 isl_upoly_free(up2);
603 return up1;
604 }
605
606 if (isl_upoly_is_nan(up2)) {
607 isl_upoly_free(up1);
608 return up2;
609 }
610
611 if (isl_upoly_is_zero(up1)) {
612 isl_upoly_free(up1);
613 return up2;
614 }
615
616 if (isl_upoly_is_zero(up2)) {
617 isl_upoly_free(up2);
618 return up1;
619 }
620
621 if (up1->var < up2->var)
622 return isl_upoly_sum(up2, up1);
623
624 if (up2->var < up1->var) {
625 struct isl_upoly_rec *rec;
626 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
627 isl_upoly_free(up1);
628 return up2;
629 }
630 up1 = isl_upoly_cow(up1);
631 rec = isl_upoly_as_rec(up1);
632 if (!rec)
633 goto error;
634 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
635 if (rec->n == 1)
636 up1 = replace_by_constant_term(up1);
637 return up1;
638 }
639
640 if (isl_upoly_is_cst(up1))
641 return isl_upoly_sum_cst(up1, up2);
642
643 rec1 = isl_upoly_as_rec(up1);
644 rec2 = isl_upoly_as_rec(up2);
645 if (!rec1 || !rec2)
646 goto error;
647
648 if (rec1->n < rec2->n)
649 return isl_upoly_sum(up2, up1);
650
651 up1 = isl_upoly_cow(up1);
652 rec1 = isl_upoly_as_rec(up1);
653 if (!rec1)
654 goto error;
655
656 for (i = rec2->n - 1; i >= 0; --i) {
657 rec1->p[i] = isl_upoly_sum(rec1->p[i],
658 isl_upoly_copy(rec2->p[i]));
659 if (!rec1->p[i])
660 goto error;
661 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
662 isl_upoly_free(rec1->p[i]);
663 rec1->n--;
664 }
665 }
666
667 if (rec1->n == 0)
668 up1 = replace_by_zero(up1);
669 else if (rec1->n == 1)
670 up1 = replace_by_constant_term(up1);
671
672 isl_upoly_free(up2);
673
674 return up1;
675 error:
676 isl_upoly_free(up1);
677 isl_upoly_free(up2);
678 return NULL;
679 }
680
681 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
682 __isl_take struct isl_upoly *up, isl_int v)
683 {
684 struct isl_upoly_cst *cst;
685
686 up = isl_upoly_cow(up);
687 if (!up)
688 return NULL;
689
690 cst = isl_upoly_as_cst(up);
691
692 isl_int_addmul(cst->n, cst->d, v);
693
694 return up;
695 }
696
697 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
698 __isl_take struct isl_upoly *up, isl_int v)
699 {
700 struct isl_upoly_rec *rec;
701
702 if (!up)
703 return NULL;
704
705 if (isl_upoly_is_cst(up))
706 return isl_upoly_cst_add_isl_int(up, v);
707
708 up = isl_upoly_cow(up);
709 rec = isl_upoly_as_rec(up);
710 if (!rec)
711 goto error;
712
713 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
714 if (!rec->p[0])
715 goto error;
716
717 return up;
718 error:
719 isl_upoly_free(up);
720 return NULL;
721 }
722
723 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
724 __isl_take struct isl_upoly *up, isl_int v)
725 {
726 struct isl_upoly_cst *cst;
727
728 if (isl_upoly_is_zero(up))
729 return up;
730
731 up = isl_upoly_cow(up);
732 if (!up)
733 return NULL;
734
735 cst = isl_upoly_as_cst(up);
736
737 isl_int_mul(cst->n, cst->n, v);
738
739 return up;
740 }
741
742 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
743 __isl_take struct isl_upoly *up, isl_int v)
744 {
745 int i;
746 struct isl_upoly_rec *rec;
747
748 if (!up)
749 return NULL;
750
751 if (isl_upoly_is_cst(up))
752 return isl_upoly_cst_mul_isl_int(up, v);
753
754 up = isl_upoly_cow(up);
755 rec = isl_upoly_as_rec(up);
756 if (!rec)
757 goto error;
758
759 for (i = 0; i < rec->n; ++i) {
760 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
761 if (!rec->p[i])
762 goto error;
763 }
764
765 return up;
766 error:
767 isl_upoly_free(up);
768 return NULL;
769 }
770
771 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
772 __isl_take struct isl_upoly *up2)
773 {
774 struct isl_upoly_cst *cst1;
775 struct isl_upoly_cst *cst2;
776
777 up1 = isl_upoly_cow(up1);
778 if (!up1 || !up2)
779 goto error;
780
781 cst1 = isl_upoly_as_cst(up1);
782 cst2 = isl_upoly_as_cst(up2);
783
784 isl_int_mul(cst1->n, cst1->n, cst2->n);
785 isl_int_mul(cst1->d, cst1->d, cst2->d);
786
787 isl_upoly_cst_reduce(cst1);
788
789 isl_upoly_free(up2);
790 return up1;
791 error:
792 isl_upoly_free(up1);
793 isl_upoly_free(up2);
794 return NULL;
795 }
796
797 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
798 __isl_take struct isl_upoly *up2)
799 {
800 struct isl_upoly_rec *rec1;
801 struct isl_upoly_rec *rec2;
802 struct isl_upoly_rec *res = NULL;
803 int i, j;
804 int size;
805
806 rec1 = isl_upoly_as_rec(up1);
807 rec2 = isl_upoly_as_rec(up2);
808 if (!rec1 || !rec2)
809 goto error;
810 size = rec1->n + rec2->n - 1;
811 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
812 if (!res)
813 goto error;
814
815 for (i = 0; i < rec1->n; ++i) {
816 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
817 isl_upoly_copy(rec1->p[i]));
818 if (!res->p[i])
819 goto error;
820 res->n++;
821 }
822 for (; i < size; ++i) {
823 res->p[i] = isl_upoly_zero(up1->ctx);
824 if (!res->p[i])
825 goto error;
826 res->n++;
827 }
828 for (i = 0; i < rec1->n; ++i) {
829 for (j = 1; j < rec2->n; ++j) {
830 struct isl_upoly *up;
831 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
832 isl_upoly_copy(rec1->p[i]));
833 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
834 if (!res->p[i + j])
835 goto error;
836 }
837 }
838
839 isl_upoly_free(up1);
840 isl_upoly_free(up2);
841
842 return &res->up;
843 error:
844 isl_upoly_free(up1);
845 isl_upoly_free(up2);
846 isl_upoly_free(&res->up);
847 return NULL;
848 }
849
850 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
851 __isl_take struct isl_upoly *up2)
852 {
853 if (!up1 || !up2)
854 goto error;
855
856 if (isl_upoly_is_nan(up1)) {
857 isl_upoly_free(up2);
858 return up1;
859 }
860
861 if (isl_upoly_is_nan(up2)) {
862 isl_upoly_free(up1);
863 return up2;
864 }
865
866 if (isl_upoly_is_zero(up1)) {
867 isl_upoly_free(up2);
868 return up1;
869 }
870
871 if (isl_upoly_is_zero(up2)) {
872 isl_upoly_free(up1);
873 return up2;
874 }
875
876 if (isl_upoly_is_one(up1)) {
877 isl_upoly_free(up1);
878 return up2;
879 }
880
881 if (isl_upoly_is_one(up2)) {
882 isl_upoly_free(up2);
883 return up1;
884 }
885
886 if (up1->var < up2->var)
887 return isl_upoly_mul(up2, up1);
888
889 if (up2->var < up1->var) {
890 int i;
891 struct isl_upoly_rec *rec;
892 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
893 isl_ctx *ctx = up1->ctx;
894 isl_upoly_free(up1);
895 isl_upoly_free(up2);
896 return isl_upoly_nan(ctx);
897 }
898 up1 = isl_upoly_cow(up1);
899 rec = isl_upoly_as_rec(up1);
900 if (!rec)
901 goto error;
902
903 for (i = 0; i < rec->n; ++i) {
904 rec->p[i] = isl_upoly_mul(rec->p[i],
905 isl_upoly_copy(up2));
906 if (!rec->p[i])
907 goto error;
908 }
909 isl_upoly_free(up2);
910 return up1;
911 }
912
913 if (isl_upoly_is_cst(up1))
914 return isl_upoly_mul_cst(up1, up2);
915
916 return isl_upoly_mul_rec(up1, up2);
917 error:
918 isl_upoly_free(up1);
919 isl_upoly_free(up2);
920 return NULL;
921 }
922
923 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
924 unsigned power)
925 {
926 struct isl_upoly *res;
927
928 if (!up)
929 return NULL;
930 if (power == 1)
931 return up;
932
933 if (power % 2)
934 res = isl_upoly_copy(up);
935 else
936 res = isl_upoly_one(up->ctx);
937
938 while (power >>= 1) {
939 up = isl_upoly_mul(up, isl_upoly_copy(up));
940 if (power % 2)
941 res = isl_upoly_mul(res, isl_upoly_copy(up));
942 }
943
944 isl_upoly_free(up);
945 return res;
946 }
947
948 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
949 unsigned n_div, __isl_take struct isl_upoly *up)
950 {
951 struct isl_qpolynomial *qp = NULL;
952 unsigned total;
953
954 if (!dim || !up)
955 goto error;
956
957 total = isl_dim_total(dim);
958
959 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
960 if (!qp)
961 goto error;
962
963 qp->ref = 1;
964 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
965 if (!qp->div)
966 goto error;
967
968 qp->dim = dim;
969 qp->upoly = up;
970
971 return qp;
972 error:
973 isl_dim_free(dim);
974 isl_upoly_free(up);
975 isl_qpolynomial_free(qp);
976 return NULL;
977 }
978
979 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
980 {
981 if (!qp)
982 return NULL;
983
984 qp->ref++;
985 return qp;
986 }
987
988 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
989 {
990 struct isl_qpolynomial *dup;
991
992 if (!qp)
993 return NULL;
994
995 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
996 isl_upoly_copy(qp->upoly));
997 if (!dup)
998 return NULL;
999 isl_mat_free(dup->div);
1000 dup->div = isl_mat_copy(qp->div);
1001 if (!dup->div)
1002 goto error;
1003
1004 return dup;
1005 error:
1006 isl_qpolynomial_free(dup);
1007 return NULL;
1008 }
1009
1010 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1011 {
1012 if (!qp)
1013 return NULL;
1014
1015 if (qp->ref == 1)
1016 return qp;
1017 qp->ref--;
1018 return isl_qpolynomial_dup(qp);
1019 }
1020
1021 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1022 {
1023 if (!qp)
1024 return;
1025
1026 if (--qp->ref > 0)
1027 return;
1028
1029 isl_dim_free(qp->dim);
1030 isl_mat_free(qp->div);
1031 isl_upoly_free(qp->upoly);
1032
1033 free(qp);
1034 }
1035
1036 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1037 {
1038 int i;
1039 struct isl_upoly_rec *rec;
1040 struct isl_upoly_cst *cst;
1041
1042 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1043 if (!rec)
1044 return NULL;
1045 for (i = 0; i < 1 + power; ++i) {
1046 rec->p[i] = isl_upoly_zero(ctx);
1047 if (!rec->p[i])
1048 goto error;
1049 rec->n++;
1050 }
1051 cst = isl_upoly_as_cst(rec->p[power]);
1052 isl_int_set_si(cst->n, 1);
1053
1054 return &rec->up;
1055 error:
1056 isl_upoly_free(&rec->up);
1057 return NULL;
1058 }
1059
1060 /* r array maps original positions to new positions.
1061 */
1062 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1063 int *r)
1064 {
1065 int i;
1066 struct isl_upoly_rec *rec;
1067 struct isl_upoly *base;
1068 struct isl_upoly *res;
1069
1070 if (isl_upoly_is_cst(up))
1071 return up;
1072
1073 rec = isl_upoly_as_rec(up);
1074 if (!rec)
1075 goto error;
1076
1077 isl_assert(up->ctx, rec->n >= 1, goto error);
1078
1079 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1080 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1081
1082 for (i = rec->n - 2; i >= 0; --i) {
1083 res = isl_upoly_mul(res, isl_upoly_copy(base));
1084 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1085 }
1086
1087 isl_upoly_free(base);
1088 isl_upoly_free(up);
1089
1090 return res;
1091 error:
1092 isl_upoly_free(up);
1093 return NULL;
1094 }
1095
1096 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1097 {
1098 int n_row, n_col;
1099 int equal;
1100
1101 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1102 div1->n_col >= div2->n_col, return -1);
1103
1104 if (div1->n_row == div2->n_row)
1105 return isl_mat_is_equal(div1, div2);
1106
1107 n_row = div1->n_row;
1108 n_col = div1->n_col;
1109 div1->n_row = div2->n_row;
1110 div1->n_col = div2->n_col;
1111
1112 equal = isl_mat_is_equal(div1, div2);
1113
1114 div1->n_row = n_row;
1115 div1->n_col = n_col;
1116
1117 return equal;
1118 }
1119
1120 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1121 {
1122 int li, lj;
1123
1124 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1125 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1126
1127 if (li != lj)
1128 return li - lj;
1129
1130 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1131 }
1132
1133 struct isl_div_sort_info {
1134 isl_mat *div;
1135 int row;
1136 };
1137
1138 static int div_sort_cmp(const void *p1, const void *p2)
1139 {
1140 const struct isl_div_sort_info *i1, *i2;
1141 i1 = (const struct isl_div_sort_info *) p1;
1142 i2 = (const struct isl_div_sort_info *) p2;
1143
1144 return cmp_row(i1->div, i1->row, i2->row);
1145 }
1146
1147 /* Sort divs and remove duplicates.
1148 */
1149 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1150 {
1151 int i;
1152 int skip;
1153 int len;
1154 struct isl_div_sort_info *array = NULL;
1155 int *pos = NULL, *at = NULL;
1156 int *reordering = NULL;
1157 unsigned div_pos;
1158
1159 if (!qp)
1160 return NULL;
1161 if (qp->div->n_row <= 1)
1162 return qp;
1163
1164 div_pos = isl_dim_total(qp->dim);
1165
1166 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1167 qp->div->n_row);
1168 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1169 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1170 len = qp->div->n_col - 2;
1171 reordering = isl_alloc_array(qp->div->ctx, int, len);
1172 if (!array || !pos || !at || !reordering)
1173 goto error;
1174
1175 for (i = 0; i < qp->div->n_row; ++i) {
1176 array[i].div = qp->div;
1177 array[i].row = i;
1178 pos[i] = i;
1179 at[i] = i;
1180 }
1181
1182 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1183 div_sort_cmp);
1184
1185 for (i = 0; i < div_pos; ++i)
1186 reordering[i] = i;
1187
1188 for (i = 0; i < qp->div->n_row; ++i) {
1189 if (pos[array[i].row] == i)
1190 continue;
1191 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1192 pos[at[i]] = pos[array[i].row];
1193 at[pos[array[i].row]] = at[i];
1194 at[i] = array[i].row;
1195 pos[array[i].row] = i;
1196 }
1197
1198 skip = 0;
1199 for (i = 0; i < len - div_pos; ++i) {
1200 if (i > 0 &&
1201 isl_seq_eq(qp->div->row[i - skip - 1],
1202 qp->div->row[i - skip], qp->div->n_col)) {
1203 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1204 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1205 2 + div_pos + i - skip);
1206 qp->div = isl_mat_drop_cols(qp->div,
1207 2 + div_pos + i - skip, 1);
1208 skip++;
1209 }
1210 reordering[div_pos + array[i].row] = div_pos + i - skip;
1211 }
1212
1213 qp->upoly = reorder(qp->upoly, reordering);
1214
1215 if (!qp->upoly || !qp->div)
1216 goto error;
1217
1218 free(at);
1219 free(pos);
1220 free(array);
1221 free(reordering);
1222
1223 return qp;
1224 error:
1225 free(at);
1226 free(pos);
1227 free(array);
1228 free(reordering);
1229 isl_qpolynomial_free(qp);
1230 return NULL;
1231 }
1232
1233 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1234 int *exp, int first)
1235 {
1236 int i;
1237 struct isl_upoly_rec *rec;
1238
1239 if (isl_upoly_is_cst(up))
1240 return up;
1241
1242 if (up->var < first)
1243 return up;
1244
1245 if (exp[up->var - first] == up->var - first)
1246 return up;
1247
1248 up = isl_upoly_cow(up);
1249 if (!up)
1250 goto error;
1251
1252 up->var = exp[up->var - first] + first;
1253
1254 rec = isl_upoly_as_rec(up);
1255 if (!rec)
1256 goto error;
1257
1258 for (i = 0; i < rec->n; ++i) {
1259 rec->p[i] = expand(rec->p[i], exp, first);
1260 if (!rec->p[i])
1261 goto error;
1262 }
1263
1264 return up;
1265 error:
1266 isl_upoly_free(up);
1267 return NULL;
1268 }
1269
1270 static __isl_give isl_qpolynomial *with_merged_divs(
1271 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1272 __isl_take isl_qpolynomial *qp2),
1273 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1274 {
1275 int *exp1 = NULL;
1276 int *exp2 = NULL;
1277 isl_mat *div = NULL;
1278
1279 qp1 = isl_qpolynomial_cow(qp1);
1280 qp2 = isl_qpolynomial_cow(qp2);
1281
1282 if (!qp1 || !qp2)
1283 goto error;
1284
1285 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1286 qp1->div->n_col >= qp2->div->n_col, goto error);
1287
1288 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1289 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1290 if (!exp1 || !exp2)
1291 goto error;
1292
1293 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1294 if (!div)
1295 goto error;
1296
1297 isl_mat_free(qp1->div);
1298 qp1->div = isl_mat_copy(div);
1299 isl_mat_free(qp2->div);
1300 qp2->div = isl_mat_copy(div);
1301
1302 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1303 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1304
1305 if (!qp1->upoly || !qp2->upoly)
1306 goto error;
1307
1308 isl_mat_free(div);
1309 free(exp1);
1310 free(exp2);
1311
1312 return fn(qp1, qp2);
1313 error:
1314 isl_mat_free(div);
1315 free(exp1);
1316 free(exp2);
1317 isl_qpolynomial_free(qp1);
1318 isl_qpolynomial_free(qp2);
1319 return NULL;
1320 }
1321
1322 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1323 __isl_take isl_qpolynomial *qp2)
1324 {
1325 qp1 = isl_qpolynomial_cow(qp1);
1326
1327 if (!qp1 || !qp2)
1328 goto error;
1329
1330 if (qp1->div->n_row < qp2->div->n_row)
1331 return isl_qpolynomial_add(qp2, qp1);
1332
1333 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1334 if (!compatible_divs(qp1->div, qp2->div))
1335 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1336
1337 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1338 if (!qp1->upoly)
1339 goto error;
1340
1341 isl_qpolynomial_free(qp2);
1342
1343 return qp1;
1344 error:
1345 isl_qpolynomial_free(qp1);
1346 isl_qpolynomial_free(qp2);
1347 return NULL;
1348 }
1349
1350 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1351 __isl_keep isl_set *dom,
1352 __isl_take isl_qpolynomial *qp1,
1353 __isl_take isl_qpolynomial *qp2)
1354 {
1355 qp1 = isl_qpolynomial_add(qp1, qp2);
1356 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1357 return qp1;
1358 }
1359
1360 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1361 __isl_take isl_qpolynomial *qp2)
1362 {
1363 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1364 }
1365
1366 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1367 __isl_take isl_qpolynomial *qp, isl_int v)
1368 {
1369 if (isl_int_is_zero(v))
1370 return qp;
1371
1372 qp = isl_qpolynomial_cow(qp);
1373 if (!qp)
1374 return NULL;
1375
1376 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1377 if (!qp->upoly)
1378 goto error;
1379
1380 return qp;
1381 error:
1382 isl_qpolynomial_free(qp);
1383 return NULL;
1384
1385 }
1386
1387 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1388 {
1389 if (!qp)
1390 return NULL;
1391
1392 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1393 }
1394
1395 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1396 __isl_take isl_qpolynomial *qp, isl_int v)
1397 {
1398 if (isl_int_is_one(v))
1399 return qp;
1400
1401 if (qp && isl_int_is_zero(v)) {
1402 isl_qpolynomial *zero;
1403 zero = isl_qpolynomial_zero(isl_dim_copy(qp->dim));
1404 isl_qpolynomial_free(qp);
1405 return zero;
1406 }
1407
1408 qp = isl_qpolynomial_cow(qp);
1409 if (!qp)
1410 return NULL;
1411
1412 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1413 if (!qp->upoly)
1414 goto error;
1415
1416 return qp;
1417 error:
1418 isl_qpolynomial_free(qp);
1419 return NULL;
1420 }
1421
1422 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
1423 __isl_take isl_qpolynomial *qp, isl_int v)
1424 {
1425 return isl_qpolynomial_mul_isl_int(qp, v);
1426 }
1427
1428 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1429 __isl_take isl_qpolynomial *qp2)
1430 {
1431 qp1 = isl_qpolynomial_cow(qp1);
1432
1433 if (!qp1 || !qp2)
1434 goto error;
1435
1436 if (qp1->div->n_row < qp2->div->n_row)
1437 return isl_qpolynomial_mul(qp2, qp1);
1438
1439 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1440 if (!compatible_divs(qp1->div, qp2->div))
1441 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1442
1443 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1444 if (!qp1->upoly)
1445 goto error;
1446
1447 isl_qpolynomial_free(qp2);
1448
1449 return qp1;
1450 error:
1451 isl_qpolynomial_free(qp1);
1452 isl_qpolynomial_free(qp2);
1453 return NULL;
1454 }
1455
1456 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1457 unsigned power)
1458 {
1459 qp = isl_qpolynomial_cow(qp);
1460
1461 if (!qp)
1462 return NULL;
1463
1464 qp->upoly = isl_upoly_pow(qp->upoly, power);
1465 if (!qp->upoly)
1466 goto error;
1467
1468 return qp;
1469 error:
1470 isl_qpolynomial_free(qp);
1471 return NULL;
1472 }
1473
1474 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1475 {
1476 if (!dim)
1477 return NULL;
1478 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1479 }
1480
1481 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1482 {
1483 if (!dim)
1484 return NULL;
1485 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1486 }
1487
1488 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1489 {
1490 if (!dim)
1491 return NULL;
1492 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1493 }
1494
1495 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1496 {
1497 if (!dim)
1498 return NULL;
1499 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1500 }
1501
1502 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1503 {
1504 if (!dim)
1505 return NULL;
1506 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1507 }
1508
1509 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1510 isl_int v)
1511 {
1512 struct isl_qpolynomial *qp;
1513 struct isl_upoly_cst *cst;
1514
1515 if (!dim)
1516 return NULL;
1517
1518 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1519 if (!qp)
1520 return NULL;
1521
1522 cst = isl_upoly_as_cst(qp->upoly);
1523 isl_int_set(cst->n, v);
1524
1525 return qp;
1526 }
1527
1528 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1529 isl_int *n, isl_int *d)
1530 {
1531 struct isl_upoly_cst *cst;
1532
1533 if (!qp)
1534 return -1;
1535
1536 if (!isl_upoly_is_cst(qp->upoly))
1537 return 0;
1538
1539 cst = isl_upoly_as_cst(qp->upoly);
1540 if (!cst)
1541 return -1;
1542
1543 if (n)
1544 isl_int_set(*n, cst->n);
1545 if (d)
1546 isl_int_set(*d, cst->d);
1547
1548 return 1;
1549 }
1550
1551 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1552 {
1553 int is_cst;
1554 struct isl_upoly_rec *rec;
1555
1556 if (!up)
1557 return -1;
1558
1559 if (up->var < 0)
1560 return 1;
1561
1562 rec = isl_upoly_as_rec(up);
1563 if (!rec)
1564 return -1;
1565
1566 if (rec->n > 2)
1567 return 0;
1568
1569 isl_assert(up->ctx, rec->n > 1, return -1);
1570
1571 is_cst = isl_upoly_is_cst(rec->p[1]);
1572 if (is_cst < 0)
1573 return -1;
1574 if (!is_cst)
1575 return 0;
1576
1577 return isl_upoly_is_affine(rec->p[0]);
1578 }
1579
1580 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1581 {
1582 if (!qp)
1583 return -1;
1584
1585 if (qp->div->n_row > 0)
1586 return 0;
1587
1588 return isl_upoly_is_affine(qp->upoly);
1589 }
1590
1591 static void update_coeff(__isl_keep isl_vec *aff,
1592 __isl_keep struct isl_upoly_cst *cst, int pos)
1593 {
1594 isl_int gcd;
1595 isl_int f;
1596
1597 if (isl_int_is_zero(cst->n))
1598 return;
1599
1600 isl_int_init(gcd);
1601 isl_int_init(f);
1602 isl_int_gcd(gcd, cst->d, aff->el[0]);
1603 isl_int_divexact(f, cst->d, gcd);
1604 isl_int_divexact(gcd, aff->el[0], gcd);
1605 isl_seq_scale(aff->el, aff->el, f, aff->size);
1606 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1607 isl_int_clear(gcd);
1608 isl_int_clear(f);
1609 }
1610
1611 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1612 __isl_keep isl_vec *aff)
1613 {
1614 struct isl_upoly_cst *cst;
1615 struct isl_upoly_rec *rec;
1616
1617 if (!up || !aff)
1618 return -1;
1619
1620 if (up->var < 0) {
1621 struct isl_upoly_cst *cst;
1622
1623 cst = isl_upoly_as_cst(up);
1624 if (!cst)
1625 return -1;
1626 update_coeff(aff, cst, 0);
1627 return 0;
1628 }
1629
1630 rec = isl_upoly_as_rec(up);
1631 if (!rec)
1632 return -1;
1633 isl_assert(up->ctx, rec->n == 2, return -1);
1634
1635 cst = isl_upoly_as_cst(rec->p[1]);
1636 if (!cst)
1637 return -1;
1638 update_coeff(aff, cst, 1 + up->var);
1639
1640 return isl_upoly_update_affine(rec->p[0], aff);
1641 }
1642
1643 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1644 __isl_keep isl_qpolynomial *qp)
1645 {
1646 isl_vec *aff;
1647 unsigned d;
1648
1649 if (!qp)
1650 return NULL;
1651
1652 d = isl_dim_total(qp->dim);
1653 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1654 if (!aff)
1655 return NULL;
1656
1657 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1658 isl_int_set_si(aff->el[0], 1);
1659
1660 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1661 goto error;
1662
1663 return aff;
1664 error:
1665 isl_vec_free(aff);
1666 return NULL;
1667 }
1668
1669 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1670 __isl_keep isl_qpolynomial *qp2)
1671 {
1672 int equal;
1673
1674 if (!qp1 || !qp2)
1675 return -1;
1676
1677 equal = isl_dim_equal(qp1->dim, qp2->dim);
1678 if (equal < 0 || !equal)
1679 return equal;
1680
1681 equal = isl_mat_is_equal(qp1->div, qp2->div);
1682 if (equal < 0 || !equal)
1683 return equal;
1684
1685 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1686 }
1687
1688 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1689 {
1690 int i;
1691 struct isl_upoly_rec *rec;
1692
1693 if (isl_upoly_is_cst(up)) {
1694 struct isl_upoly_cst *cst;
1695 cst = isl_upoly_as_cst(up);
1696 if (!cst)
1697 return;
1698 isl_int_lcm(*d, *d, cst->d);
1699 return;
1700 }
1701
1702 rec = isl_upoly_as_rec(up);
1703 if (!rec)
1704 return;
1705
1706 for (i = 0; i < rec->n; ++i)
1707 upoly_update_den(rec->p[i], d);
1708 }
1709
1710 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1711 {
1712 isl_int_set_si(*d, 1);
1713 if (!qp)
1714 return;
1715 upoly_update_den(qp->upoly, d);
1716 }
1717
1718 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1719 int pos, int power)
1720 {
1721 struct isl_ctx *ctx;
1722
1723 if (!dim)
1724 return NULL;
1725
1726 ctx = dim->ctx;
1727
1728 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1729 }
1730
1731 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1732 enum isl_dim_type type, unsigned pos)
1733 {
1734 if (!dim)
1735 return NULL;
1736
1737 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1738 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1739
1740 if (type == isl_dim_set)
1741 pos += isl_dim_size(dim, isl_dim_param);
1742
1743 return isl_qpolynomial_var_pow(dim, pos, 1);
1744 error:
1745 isl_dim_free(dim);
1746 return NULL;
1747 }
1748
1749 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1750 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1751 {
1752 int i;
1753 struct isl_upoly_rec *rec;
1754 struct isl_upoly *base, *res;
1755
1756 if (!up)
1757 return NULL;
1758
1759 if (isl_upoly_is_cst(up))
1760 return up;
1761
1762 if (up->var < first)
1763 return up;
1764
1765 rec = isl_upoly_as_rec(up);
1766 if (!rec)
1767 goto error;
1768
1769 isl_assert(up->ctx, rec->n >= 1, goto error);
1770
1771 if (up->var >= first + n)
1772 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1773 else
1774 base = isl_upoly_copy(subs[up->var - first]);
1775
1776 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1777 for (i = rec->n - 2; i >= 0; --i) {
1778 struct isl_upoly *t;
1779 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1780 res = isl_upoly_mul(res, isl_upoly_copy(base));
1781 res = isl_upoly_sum(res, t);
1782 }
1783
1784 isl_upoly_free(base);
1785 isl_upoly_free(up);
1786
1787 return res;
1788 error:
1789 isl_upoly_free(up);
1790 return NULL;
1791 }
1792
1793 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1794 isl_int denom, unsigned len)
1795 {
1796 int i;
1797 struct isl_upoly *up;
1798
1799 isl_assert(ctx, len >= 1, return NULL);
1800
1801 up = isl_upoly_rat_cst(ctx, f[0], denom);
1802 for (i = 0; i < len - 1; ++i) {
1803 struct isl_upoly *t;
1804 struct isl_upoly *c;
1805
1806 if (isl_int_is_zero(f[1 + i]))
1807 continue;
1808
1809 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1810 t = isl_upoly_var_pow(ctx, i, 1);
1811 t = isl_upoly_mul(c, t);
1812 up = isl_upoly_sum(up, t);
1813 }
1814
1815 return up;
1816 }
1817
1818 /* Remove common factor of non-constant terms and denominator.
1819 */
1820 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1821 {
1822 isl_ctx *ctx = qp->div->ctx;
1823 unsigned total = qp->div->n_col - 2;
1824
1825 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1826 isl_int_gcd(ctx->normalize_gcd,
1827 ctx->normalize_gcd, qp->div->row[div][0]);
1828 if (isl_int_is_one(ctx->normalize_gcd))
1829 return;
1830
1831 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1832 ctx->normalize_gcd, total);
1833 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1834 ctx->normalize_gcd);
1835 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1836 ctx->normalize_gcd);
1837 }
1838
1839 /* Replace the integer division identified by "div" by the polynomial "s".
1840 * The integer division is assumed not to appear in the definition
1841 * of any other integer divisions.
1842 */
1843 static __isl_give isl_qpolynomial *substitute_div(
1844 __isl_take isl_qpolynomial *qp,
1845 int div, __isl_take struct isl_upoly *s)
1846 {
1847 int i;
1848 int total;
1849 int *reordering;
1850
1851 if (!qp || !s)
1852 goto error;
1853
1854 qp = isl_qpolynomial_cow(qp);
1855 if (!qp)
1856 goto error;
1857
1858 total = isl_dim_total(qp->dim);
1859 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1860 if (!qp->upoly)
1861 goto error;
1862
1863 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1864 if (!reordering)
1865 goto error;
1866 for (i = 0; i < total + div; ++i)
1867 reordering[i] = i;
1868 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1869 reordering[i] = i - 1;
1870 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1871 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1872 qp->upoly = reorder(qp->upoly, reordering);
1873 free(reordering);
1874
1875 if (!qp->upoly || !qp->div)
1876 goto error;
1877
1878 isl_upoly_free(s);
1879 return qp;
1880 error:
1881 isl_qpolynomial_free(qp);
1882 isl_upoly_free(s);
1883 return NULL;
1884 }
1885
1886 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1887 * divisions because d is equal to 1 by their definition, i.e., e.
1888 */
1889 static __isl_give isl_qpolynomial *substitute_non_divs(
1890 __isl_take isl_qpolynomial *qp)
1891 {
1892 int i, j;
1893 int total;
1894 struct isl_upoly *s;
1895
1896 if (!qp)
1897 return NULL;
1898
1899 total = isl_dim_total(qp->dim);
1900 for (i = 0; qp && i < qp->div->n_row; ++i) {
1901 if (!isl_int_is_one(qp->div->row[i][0]))
1902 continue;
1903 for (j = i + 1; j < qp->div->n_row; ++j) {
1904 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1905 continue;
1906 isl_seq_combine(qp->div->row[j] + 1,
1907 qp->div->ctx->one, qp->div->row[j] + 1,
1908 qp->div->row[j][2 + total + i],
1909 qp->div->row[i] + 1, 1 + total + i);
1910 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1911 normalize_div(qp, j);
1912 }
1913 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1914 qp->div->row[i][0], qp->div->n_col - 1);
1915 qp = substitute_div(qp, i, s);
1916 --i;
1917 }
1918
1919 return qp;
1920 }
1921
1922 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1923 * with d the denominator. When replacing the coefficient e of x by
1924 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1925 * inside the division, so we need to add floor(e/d) * x outside.
1926 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1927 * to adjust the coefficient of x in each later div that depends on the
1928 * current div "div" and also in the affine expression "aff"
1929 * (if it too depends on "div").
1930 */
1931 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1932 __isl_keep isl_vec *aff)
1933 {
1934 int i, j;
1935 isl_int v;
1936 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1937
1938 isl_int_init(v);
1939 for (i = 0; i < 1 + total + div; ++i) {
1940 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1941 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1942 continue;
1943 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1944 isl_int_fdiv_r(qp->div->row[div][1 + i],
1945 qp->div->row[div][1 + i], qp->div->row[div][0]);
1946 if (!isl_int_is_zero(aff->el[1 + total + div]))
1947 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1948 for (j = div + 1; j < qp->div->n_row; ++j) {
1949 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1950 continue;
1951 isl_int_addmul(qp->div->row[j][1 + i],
1952 v, qp->div->row[j][2 + total + div]);
1953 }
1954 }
1955 isl_int_clear(v);
1956 }
1957
1958 /* Check if the last non-zero coefficient is bigger that half of the
1959 * denominator. If so, we will invert the div to further reduce the number
1960 * of distinct divs that may appear.
1961 * If the last non-zero coefficient is exactly half the denominator,
1962 * then we continue looking for earlier coefficients that are bigger
1963 * than half the denominator.
1964 */
1965 static int needs_invert(__isl_keep isl_mat *div, int row)
1966 {
1967 int i;
1968 int cmp;
1969
1970 for (i = div->n_col - 1; i >= 1; --i) {
1971 if (isl_int_is_zero(div->row[row][i]))
1972 continue;
1973 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1974 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1975 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1976 if (cmp)
1977 return cmp > 0;
1978 if (i == 1)
1979 return 1;
1980 }
1981
1982 return 0;
1983 }
1984
1985 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1986 * We only invert the coefficients of e (and the coefficient of q in
1987 * later divs and in "aff"). After calling this function, the
1988 * coefficients of e should be reduced again.
1989 */
1990 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1991 __isl_keep isl_vec *aff)
1992 {
1993 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1994
1995 isl_seq_neg(qp->div->row[div] + 1,
1996 qp->div->row[div] + 1, qp->div->n_col - 1);
1997 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
1998 isl_int_add(qp->div->row[div][1],
1999 qp->div->row[div][1], qp->div->row[div][0]);
2000 if (!isl_int_is_zero(aff->el[1 + total + div]))
2001 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2002 isl_mat_col_mul(qp->div, 2 + total + div,
2003 qp->div->ctx->negone, 2 + total + div);
2004 }
2005
2006 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2007 * in the interval [0, d-1], with d the denominator and such that the
2008 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2009 *
2010 * After the reduction, some divs may have become redundant or identical,
2011 * so we call substitute_non_divs and sort_divs. If these functions
2012 * eliminate divs or merge two or more divs into one, the coefficients
2013 * of the enclosing divs may have to be reduced again, so we call
2014 * ourselves recursively if the number of divs decreases.
2015 */
2016 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2017 {
2018 int i;
2019 isl_vec *aff = NULL;
2020 struct isl_upoly *s;
2021 unsigned n_div;
2022
2023 if (!qp)
2024 return NULL;
2025
2026 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2027 aff = isl_vec_clr(aff);
2028 if (!aff)
2029 goto error;
2030
2031 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2032
2033 for (i = 0; i < qp->div->n_row; ++i) {
2034 normalize_div(qp, i);
2035 reduce_div(qp, i, aff);
2036 if (needs_invert(qp->div, i)) {
2037 invert_div(qp, i, aff);
2038 reduce_div(qp, i, aff);
2039 }
2040 }
2041
2042 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2043 qp->div->ctx->one, aff->size);
2044 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2045 isl_upoly_free(s);
2046 if (!qp->upoly)
2047 goto error;
2048
2049 isl_vec_free(aff);
2050
2051 n_div = qp->div->n_row;
2052 qp = substitute_non_divs(qp);
2053 qp = sort_divs(qp);
2054 if (qp && qp->div->n_row < n_div)
2055 return reduce_divs(qp);
2056
2057 return qp;
2058 error:
2059 isl_qpolynomial_free(qp);
2060 isl_vec_free(aff);
2061 return NULL;
2062 }
2063
2064 /* Assumes each div only depends on earlier divs.
2065 */
2066 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2067 int power)
2068 {
2069 struct isl_qpolynomial *qp = NULL;
2070 struct isl_upoly_rec *rec;
2071 struct isl_upoly_cst *cst;
2072 int i, d;
2073 int pos;
2074
2075 if (!div)
2076 return NULL;
2077
2078 d = div->line - div->bmap->div;
2079
2080 pos = isl_dim_total(div->bmap->dim) + d;
2081 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2082 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2083 div->bmap->n_div, &rec->up);
2084 if (!qp)
2085 goto error;
2086
2087 for (i = 0; i < div->bmap->n_div; ++i)
2088 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2089
2090 for (i = 0; i < 1 + power; ++i) {
2091 rec->p[i] = isl_upoly_zero(div->ctx);
2092 if (!rec->p[i])
2093 goto error;
2094 rec->n++;
2095 }
2096 cst = isl_upoly_as_cst(rec->p[power]);
2097 isl_int_set_si(cst->n, 1);
2098
2099 isl_div_free(div);
2100
2101 qp = reduce_divs(qp);
2102
2103 return qp;
2104 error:
2105 isl_qpolynomial_free(qp);
2106 isl_div_free(div);
2107 return NULL;
2108 }
2109
2110 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2111 {
2112 return isl_qpolynomial_div_pow(div, 1);
2113 }
2114
2115 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2116 const isl_int n, const isl_int d)
2117 {
2118 struct isl_qpolynomial *qp;
2119 struct isl_upoly_cst *cst;
2120
2121 if (!dim)
2122 return NULL;
2123
2124 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2125 if (!qp)
2126 return NULL;
2127
2128 cst = isl_upoly_as_cst(qp->upoly);
2129 isl_int_set(cst->n, n);
2130 isl_int_set(cst->d, d);
2131
2132 return qp;
2133 }
2134
2135 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2136 {
2137 struct isl_upoly_rec *rec;
2138 int i;
2139
2140 if (!up)
2141 return -1;
2142
2143 if (isl_upoly_is_cst(up))
2144 return 0;
2145
2146 if (up->var < d)
2147 active[up->var] = 1;
2148
2149 rec = isl_upoly_as_rec(up);
2150 for (i = 0; i < rec->n; ++i)
2151 if (up_set_active(rec->p[i], active, d) < 0)
2152 return -1;
2153
2154 return 0;
2155 }
2156
2157 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2158 {
2159 int i, j;
2160 int d = isl_dim_total(qp->dim);
2161
2162 if (!qp || !active)
2163 return -1;
2164
2165 for (i = 0; i < d; ++i)
2166 for (j = 0; j < qp->div->n_row; ++j) {
2167 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2168 continue;
2169 active[i] = 1;
2170 break;
2171 }
2172
2173 return up_set_active(qp->upoly, active, d);
2174 }
2175
2176 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2177 enum isl_dim_type type, unsigned first, unsigned n)
2178 {
2179 int i;
2180 int *active = NULL;
2181 int involves = 0;
2182
2183 if (!qp)
2184 return -1;
2185 if (n == 0)
2186 return 0;
2187
2188 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2189 return -1);
2190 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2191 type == isl_dim_set, return -1);
2192
2193 active = isl_calloc_array(qp->dim->ctx, int, isl_dim_total(qp->dim));
2194 if (set_active(qp, active) < 0)
2195 goto error;
2196
2197 if (type == isl_dim_set)
2198 first += isl_dim_size(qp->dim, isl_dim_param);
2199 for (i = 0; i < n; ++i)
2200 if (active[first + i]) {
2201 involves = 1;
2202 break;
2203 }
2204
2205 free(active);
2206
2207 return involves;
2208 error:
2209 free(active);
2210 return -1;
2211 }
2212
2213 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2214 * of the divs that do appear in the quasi-polynomial.
2215 */
2216 static __isl_give isl_qpolynomial *remove_redundant_divs(
2217 __isl_take isl_qpolynomial *qp)
2218 {
2219 int i, j;
2220 int d;
2221 int len;
2222 int skip;
2223 int *active = NULL;
2224 int *reordering = NULL;
2225 int redundant = 0;
2226 int n_div;
2227 isl_ctx *ctx;
2228
2229 if (!qp)
2230 return NULL;
2231 if (qp->div->n_row == 0)
2232 return qp;
2233
2234 d = isl_dim_total(qp->dim);
2235 len = qp->div->n_col - 2;
2236 ctx = isl_qpolynomial_get_ctx(qp);
2237 active = isl_calloc_array(ctx, int, len);
2238 if (!active)
2239 goto error;
2240
2241 if (up_set_active(qp->upoly, active, len) < 0)
2242 goto error;
2243
2244 for (i = qp->div->n_row - 1; i >= 0; --i) {
2245 if (!active[d + i]) {
2246 redundant = 1;
2247 continue;
2248 }
2249 for (j = 0; j < i; ++j) {
2250 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2251 continue;
2252 active[d + j] = 1;
2253 break;
2254 }
2255 }
2256
2257 if (!redundant) {
2258 free(active);
2259 return qp;
2260 }
2261
2262 reordering = isl_alloc_array(qp->div->ctx, int, len);
2263 if (!reordering)
2264 goto error;
2265
2266 for (i = 0; i < d; ++i)
2267 reordering[i] = i;
2268
2269 skip = 0;
2270 n_div = qp->div->n_row;
2271 for (i = 0; i < n_div; ++i) {
2272 if (!active[d + i]) {
2273 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2274 qp->div = isl_mat_drop_cols(qp->div,
2275 2 + d + i - skip, 1);
2276 skip++;
2277 }
2278 reordering[d + i] = d + i - skip;
2279 }
2280
2281 qp->upoly = reorder(qp->upoly, reordering);
2282
2283 if (!qp->upoly || !qp->div)
2284 goto error;
2285
2286 free(active);
2287 free(reordering);
2288
2289 return qp;
2290 error:
2291 free(active);
2292 free(reordering);
2293 isl_qpolynomial_free(qp);
2294 return NULL;
2295 }
2296
2297 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2298 unsigned first, unsigned n)
2299 {
2300 int i;
2301 struct isl_upoly_rec *rec;
2302
2303 if (!up)
2304 return NULL;
2305 if (n == 0 || up->var < 0 || up->var < first)
2306 return up;
2307 if (up->var < first + n) {
2308 up = replace_by_constant_term(up);
2309 return isl_upoly_drop(up, first, n);
2310 }
2311 up = isl_upoly_cow(up);
2312 if (!up)
2313 return NULL;
2314 up->var -= n;
2315 rec = isl_upoly_as_rec(up);
2316 if (!rec)
2317 goto error;
2318
2319 for (i = 0; i < rec->n; ++i) {
2320 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2321 if (!rec->p[i])
2322 goto error;
2323 }
2324
2325 return up;
2326 error:
2327 isl_upoly_free(up);
2328 return NULL;
2329 }
2330
2331 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2332 __isl_take isl_qpolynomial *qp,
2333 enum isl_dim_type type, unsigned pos, const char *s)
2334 {
2335 qp = isl_qpolynomial_cow(qp);
2336 if (!qp)
2337 return NULL;
2338 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2339 if (!qp->dim)
2340 goto error;
2341 return qp;
2342 error:
2343 isl_qpolynomial_free(qp);
2344 return NULL;
2345 }
2346
2347 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2348 __isl_take isl_qpolynomial *qp,
2349 enum isl_dim_type type, unsigned first, unsigned n)
2350 {
2351 if (!qp)
2352 return NULL;
2353 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2354 return qp;
2355
2356 qp = isl_qpolynomial_cow(qp);
2357 if (!qp)
2358 return NULL;
2359
2360 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2361 goto error);
2362 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2363 type == isl_dim_set, goto error);
2364
2365 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2366 if (!qp->dim)
2367 goto error;
2368
2369 if (type == isl_dim_set)
2370 first += isl_dim_size(qp->dim, isl_dim_param);
2371
2372 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2373 if (!qp->div)
2374 goto error;
2375
2376 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2377 if (!qp->upoly)
2378 goto error;
2379
2380 return qp;
2381 error:
2382 isl_qpolynomial_free(qp);
2383 return NULL;
2384 }
2385
2386 static __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities_lifted(
2387 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2388 {
2389 int i, j, k;
2390 isl_int denom;
2391 unsigned total;
2392 unsigned n_div;
2393 struct isl_upoly *up;
2394
2395 if (!eq)
2396 goto error;
2397 if (eq->n_eq == 0) {
2398 isl_basic_set_free(eq);
2399 return qp;
2400 }
2401
2402 qp = isl_qpolynomial_cow(qp);
2403 if (!qp)
2404 goto error;
2405 qp->div = isl_mat_cow(qp->div);
2406 if (!qp->div)
2407 goto error;
2408
2409 total = 1 + isl_dim_total(eq->dim);
2410 n_div = eq->n_div;
2411 isl_int_init(denom);
2412 for (i = 0; i < eq->n_eq; ++i) {
2413 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2414 if (j < 0 || j == 0 || j >= total)
2415 continue;
2416
2417 for (k = 0; k < qp->div->n_row; ++k) {
2418 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2419 continue;
2420 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2421 &qp->div->row[k][0]);
2422 normalize_div(qp, k);
2423 }
2424
2425 if (isl_int_is_pos(eq->eq[i][j]))
2426 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2427 isl_int_abs(denom, eq->eq[i][j]);
2428 isl_int_set_si(eq->eq[i][j], 0);
2429
2430 up = isl_upoly_from_affine(qp->dim->ctx,
2431 eq->eq[i], denom, total);
2432 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2433 isl_upoly_free(up);
2434 }
2435 isl_int_clear(denom);
2436
2437 if (!qp->upoly)
2438 goto error;
2439
2440 isl_basic_set_free(eq);
2441
2442 qp = substitute_non_divs(qp);
2443 qp = sort_divs(qp);
2444
2445 return qp;
2446 error:
2447 isl_basic_set_free(eq);
2448 isl_qpolynomial_free(qp);
2449 return NULL;
2450 }
2451
2452 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2453 */
2454 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2455 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2456 {
2457 if (!qp || !eq)
2458 goto error;
2459 if (qp->div->n_row > 0)
2460 eq = isl_basic_set_add(eq, isl_dim_set, qp->div->n_row);
2461 return isl_qpolynomial_substitute_equalities_lifted(qp, eq);
2462 error:
2463 isl_basic_set_free(eq);
2464 isl_qpolynomial_free(qp);
2465 return NULL;
2466 }
2467
2468 static __isl_give isl_basic_set *add_div_constraints(
2469 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2470 {
2471 int i;
2472 unsigned total;
2473
2474 if (!bset || !div)
2475 goto error;
2476
2477 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2478 if (!bset)
2479 goto error;
2480 total = isl_basic_set_total_dim(bset);
2481 for (i = 0; i < div->n_row; ++i)
2482 if (isl_basic_set_add_div_constraints_var(bset,
2483 total - div->n_row + i, div->row[i]) < 0)
2484 goto error;
2485
2486 isl_mat_free(div);
2487 return bset;
2488 error:
2489 isl_mat_free(div);
2490 isl_basic_set_free(bset);
2491 return NULL;
2492 }
2493
2494 /* Look for equalities among the variables shared by context and qp
2495 * and the integer divisions of qp, if any.
2496 * The equalities are then used to eliminate variables and/or integer
2497 * divisions from qp.
2498 */
2499 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2500 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2501 {
2502 isl_basic_set *aff;
2503
2504 if (!qp)
2505 goto error;
2506 if (qp->div->n_row > 0) {
2507 isl_basic_set *bset;
2508 context = isl_set_add_dims(context, isl_dim_set,
2509 qp->div->n_row);
2510 bset = isl_basic_set_universe(isl_set_get_dim(context));
2511 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2512 context = isl_set_intersect(context,
2513 isl_set_from_basic_set(bset));
2514 }
2515
2516 aff = isl_set_affine_hull(context);
2517 return isl_qpolynomial_substitute_equalities_lifted(qp, aff);
2518 error:
2519 isl_qpolynomial_free(qp);
2520 isl_set_free(context);
2521 return NULL;
2522 }
2523
2524 #undef PW
2525 #define PW isl_pw_qpolynomial
2526 #undef EL
2527 #define EL isl_qpolynomial
2528 #undef EL_IS_ZERO
2529 #define EL_IS_ZERO is_zero
2530 #undef ZERO
2531 #define ZERO zero
2532 #undef IS_ZERO
2533 #define IS_ZERO is_zero
2534 #undef FIELD
2535 #define FIELD qp
2536
2537 #include <isl_pw_templ.c>
2538
2539 #undef UNION
2540 #define UNION isl_union_pw_qpolynomial
2541 #undef PART
2542 #define PART isl_pw_qpolynomial
2543 #undef PARTS
2544 #define PARTS pw_qpolynomial
2545
2546 #include <isl_union_templ.c>
2547
2548 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2549 {
2550 if (!pwqp)
2551 return -1;
2552
2553 if (pwqp->n != -1)
2554 return 0;
2555
2556 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2557 return 0;
2558
2559 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2560 }
2561
2562 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2563 __isl_take isl_pw_qpolynomial *pwqp1,
2564 __isl_take isl_pw_qpolynomial *pwqp2)
2565 {
2566 int i, j, n;
2567 struct isl_pw_qpolynomial *res;
2568
2569 if (!pwqp1 || !pwqp2)
2570 goto error;
2571
2572 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2573 goto error);
2574
2575 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2576 isl_pw_qpolynomial_free(pwqp2);
2577 return pwqp1;
2578 }
2579
2580 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2581 isl_pw_qpolynomial_free(pwqp1);
2582 return pwqp2;
2583 }
2584
2585 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2586 isl_pw_qpolynomial_free(pwqp1);
2587 return pwqp2;
2588 }
2589
2590 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2591 isl_pw_qpolynomial_free(pwqp2);
2592 return pwqp1;
2593 }
2594
2595 n = pwqp1->n * pwqp2->n;
2596 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2597
2598 for (i = 0; i < pwqp1->n; ++i) {
2599 for (j = 0; j < pwqp2->n; ++j) {
2600 struct isl_set *common;
2601 struct isl_qpolynomial *prod;
2602 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2603 isl_set_copy(pwqp2->p[j].set));
2604 if (isl_set_plain_is_empty(common)) {
2605 isl_set_free(common);
2606 continue;
2607 }
2608
2609 prod = isl_qpolynomial_mul(
2610 isl_qpolynomial_copy(pwqp1->p[i].qp),
2611 isl_qpolynomial_copy(pwqp2->p[j].qp));
2612
2613 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2614 }
2615 }
2616
2617 isl_pw_qpolynomial_free(pwqp1);
2618 isl_pw_qpolynomial_free(pwqp2);
2619
2620 return res;
2621 error:
2622 isl_pw_qpolynomial_free(pwqp1);
2623 isl_pw_qpolynomial_free(pwqp2);
2624 return NULL;
2625 }
2626
2627 __isl_give struct isl_upoly *isl_upoly_eval(
2628 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2629 {
2630 int i;
2631 struct isl_upoly_rec *rec;
2632 struct isl_upoly *res;
2633 struct isl_upoly *base;
2634
2635 if (isl_upoly_is_cst(up)) {
2636 isl_vec_free(vec);
2637 return up;
2638 }
2639
2640 rec = isl_upoly_as_rec(up);
2641 if (!rec)
2642 goto error;
2643
2644 isl_assert(up->ctx, rec->n >= 1, goto error);
2645
2646 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2647
2648 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2649 isl_vec_copy(vec));
2650
2651 for (i = rec->n - 2; i >= 0; --i) {
2652 res = isl_upoly_mul(res, isl_upoly_copy(base));
2653 res = isl_upoly_sum(res,
2654 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2655 isl_vec_copy(vec)));
2656 }
2657
2658 isl_upoly_free(base);
2659 isl_upoly_free(up);
2660 isl_vec_free(vec);
2661 return res;
2662 error:
2663 isl_upoly_free(up);
2664 isl_vec_free(vec);
2665 return NULL;
2666 }
2667
2668 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2669 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2670 {
2671 isl_vec *ext;
2672 struct isl_upoly *up;
2673 isl_dim *dim;
2674
2675 if (!qp || !pnt)
2676 goto error;
2677 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2678
2679 if (qp->div->n_row == 0)
2680 ext = isl_vec_copy(pnt->vec);
2681 else {
2682 int i;
2683 unsigned dim = isl_dim_total(qp->dim);
2684 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2685 if (!ext)
2686 goto error;
2687
2688 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2689 for (i = 0; i < qp->div->n_row; ++i) {
2690 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2691 1 + dim + i, &ext->el[1+dim+i]);
2692 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2693 qp->div->row[i][0]);
2694 }
2695 }
2696
2697 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2698 if (!up)
2699 goto error;
2700
2701 dim = isl_dim_copy(qp->dim);
2702 isl_qpolynomial_free(qp);
2703 isl_point_free(pnt);
2704
2705 return isl_qpolynomial_alloc(dim, 0, up);
2706 error:
2707 isl_qpolynomial_free(qp);
2708 isl_point_free(pnt);
2709 return NULL;
2710 }
2711
2712 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2713 __isl_keep struct isl_upoly_cst *cst2)
2714 {
2715 int cmp;
2716 isl_int t;
2717 isl_int_init(t);
2718 isl_int_mul(t, cst1->n, cst2->d);
2719 isl_int_submul(t, cst2->n, cst1->d);
2720 cmp = isl_int_sgn(t);
2721 isl_int_clear(t);
2722 return cmp;
2723 }
2724
2725 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2726 __isl_keep isl_qpolynomial *qp2)
2727 {
2728 struct isl_upoly_cst *cst1, *cst2;
2729
2730 if (!qp1 || !qp2)
2731 return -1;
2732 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2733 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2734 if (isl_qpolynomial_is_nan(qp1))
2735 return -1;
2736 if (isl_qpolynomial_is_nan(qp2))
2737 return -1;
2738 cst1 = isl_upoly_as_cst(qp1->upoly);
2739 cst2 = isl_upoly_as_cst(qp2->upoly);
2740
2741 return isl_upoly_cmp(cst1, cst2) <= 0;
2742 }
2743
2744 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2745 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2746 {
2747 struct isl_upoly_cst *cst1, *cst2;
2748 int cmp;
2749
2750 if (!qp1 || !qp2)
2751 goto error;
2752 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2753 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2754 cst1 = isl_upoly_as_cst(qp1->upoly);
2755 cst2 = isl_upoly_as_cst(qp2->upoly);
2756 cmp = isl_upoly_cmp(cst1, cst2);
2757
2758 if (cmp <= 0) {
2759 isl_qpolynomial_free(qp2);
2760 } else {
2761 isl_qpolynomial_free(qp1);
2762 qp1 = qp2;
2763 }
2764 return qp1;
2765 error:
2766 isl_qpolynomial_free(qp1);
2767 isl_qpolynomial_free(qp2);
2768 return NULL;
2769 }
2770
2771 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2772 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2773 {
2774 struct isl_upoly_cst *cst1, *cst2;
2775 int cmp;
2776
2777 if (!qp1 || !qp2)
2778 goto error;
2779 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2780 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2781 cst1 = isl_upoly_as_cst(qp1->upoly);
2782 cst2 = isl_upoly_as_cst(qp2->upoly);
2783 cmp = isl_upoly_cmp(cst1, cst2);
2784
2785 if (cmp >= 0) {
2786 isl_qpolynomial_free(qp2);
2787 } else {
2788 isl_qpolynomial_free(qp1);
2789 qp1 = qp2;
2790 }
2791 return qp1;
2792 error:
2793 isl_qpolynomial_free(qp1);
2794 isl_qpolynomial_free(qp2);
2795 return NULL;
2796 }
2797
2798 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2799 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2800 unsigned first, unsigned n)
2801 {
2802 unsigned total;
2803 unsigned g_pos;
2804 int *exp;
2805
2806 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2807 return qp;
2808
2809 qp = isl_qpolynomial_cow(qp);
2810 if (!qp)
2811 return NULL;
2812
2813 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2814 goto error);
2815
2816 g_pos = pos(qp->dim, type) + first;
2817
2818 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2819 if (!qp->div)
2820 goto error;
2821
2822 total = qp->div->n_col - 2;
2823 if (total > g_pos) {
2824 int i;
2825 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2826 if (!exp)
2827 goto error;
2828 for (i = 0; i < total - g_pos; ++i)
2829 exp[i] = i + n;
2830 qp->upoly = expand(qp->upoly, exp, g_pos);
2831 free(exp);
2832 if (!qp->upoly)
2833 goto error;
2834 }
2835
2836 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2837 if (!qp->dim)
2838 goto error;
2839
2840 return qp;
2841 error:
2842 isl_qpolynomial_free(qp);
2843 return NULL;
2844 }
2845
2846 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2847 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2848 {
2849 unsigned pos;
2850
2851 pos = isl_qpolynomial_dim(qp, type);
2852
2853 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2854 }
2855
2856 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2857 __isl_take isl_pw_qpolynomial *pwqp,
2858 enum isl_dim_type type, unsigned n)
2859 {
2860 unsigned pos;
2861
2862 pos = isl_pw_qpolynomial_dim(pwqp, type);
2863
2864 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2865 }
2866
2867 static int *reordering_move(isl_ctx *ctx,
2868 unsigned len, unsigned dst, unsigned src, unsigned n)
2869 {
2870 int i;
2871 int *reordering;
2872
2873 reordering = isl_alloc_array(ctx, int, len);
2874 if (!reordering)
2875 return NULL;
2876
2877 if (dst <= src) {
2878 for (i = 0; i < dst; ++i)
2879 reordering[i] = i;
2880 for (i = 0; i < n; ++i)
2881 reordering[src + i] = dst + i;
2882 for (i = 0; i < src - dst; ++i)
2883 reordering[dst + i] = dst + n + i;
2884 for (i = 0; i < len - src - n; ++i)
2885 reordering[src + n + i] = src + n + i;
2886 } else {
2887 for (i = 0; i < src; ++i)
2888 reordering[i] = i;
2889 for (i = 0; i < n; ++i)
2890 reordering[src + i] = dst + i;
2891 for (i = 0; i < dst - src; ++i)
2892 reordering[src + n + i] = src + i;
2893 for (i = 0; i < len - dst - n; ++i)
2894 reordering[dst + n + i] = dst + n + i;
2895 }
2896
2897 return reordering;
2898 }
2899
2900 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2901 __isl_take isl_qpolynomial *qp,
2902 enum isl_dim_type dst_type, unsigned dst_pos,
2903 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2904 {
2905 unsigned g_dst_pos;
2906 unsigned g_src_pos;
2907 int *reordering;
2908
2909 qp = isl_qpolynomial_cow(qp);
2910 if (!qp)
2911 return NULL;
2912
2913 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2914 goto error);
2915
2916 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2917 g_src_pos = pos(qp->dim, src_type) + src_pos;
2918 if (dst_type > src_type)
2919 g_dst_pos -= n;
2920
2921 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2922 if (!qp->div)
2923 goto error;
2924 qp = sort_divs(qp);
2925 if (!qp)
2926 goto error;
2927
2928 reordering = reordering_move(qp->dim->ctx,
2929 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2930 if (!reordering)
2931 goto error;
2932
2933 qp->upoly = reorder(qp->upoly, reordering);
2934 free(reordering);
2935 if (!qp->upoly)
2936 goto error;
2937
2938 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2939 if (!qp->dim)
2940 goto error;
2941
2942 return qp;
2943 error:
2944 isl_qpolynomial_free(qp);
2945 return NULL;
2946 }
2947
2948 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2949 isl_int *f, isl_int denom)
2950 {
2951 struct isl_upoly *up;
2952
2953 if (!dim)
2954 return NULL;
2955
2956 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2957
2958 return isl_qpolynomial_alloc(dim, 0, up);
2959 }
2960
2961 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
2962 {
2963 isl_ctx *ctx;
2964 struct isl_upoly *up;
2965 isl_qpolynomial *qp;
2966
2967 if (!aff)
2968 return NULL;
2969
2970 ctx = isl_aff_get_ctx(aff);
2971 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
2972 aff->v->size - 1);
2973
2974 qp = isl_qpolynomial_alloc(isl_aff_get_dim(aff),
2975 aff->ls->div->n_row, up);
2976 if (!qp)
2977 goto error;
2978
2979 isl_mat_free(qp->div);
2980 qp->div = isl_mat_copy(aff->ls->div);
2981 qp->div = isl_mat_cow(qp->div);
2982 if (!qp->div)
2983 goto error;
2984
2985 isl_aff_free(aff);
2986 qp = reduce_divs(qp);
2987 qp = remove_redundant_divs(qp);
2988 return qp;
2989 error:
2990 isl_aff_free(aff);
2991 return NULL;
2992 }
2993
2994 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2995 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2996 {
2997 isl_aff *aff;
2998
2999 aff = isl_constraint_get_bound(c, type, pos);
3000 isl_constraint_free(c);
3001 return isl_qpolynomial_from_aff(aff);
3002 }
3003
3004 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3005 * in "qp" by subs[i].
3006 */
3007 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3008 __isl_take isl_qpolynomial *qp,
3009 enum isl_dim_type type, unsigned first, unsigned n,
3010 __isl_keep isl_qpolynomial **subs)
3011 {
3012 int i;
3013 struct isl_upoly **ups;
3014
3015 if (n == 0)
3016 return qp;
3017
3018 qp = isl_qpolynomial_cow(qp);
3019 if (!qp)
3020 return NULL;
3021 for (i = 0; i < n; ++i)
3022 if (!subs[i])
3023 goto error;
3024
3025 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
3026 goto error);
3027
3028 for (i = 0; i < n; ++i)
3029 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
3030 goto error);
3031
3032 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3033 for (i = 0; i < n; ++i)
3034 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3035
3036 first += pos(qp->dim, type);
3037
3038 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3039 if (!ups)
3040 goto error;
3041 for (i = 0; i < n; ++i)
3042 ups[i] = subs[i]->upoly;
3043
3044 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3045
3046 free(ups);
3047
3048 if (!qp->upoly)
3049 goto error;
3050
3051 return qp;
3052 error:
3053 isl_qpolynomial_free(qp);
3054 return NULL;
3055 }
3056
3057 /* Extend "bset" with extra set dimensions for each integer division
3058 * in "qp" and then call "fn" with the extended bset and the polynomial
3059 * that results from replacing each of the integer divisions by the
3060 * corresponding extra set dimension.
3061 */
3062 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3063 __isl_keep isl_basic_set *bset,
3064 int (*fn)(__isl_take isl_basic_set *bset,
3065 __isl_take isl_qpolynomial *poly, void *user), void *user)
3066 {
3067 isl_dim *dim;
3068 isl_mat *div;
3069 isl_qpolynomial *poly;
3070
3071 if (!qp || !bset)
3072 goto error;
3073 if (qp->div->n_row == 0)
3074 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3075 user);
3076
3077 div = isl_mat_copy(qp->div);
3078 dim = isl_dim_copy(qp->dim);
3079 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3080 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3081 bset = isl_basic_set_copy(bset);
3082 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3083 bset = add_div_constraints(bset, div);
3084
3085 return fn(bset, poly, user);
3086 error:
3087 return -1;
3088 }
3089
3090 /* Return total degree in variables first (inclusive) up to last (exclusive).
3091 */
3092 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3093 {
3094 int deg = -1;
3095 int i;
3096 struct isl_upoly_rec *rec;
3097
3098 if (!up)
3099 return -2;
3100 if (isl_upoly_is_zero(up))
3101 return -1;
3102 if (isl_upoly_is_cst(up) || up->var < first)
3103 return 0;
3104
3105 rec = isl_upoly_as_rec(up);
3106 if (!rec)
3107 return -2;
3108
3109 for (i = 0; i < rec->n; ++i) {
3110 int d;
3111
3112 if (isl_upoly_is_zero(rec->p[i]))
3113 continue;
3114 d = isl_upoly_degree(rec->p[i], first, last);
3115 if (up->var < last)
3116 d += i;
3117 if (d > deg)
3118 deg = d;
3119 }
3120
3121 return deg;
3122 }
3123
3124 /* Return total degree in set variables.
3125 */
3126 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3127 {
3128 unsigned ovar;
3129 unsigned nvar;
3130
3131 if (!poly)
3132 return -2;
3133
3134 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3135 nvar = isl_dim_size(poly->dim, isl_dim_set);
3136 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3137 }
3138
3139 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3140 unsigned pos, int deg)
3141 {
3142 int i;
3143 struct isl_upoly_rec *rec;
3144
3145 if (!up)
3146 return NULL;
3147
3148 if (isl_upoly_is_cst(up) || up->var < pos) {
3149 if (deg == 0)
3150 return isl_upoly_copy(up);
3151 else
3152 return isl_upoly_zero(up->ctx);
3153 }
3154
3155 rec = isl_upoly_as_rec(up);
3156 if (!rec)
3157 return NULL;
3158
3159 if (up->var == pos) {
3160 if (deg < rec->n)
3161 return isl_upoly_copy(rec->p[deg]);
3162 else
3163 return isl_upoly_zero(up->ctx);
3164 }
3165
3166 up = isl_upoly_copy(up);
3167 up = isl_upoly_cow(up);
3168 rec = isl_upoly_as_rec(up);
3169 if (!rec)
3170 goto error;
3171
3172 for (i = 0; i < rec->n; ++i) {
3173 struct isl_upoly *t;
3174 t = isl_upoly_coeff(rec->p[i], pos, deg);
3175 if (!t)
3176 goto error;
3177 isl_upoly_free(rec->p[i]);
3178 rec->p[i] = t;
3179 }
3180
3181 return up;
3182 error:
3183 isl_upoly_free(up);
3184 return NULL;
3185 }
3186
3187 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3188 */
3189 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3190 __isl_keep isl_qpolynomial *qp,
3191 enum isl_dim_type type, unsigned t_pos, int deg)
3192 {
3193 unsigned g_pos;
3194 struct isl_upoly *up;
3195 isl_qpolynomial *c;
3196
3197 if (!qp)
3198 return NULL;
3199
3200 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3201 return NULL);
3202
3203 g_pos = pos(qp->dim, type) + t_pos;
3204 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3205
3206 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3207 if (!c)
3208 return NULL;
3209 isl_mat_free(c->div);
3210 c->div = isl_mat_copy(qp->div);
3211 if (!c->div)
3212 goto error;
3213 return c;
3214 error:
3215 isl_qpolynomial_free(c);
3216 return NULL;
3217 }
3218
3219 /* Homogenize the polynomial in the variables first (inclusive) up to
3220 * last (exclusive) by inserting powers of variable first.
3221 * Variable first is assumed not to appear in the input.
3222 */
3223 __isl_give struct isl_upoly *isl_upoly_homogenize(
3224 __isl_take struct isl_upoly *up, int deg, int target,
3225 int first, int last)
3226 {
3227 int i;
3228 struct isl_upoly_rec *rec;
3229
3230 if (!up)
3231 return NULL;
3232 if (isl_upoly_is_zero(up))
3233 return up;
3234 if (deg == target)
3235 return up;
3236 if (isl_upoly_is_cst(up) || up->var < first) {
3237 struct isl_upoly *hom;
3238
3239 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3240 if (!hom)
3241 goto error;
3242 rec = isl_upoly_as_rec(hom);
3243 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3244
3245 return hom;
3246 }
3247
3248 up = isl_upoly_cow(up);
3249 rec = isl_upoly_as_rec(up);
3250 if (!rec)
3251 goto error;
3252
3253 for (i = 0; i < rec->n; ++i) {
3254 if (isl_upoly_is_zero(rec->p[i]))
3255 continue;
3256 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3257 up->var < last ? deg + i : i, target,
3258 first, last);
3259 if (!rec->p[i])
3260 goto error;
3261 }
3262
3263 return up;
3264 error:
3265 isl_upoly_free(up);
3266 return NULL;
3267 }
3268
3269 /* Homogenize the polynomial in the set variables by introducing
3270 * powers of an extra set variable at position 0.
3271 */
3272 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3273 __isl_take isl_qpolynomial *poly)
3274 {
3275 unsigned ovar;
3276 unsigned nvar;
3277 int deg = isl_qpolynomial_degree(poly);
3278
3279 if (deg < -1)
3280 goto error;
3281
3282 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3283 poly = isl_qpolynomial_cow(poly);
3284 if (!poly)
3285 goto error;
3286
3287 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3288 nvar = isl_dim_size(poly->dim, isl_dim_set);
3289 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3290 ovar, ovar + nvar);
3291 if (!poly->upoly)
3292 goto error;
3293
3294 return poly;
3295 error:
3296 isl_qpolynomial_free(poly);
3297 return NULL;
3298 }
3299
3300 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3301 __isl_take isl_mat *div)
3302 {
3303 isl_term *term;
3304 int n;
3305
3306 if (!dim || !div)
3307 goto error;
3308
3309 n = isl_dim_total(dim) + div->n_row;
3310
3311 term = isl_calloc(dim->ctx, struct isl_term,
3312 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3313 if (!term)
3314 goto error;
3315
3316 term->ref = 1;
3317 term->dim = dim;
3318 term->div = div;
3319 isl_int_init(term->n);
3320 isl_int_init(term->d);
3321
3322 return term;
3323 error:
3324 isl_dim_free(dim);
3325 isl_mat_free(div);
3326 return NULL;
3327 }
3328
3329 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3330 {
3331 if (!term)
3332 return NULL;
3333
3334 term->ref++;
3335 return term;
3336 }
3337
3338 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3339 {
3340 int i;
3341 isl_term *dup;
3342 unsigned total;
3343
3344 if (term)
3345 return NULL;
3346
3347 total = isl_dim_total(term->dim) + term->div->n_row;
3348
3349 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3350 if (!dup)
3351 return NULL;
3352
3353 isl_int_set(dup->n, term->n);
3354 isl_int_set(dup->d, term->d);
3355
3356 for (i = 0; i < total; ++i)
3357 dup->pow[i] = term->pow[i];
3358
3359 return dup;
3360 }
3361
3362 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3363 {
3364 if (!term)
3365 return NULL;
3366
3367 if (term->ref == 1)
3368 return term;
3369 term->ref--;
3370 return isl_term_dup(term);
3371 }
3372
3373 void isl_term_free(__isl_take isl_term *term)
3374 {
3375 if (!term)
3376 return;
3377
3378 if (--term->ref > 0)
3379 return;
3380
3381 isl_dim_free(term->dim);
3382 isl_mat_free(term->div);
3383 isl_int_clear(term->n);
3384 isl_int_clear(term->d);
3385 free(term);
3386 }
3387
3388 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3389 {
3390 if (!term)
3391 return 0;
3392
3393 switch (type) {
3394 case isl_dim_param:
3395 case isl_dim_in:
3396 case isl_dim_out: return isl_dim_size(term->dim, type);
3397 case isl_dim_div: return term->div->n_row;
3398 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3399 default: return 0;
3400 }
3401 }
3402
3403 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3404 {
3405 return term ? term->dim->ctx : NULL;
3406 }
3407
3408 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3409 {
3410 if (!term)
3411 return;
3412 isl_int_set(*n, term->n);
3413 }
3414
3415 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3416 {
3417 if (!term)
3418 return;
3419 isl_int_set(*d, term->d);
3420 }
3421
3422 int isl_term_get_exp(__isl_keep isl_term *term,
3423 enum isl_dim_type type, unsigned pos)
3424 {
3425 if (!term)
3426 return -1;
3427
3428 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3429
3430 if (type >= isl_dim_set)
3431 pos += isl_dim_size(term->dim, isl_dim_param);
3432 if (type >= isl_dim_div)
3433 pos += isl_dim_size(term->dim, isl_dim_set);
3434
3435 return term->pow[pos];
3436 }
3437
3438 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3439 {
3440 isl_basic_map *bmap;
3441 unsigned total;
3442 int k;
3443
3444 if (!term)
3445 return NULL;
3446
3447 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3448 return NULL);
3449
3450 total = term->div->n_col - term->div->n_row - 2;
3451 /* No nested divs for now */
3452 isl_assert(term->dim->ctx,
3453 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3454 term->div->n_row) == -1,
3455 return NULL);
3456
3457 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3458 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3459 goto error;
3460
3461 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3462
3463 return isl_basic_map_div(bmap, k);
3464 error:
3465 isl_basic_map_free(bmap);
3466 return NULL;
3467 }
3468
3469 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3470 int (*fn)(__isl_take isl_term *term, void *user),
3471 __isl_take isl_term *term, void *user)
3472 {
3473 int i;
3474 struct isl_upoly_rec *rec;
3475
3476 if (!up || !term)
3477 goto error;
3478
3479 if (isl_upoly_is_zero(up))
3480 return term;
3481
3482 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3483 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3484 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3485
3486 if (isl_upoly_is_cst(up)) {
3487 struct isl_upoly_cst *cst;
3488 cst = isl_upoly_as_cst(up);
3489 if (!cst)
3490 goto error;
3491 term = isl_term_cow(term);
3492 if (!term)
3493 goto error;
3494 isl_int_set(term->n, cst->n);
3495 isl_int_set(term->d, cst->d);
3496 if (fn(isl_term_copy(term), user) < 0)
3497 goto error;
3498 return term;
3499 }
3500
3501 rec = isl_upoly_as_rec(up);
3502 if (!rec)
3503 goto error;
3504
3505 for (i = 0; i < rec->n; ++i) {
3506 term = isl_term_cow(term);
3507 if (!term)
3508 goto error;
3509 term->pow[up->var] = i;
3510 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3511 if (!term)
3512 goto error;
3513 }
3514 term->pow[up->var] = 0;
3515
3516 return term;
3517 error:
3518 isl_term_free(term);
3519 return NULL;
3520 }
3521
3522 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3523 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3524 {
3525 isl_term *term;
3526
3527 if (!qp)
3528 return -1;
3529
3530 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3531 if (!term)
3532 return -1;
3533
3534 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3535
3536 isl_term_free(term);
3537
3538 return term ? 0 : -1;
3539 }
3540
3541 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3542 {
3543 struct isl_upoly *up;
3544 isl_qpolynomial *qp;
3545 int i, n;
3546
3547 if (!term)
3548 return NULL;
3549
3550 n = isl_dim_total(term->dim) + term->div->n_row;
3551
3552 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3553 for (i = 0; i < n; ++i) {
3554 if (!term->pow[i])
3555 continue;
3556 up = isl_upoly_mul(up,
3557 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3558 }
3559
3560 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3561 if (!qp)
3562 goto error;
3563 isl_mat_free(qp->div);
3564 qp->div = isl_mat_copy(term->div);
3565 if (!qp->div)
3566 goto error;
3567
3568 isl_term_free(term);
3569 return qp;
3570 error:
3571 isl_qpolynomial_free(qp);
3572 isl_term_free(term);
3573 return NULL;
3574 }
3575
3576 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3577 __isl_take isl_dim *dim)
3578 {
3579 int i;
3580 int extra;
3581 unsigned total;
3582
3583 if (!qp || !dim)
3584 goto error;
3585
3586 if (isl_dim_equal(qp->dim, dim)) {
3587 isl_dim_free(dim);
3588 return qp;
3589 }
3590
3591 qp = isl_qpolynomial_cow(qp);
3592 if (!qp)
3593 goto error;
3594
3595 extra = isl_dim_size(dim, isl_dim_set) -
3596 isl_dim_size(qp->dim, isl_dim_set);
3597 total = isl_dim_total(qp->dim);
3598 if (qp->div->n_row) {
3599 int *exp;
3600
3601 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3602 if (!exp)
3603 goto error;
3604 for (i = 0; i < qp->div->n_row; ++i)
3605 exp[i] = extra + i;
3606 qp->upoly = expand(qp->upoly, exp, total);
3607 free(exp);
3608 if (!qp->upoly)
3609 goto error;
3610 }
3611 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3612 if (!qp->div)
3613 goto error;
3614 for (i = 0; i < qp->div->n_row; ++i)
3615 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3616
3617 isl_dim_free(qp->dim);
3618 qp->dim = dim;
3619
3620 return qp;
3621 error:
3622 isl_dim_free(dim);
3623 isl_qpolynomial_free(qp);
3624 return NULL;
3625 }
3626
3627 /* For each parameter or variable that does not appear in qp,
3628 * first eliminate the variable from all constraints and then set it to zero.
3629 */
3630 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3631 __isl_keep isl_qpolynomial *qp)
3632 {
3633 int *active = NULL;
3634 int i;
3635 int d;
3636 unsigned nparam;
3637 unsigned nvar;
3638
3639 if (!set || !qp)
3640 goto error;
3641
3642 d = isl_dim_total(set->dim);
3643 active = isl_calloc_array(set->ctx, int, d);
3644 if (set_active(qp, active) < 0)
3645 goto error;
3646
3647 for (i = 0; i < d; ++i)
3648 if (!active[i])
3649 break;
3650
3651 if (i == d) {
3652 free(active);
3653 return set;
3654 }
3655
3656 nparam = isl_dim_size(set->dim, isl_dim_param);
3657 nvar = isl_dim_size(set->dim, isl_dim_set);
3658 for (i = 0; i < nparam; ++i) {
3659 if (active[i])
3660 continue;
3661 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3662 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3663 }
3664 for (i = 0; i < nvar; ++i) {
3665 if (active[nparam + i])
3666 continue;
3667 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3668 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3669 }
3670
3671 free(active);
3672
3673 return set;
3674 error:
3675 free(active);
3676 isl_set_free(set);
3677 return NULL;
3678 }
3679
3680 struct isl_opt_data {
3681 isl_qpolynomial *qp;
3682 int first;
3683 isl_qpolynomial *opt;
3684 int max;
3685 };
3686
3687 static int opt_fn(__isl_take isl_point *pnt, void *user)
3688 {
3689 struct isl_opt_data *data = (struct isl_opt_data *)user;
3690 isl_qpolynomial *val;
3691
3692 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3693 if (data->first) {
3694 data->first = 0;
3695 data->opt = val;
3696 } else if (data->max) {
3697 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3698 } else {
3699 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3700 }
3701
3702 return 0;
3703 }
3704
3705 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3706 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3707 {
3708 struct isl_opt_data data = { NULL, 1, NULL, max };
3709
3710 if (!set || !qp)
3711 goto error;
3712
3713 if (isl_upoly_is_cst(qp->upoly)) {
3714 isl_set_free(set);
3715 return qp;
3716 }
3717
3718 set = fix_inactive(set, qp);
3719
3720 data.qp = qp;
3721 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3722 goto error;
3723
3724 if (data.first)
3725 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3726
3727 isl_set_free(set);
3728 isl_qpolynomial_free(qp);
3729 return data.opt;
3730 error:
3731 isl_set_free(set);
3732 isl_qpolynomial_free(qp);
3733 isl_qpolynomial_free(data.opt);
3734 return NULL;
3735 }
3736
3737 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3738 __isl_take isl_morph *morph)
3739 {
3740 int i;
3741 int n_sub;
3742 isl_ctx *ctx;
3743 struct isl_upoly **subs;
3744 isl_mat *mat;
3745
3746 qp = isl_qpolynomial_cow(qp);
3747 if (!qp || !morph)
3748 goto error;
3749
3750 ctx = qp->dim->ctx;
3751 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3752
3753 n_sub = morph->inv->n_row - 1;
3754 if (morph->inv->n_row != morph->inv->n_col)
3755 n_sub += qp->div->n_row;
3756 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3757 if (!subs)
3758 goto error;
3759
3760 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3761 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3762 morph->inv->row[0][0], morph->inv->n_col);
3763 if (morph->inv->n_row != morph->inv->n_col)
3764 for (i = 0; i < qp->div->n_row; ++i)
3765 subs[morph->inv->n_row - 1 + i] =
3766 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3767
3768 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3769
3770 for (i = 0; i < n_sub; ++i)
3771 isl_upoly_free(subs[i]);
3772 free(subs);
3773
3774 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3775 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3776 qp->div = isl_mat_product(qp->div, mat);
3777 isl_dim_free(qp->dim);
3778 qp->dim = isl_dim_copy(morph->ran->dim);
3779
3780 if (!qp->upoly || !qp->div || !qp->dim)
3781 goto error;
3782
3783 isl_morph_free(morph);
3784
3785 return qp;
3786 error:
3787 isl_qpolynomial_free(qp);
3788 isl_morph_free(morph);
3789 return NULL;
3790 }
3791
3792 static int neg_entry(void **entry, void *user)
3793 {
3794 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3795
3796 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3797
3798 return *pwqp ? 0 : -1;
3799 }
3800
3801 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3802 __isl_take isl_union_pw_qpolynomial *upwqp)
3803 {
3804 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3805 if (!upwqp)
3806 return NULL;
3807
3808 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3809 &neg_entry, NULL) < 0)
3810 goto error;
3811
3812 return upwqp;
3813 error:
3814 isl_union_pw_qpolynomial_free(upwqp);
3815 return NULL;
3816 }
3817
3818 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3819 __isl_take isl_union_pw_qpolynomial *upwqp1,
3820 __isl_take isl_union_pw_qpolynomial *upwqp2)
3821 {
3822 return isl_union_pw_qpolynomial_add(upwqp1,
3823 isl_union_pw_qpolynomial_neg(upwqp2));
3824 }
3825
3826 static int mul_entry(void **entry, void *user)
3827 {
3828 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3829 uint32_t hash;
3830 struct isl_hash_table_entry *entry2;
3831 isl_pw_qpolynomial *pwpq = *entry;
3832 int empty;
3833
3834 hash = isl_dim_get_hash(pwpq->dim);
3835 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3836 hash, &has_dim, pwpq->dim, 0);
3837 if (!entry2)
3838 return 0;
3839
3840 pwpq = isl_pw_qpolynomial_copy(pwpq);
3841 pwpq = isl_pw_qpolynomial_mul(pwpq,
3842 isl_pw_qpolynomial_copy(entry2->data));
3843
3844 empty = isl_pw_qpolynomial_is_zero(pwpq);
3845 if (empty < 0) {
3846 isl_pw_qpolynomial_free(pwpq);
3847 return -1;
3848 }
3849 if (empty) {
3850 isl_pw_qpolynomial_free(pwpq);
3851 return 0;
3852 }
3853
3854 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3855
3856 return 0;
3857 }
3858
3859 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3860 __isl_take isl_union_pw_qpolynomial *upwqp1,
3861 __isl_take isl_union_pw_qpolynomial *upwqp2)
3862 {
3863 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3864 }
3865
3866 /* Reorder the columns of the given div definitions according to the
3867 * given reordering.
3868 */
3869 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3870 __isl_take isl_reordering *r)
3871 {
3872 int i, j;
3873 isl_mat *mat;
3874 int extra;
3875
3876 if (!div || !r)
3877 goto error;
3878
3879 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3880 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3881 if (!mat)
3882 goto error;
3883
3884 for (i = 0; i < div->n_row; ++i) {
3885 isl_seq_cpy(mat->row[i], div->row[i], 2);
3886 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3887 for (j = 0; j < r->len; ++j)
3888 isl_int_set(mat->row[i][2 + r->pos[j]],
3889 div->row[i][2 + j]);
3890 }
3891
3892 isl_reordering_free(r);
3893 isl_mat_free(div);
3894 return mat;
3895 error:
3896 isl_reordering_free(r);
3897 isl_mat_free(div);
3898 return NULL;
3899 }
3900
3901 /* Reorder the dimension of "qp" according to the given reordering.
3902 */
3903 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3904 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3905 {
3906 qp = isl_qpolynomial_cow(qp);
3907 if (!qp)
3908 goto error;
3909
3910 r = isl_reordering_extend(r, qp->div->n_row);
3911 if (!r)
3912 goto error;
3913
3914 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3915 if (!qp->div)
3916 goto error;
3917
3918 qp->upoly = reorder(qp->upoly, r->pos);
3919 if (!qp->upoly)
3920 goto error;
3921
3922 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3923
3924 isl_reordering_free(r);
3925 return qp;
3926 error:
3927 isl_qpolynomial_free(qp);
3928 isl_reordering_free(r);
3929 return NULL;
3930 }
3931
3932 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3933 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3934 {
3935 if (!qp || !model)
3936 goto error;
3937
3938 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
3939 isl_reordering *exp;
3940
3941 model = isl_dim_drop(model, isl_dim_in,
3942 0, isl_dim_size(model, isl_dim_in));
3943 model = isl_dim_drop(model, isl_dim_out,
3944 0, isl_dim_size(model, isl_dim_out));
3945 exp = isl_parameter_alignment_reordering(qp->dim, model);
3946 exp = isl_reordering_extend_dim(exp,
3947 isl_qpolynomial_get_dim(qp));
3948 qp = isl_qpolynomial_realign(qp, exp);
3949 }
3950
3951 isl_dim_free(model);
3952 return qp;
3953 error:
3954 isl_dim_free(model);
3955 isl_qpolynomial_free(qp);
3956 return NULL;
3957 }
3958
3959 struct isl_split_periods_data {
3960 int max_periods;
3961 isl_pw_qpolynomial *res;
3962 };
3963
3964 /* Create a slice where the integer division "div" has the fixed value "v".
3965 * In particular, if "div" refers to floor(f/m), then create a slice
3966 *
3967 * m v <= f <= m v + (m - 1)
3968 *
3969 * or
3970 *
3971 * f - m v >= 0
3972 * -f + m v + (m - 1) >= 0
3973 */
3974 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3975 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3976 {
3977 int total;
3978 isl_basic_set *bset = NULL;
3979 int k;
3980
3981 if (!dim || !qp)
3982 goto error;
3983
3984 total = isl_dim_total(dim);
3985 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3986
3987 k = isl_basic_set_alloc_inequality(bset);
3988 if (k < 0)
3989 goto error;
3990 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3991 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3992
3993 k = isl_basic_set_alloc_inequality(bset);
3994 if (k < 0)
3995 goto error;
3996 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3997 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3998 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3999 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4000
4001 isl_dim_free(dim);
4002 return isl_set_from_basic_set(bset);
4003 error:
4004 isl_basic_set_free(bset);
4005 isl_dim_free(dim);
4006 return NULL;
4007 }
4008
4009 static int split_periods(__isl_take isl_set *set,
4010 __isl_take isl_qpolynomial *qp, void *user);
4011
4012 /* Create a slice of the domain "set" such that integer division "div"
4013 * has the fixed value "v" and add the results to data->res,
4014 * replacing the integer division by "v" in "qp".
4015 */
4016 static int set_div(__isl_take isl_set *set,
4017 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4018 struct isl_split_periods_data *data)
4019 {
4020 int i;
4021 int total;
4022 isl_set *slice;
4023 struct isl_upoly *cst;
4024
4025 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
4026 set = isl_set_intersect(set, slice);
4027
4028 if (!qp)
4029 goto error;
4030
4031 total = isl_dim_total(qp->dim);
4032
4033 for (i = div + 1; i < qp->div->n_row; ++i) {
4034 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4035 continue;
4036 isl_int_addmul(qp->div->row[i][1],
4037 qp->div->row[i][2 + total + div], v);
4038 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4039 }
4040
4041 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4042 qp = substitute_div(qp, div, cst);
4043
4044 return split_periods(set, qp, data);
4045 error:
4046 isl_set_free(set);
4047 isl_qpolynomial_free(qp);
4048 return -1;
4049 }
4050
4051 /* Split the domain "set" such that integer division "div"
4052 * has a fixed value (ranging from "min" to "max") on each slice
4053 * and add the results to data->res.
4054 */
4055 static int split_div(__isl_take isl_set *set,
4056 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4057 struct isl_split_periods_data *data)
4058 {
4059 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4060 isl_set *set_i = isl_set_copy(set);
4061 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4062
4063 if (set_div(set_i, qp_i, div, min, data) < 0)
4064 goto error;
4065 }
4066 isl_set_free(set);
4067 isl_qpolynomial_free(qp);
4068 return 0;
4069 error:
4070 isl_set_free(set);
4071 isl_qpolynomial_free(qp);
4072 return -1;
4073 }
4074
4075 /* If "qp" refers to any integer division
4076 * that can only attain "max_periods" distinct values on "set"
4077 * then split the domain along those distinct values.
4078 * Add the results (or the original if no splitting occurs)
4079 * to data->res.
4080 */
4081 static int split_periods(__isl_take isl_set *set,
4082 __isl_take isl_qpolynomial *qp, void *user)
4083 {
4084 int i;
4085 isl_pw_qpolynomial *pwqp;
4086 struct isl_split_periods_data *data;
4087 isl_int min, max;
4088 int total;
4089 int r = 0;
4090
4091 data = (struct isl_split_periods_data *)user;
4092
4093 if (!set || !qp)
4094 goto error;
4095
4096 if (qp->div->n_row == 0) {
4097 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4098 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4099 return 0;
4100 }
4101
4102 isl_int_init(min);
4103 isl_int_init(max);
4104 total = isl_dim_total(qp->dim);
4105 for (i = 0; i < qp->div->n_row; ++i) {
4106 enum isl_lp_result lp_res;
4107
4108 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4109 qp->div->n_row) != -1)
4110 continue;
4111
4112 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4113 set->ctx->one, &min, NULL, NULL);
4114 if (lp_res == isl_lp_error)
4115 goto error2;
4116 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4117 continue;
4118 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4119
4120 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4121 set->ctx->one, &max, NULL, NULL);
4122 if (lp_res == isl_lp_error)
4123 goto error2;
4124 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4125 continue;
4126 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4127
4128 isl_int_sub(max, max, min);
4129 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4130 isl_int_add(max, max, min);
4131 break;
4132 }
4133 }
4134
4135 if (i < qp->div->n_row) {
4136 r = split_div(set, qp, i, min, max, data);
4137 } else {
4138 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4139 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4140 }
4141
4142 isl_int_clear(max);
4143 isl_int_clear(min);
4144
4145 return r;
4146 error2:
4147 isl_int_clear(max);
4148 isl_int_clear(min);
4149 error:
4150 isl_set_free(set);
4151 isl_qpolynomial_free(qp);
4152 return -1;
4153 }
4154
4155 /* If any quasi-polynomial in pwqp refers to any integer division
4156 * that can only attain "max_periods" distinct values on its domain
4157 * then split the domain along those distinct values.
4158 */
4159 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4160 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4161 {
4162 struct isl_split_periods_data data;
4163
4164 data.max_periods = max_periods;
4165 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4166
4167 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4168 goto error;
4169
4170 isl_pw_qpolynomial_free(pwqp);
4171
4172 return data.res;
4173 error:
4174 isl_pw_qpolynomial_free(data.res);
4175 isl_pw_qpolynomial_free(pwqp);
4176 return NULL;
4177 }
4178
4179 /* Construct a piecewise quasipolynomial that is constant on the given
4180 * domain. In particular, it is
4181 * 0 if cst == 0
4182 * 1 if cst == 1
4183 * infinity if cst == -1
4184 */
4185 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4186 __isl_take isl_basic_set *bset, int cst)
4187 {
4188 isl_dim *dim;
4189 isl_qpolynomial *qp;
4190
4191 if (!bset)
4192 return NULL;
4193
4194 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4195 dim = isl_basic_set_get_dim(bset);
4196 if (cst < 0)
4197 qp = isl_qpolynomial_infty(dim);
4198 else if (cst == 0)
4199 qp = isl_qpolynomial_zero(dim);
4200 else
4201 qp = isl_qpolynomial_one(dim);
4202 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4203 }
4204
4205 /* Factor bset, call fn on each of the factors and return the product.
4206 *
4207 * If no factors can be found, simply call fn on the input.
4208 * Otherwise, construct the factors based on the factorizer,
4209 * call fn on each factor and compute the product.
4210 */
4211 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4212 __isl_take isl_basic_set *bset,
4213 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4214 {
4215 int i, n;
4216 isl_dim *dim;
4217 isl_set *set;
4218 isl_factorizer *f;
4219 isl_qpolynomial *qp;
4220 isl_pw_qpolynomial *pwqp;
4221 unsigned nparam;
4222 unsigned nvar;
4223
4224 f = isl_basic_set_factorizer(bset);
4225 if (!f)
4226 goto error;
4227 if (f->n_group == 0) {
4228 isl_factorizer_free(f);
4229 return fn(bset);
4230 }
4231
4232 nparam = isl_basic_set_dim(bset, isl_dim_param);
4233 nvar = isl_basic_set_dim(bset, isl_dim_set);
4234
4235 dim = isl_basic_set_get_dim(bset);
4236 dim = isl_dim_domain(dim);
4237 set = isl_set_universe(isl_dim_copy(dim));
4238 qp = isl_qpolynomial_one(dim);
4239 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4240
4241 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4242
4243 for (i = 0, n = 0; i < f->n_group; ++i) {
4244 isl_basic_set *bset_i;
4245 isl_pw_qpolynomial *pwqp_i;
4246
4247 bset_i = isl_basic_set_copy(bset);
4248 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4249 nparam + n + f->len[i], nvar - n - f->len[i]);
4250 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4251 nparam, n);
4252 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4253 n + f->len[i], nvar - n - f->len[i]);
4254 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4255
4256 pwqp_i = fn(bset_i);
4257 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4258
4259 n += f->len[i];
4260 }
4261
4262 isl_basic_set_free(bset);
4263 isl_factorizer_free(f);
4264
4265 return pwqp;
4266 error:
4267 isl_basic_set_free(bset);
4268 return NULL;
4269 }
4270
4271 /* Factor bset, call fn on each of the factors and return the product.
4272 * The function is assumed to evaluate to zero on empty domains,
4273 * to one on zero-dimensional domains and to infinity on unbounded domains
4274 * and will not be called explicitly on zero-dimensional or unbounded domains.
4275 *
4276 * We first check for some special cases and remove all equalities.
4277 * Then we hand over control to compressed_multiplicative_call.
4278 */
4279 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4280 __isl_take isl_basic_set *bset,
4281 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4282 {
4283 int bounded;
4284 isl_morph *morph;
4285 isl_pw_qpolynomial *pwqp;
4286 unsigned orig_nvar, final_nvar;
4287
4288 if (!bset)
4289 return NULL;
4290
4291 if (isl_basic_set_plain_is_empty(bset))
4292 return constant_on_domain(bset, 0);
4293
4294 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4295
4296 if (orig_nvar == 0)
4297 return constant_on_domain(bset, 1);
4298
4299 bounded = isl_basic_set_is_bounded(bset);
4300 if (bounded < 0)
4301 goto error;
4302 if (!bounded)
4303 return constant_on_domain(bset, -1);
4304
4305 if (bset->n_eq == 0)
4306 return compressed_multiplicative_call(bset, fn);
4307
4308 morph = isl_basic_set_full_compression(bset);
4309 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4310
4311 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4312
4313 pwqp = compressed_multiplicative_call(bset, fn);
4314
4315 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4316 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4317 morph = isl_morph_inverse(morph);
4318
4319 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4320
4321 return pwqp;
4322 error:
4323 isl_basic_set_free(bset);
4324 return NULL;
4325 }
4326
4327 /* Drop all floors in "qp", turning each integer division [a/m] into
4328 * a rational division a/m. If "down" is set, then the integer division
4329 * is replaces by (a-(m-1))/m instead.
4330 */
4331 static __isl_give isl_qpolynomial *qp_drop_floors(
4332 __isl_take isl_qpolynomial *qp, int down)
4333 {
4334 int i;
4335 struct isl_upoly *s;
4336
4337 if (!qp)
4338 return NULL;
4339 if (qp->div->n_row == 0)
4340 return qp;
4341
4342 qp = isl_qpolynomial_cow(qp);
4343 if (!qp)
4344 return NULL;
4345
4346 for (i = qp->div->n_row - 1; i >= 0; --i) {
4347 if (down) {
4348 isl_int_sub(qp->div->row[i][1],
4349 qp->div->row[i][1], qp->div->row[i][0]);
4350 isl_int_add_ui(qp->div->row[i][1],
4351 qp->div->row[i][1], 1);
4352 }
4353 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4354 qp->div->row[i][0], qp->div->n_col - 1);
4355 qp = substitute_div(qp, i, s);
4356 if (!qp)
4357 return NULL;
4358 }
4359
4360 return qp;
4361 }
4362
4363 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4364 * a rational division a/m.
4365 */
4366 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4367 __isl_take isl_pw_qpolynomial *pwqp)
4368 {
4369 int i;
4370
4371 if (!pwqp)
4372 return NULL;
4373
4374 if (isl_pw_qpolynomial_is_zero(pwqp))
4375 return pwqp;
4376
4377 pwqp = isl_pw_qpolynomial_cow(pwqp);
4378 if (!pwqp)
4379 return NULL;
4380
4381 for (i = 0; i < pwqp->n; ++i) {
4382 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4383 if (!pwqp->p[i].qp)
4384 goto error;
4385 }
4386
4387 return pwqp;
4388 error:
4389 isl_pw_qpolynomial_free(pwqp);
4390 return NULL;
4391 }
4392
4393 /* Adjust all the integer divisions in "qp" such that they are at least
4394 * one over the given orthant (identified by "signs"). This ensures
4395 * that they will still be non-negative even after subtracting (m-1)/m.
4396 *
4397 * In particular, f is replaced by f' + v, changing f = [a/m]
4398 * to f' = [(a - m v)/m].
4399 * If the constant term k in a is smaller than m,
4400 * the constant term of v is set to floor(k/m) - 1.
4401 * For any other term, if the coefficient c and the variable x have
4402 * the same sign, then no changes are needed.
4403 * Otherwise, if the variable is positive (and c is negative),
4404 * then the coefficient of x in v is set to floor(c/m).
4405 * If the variable is negative (and c is positive),
4406 * then the coefficient of x in v is set to ceil(c/m).
4407 */
4408 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4409 int *signs)
4410 {
4411 int i, j;
4412 int total;
4413 isl_vec *v = NULL;
4414 struct isl_upoly *s;
4415
4416 qp = isl_qpolynomial_cow(qp);
4417 if (!qp)
4418 return NULL;
4419 qp->div = isl_mat_cow(qp->div);
4420 if (!qp->div)
4421 goto error;
4422
4423 total = isl_dim_total(qp->dim);
4424 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4425
4426 for (i = 0; i < qp->div->n_row; ++i) {
4427 isl_int *row = qp->div->row[i];
4428 v = isl_vec_clr(v);
4429 if (!v)
4430 goto error;
4431 if (isl_int_lt(row[1], row[0])) {
4432 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4433 isl_int_sub_ui(v->el[0], v->el[0], 1);
4434 isl_int_submul(row[1], row[0], v->el[0]);
4435 }
4436 for (j = 0; j < total; ++j) {
4437 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4438 continue;
4439 if (signs[j] < 0)
4440 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4441 else
4442 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4443 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4444 }
4445 for (j = 0; j < i; ++j) {
4446 if (isl_int_sgn(row[2 + total + j]) >= 0)
4447 continue;
4448 isl_int_fdiv_q(v->el[1 + total + j],
4449 row[2 + total + j], row[0]);
4450 isl_int_submul(row[2 + total + j],
4451 row[0], v->el[1 + total + j]);
4452 }
4453 for (j = i + 1; j < qp->div->n_row; ++j) {
4454 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4455 continue;
4456 isl_seq_combine(qp->div->row[j] + 1,
4457 qp->div->ctx->one, qp->div->row[j] + 1,
4458 qp->div->row[j][2 + total + i], v->el, v->size);
4459 }
4460 isl_int_set_si(v->el[1 + total + i], 1);
4461 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4462 qp->div->ctx->one, v->size);
4463 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4464 isl_upoly_free(s);
4465 if (!qp->upoly)
4466 goto error;
4467 }
4468
4469 isl_vec_free(v);
4470 return qp;
4471 error:
4472 isl_vec_free(v);
4473 isl_qpolynomial_free(qp);
4474 return NULL;
4475 }
4476
4477 struct isl_to_poly_data {
4478 int sign;
4479 isl_pw_qpolynomial *res;
4480 isl_qpolynomial *qp;
4481 };
4482
4483 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4484 * We first make all integer divisions positive and then split the
4485 * quasipolynomials into terms with sign data->sign (the direction
4486 * of the requested approximation) and terms with the opposite sign.
4487 * In the first set of terms, each integer division [a/m] is
4488 * overapproximated by a/m, while in the second it is underapproximated
4489 * by (a-(m-1))/m.
4490 */
4491 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4492 void *user)
4493 {
4494 struct isl_to_poly_data *data = user;
4495 isl_pw_qpolynomial *t;
4496 isl_qpolynomial *qp, *up, *down;
4497
4498 qp = isl_qpolynomial_copy(data->qp);
4499 qp = make_divs_pos(qp, signs);
4500
4501 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4502 up = qp_drop_floors(up, 0);
4503 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4504 down = qp_drop_floors(down, 1);
4505
4506 isl_qpolynomial_free(qp);
4507 qp = isl_qpolynomial_add(up, down);
4508
4509 t = isl_pw_qpolynomial_alloc(orthant, qp);
4510 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4511
4512 return 0;
4513 }
4514
4515 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4516 * the polynomial will be an overapproximation. If "sign" is negative,
4517 * it will be an underapproximation. If "sign" is zero, the approximation
4518 * will lie somewhere in between.
4519 *
4520 * In particular, is sign == 0, we simply drop the floors, turning
4521 * the integer divisions into rational divisions.
4522 * Otherwise, we split the domains into orthants, make all integer divisions
4523 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4524 * depending on the requested sign and the sign of the term in which
4525 * the integer division appears.
4526 */
4527 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4528 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4529 {
4530 int i;
4531 struct isl_to_poly_data data;
4532
4533 if (sign == 0)
4534 return pwqp_drop_floors(pwqp);
4535
4536 if (!pwqp)
4537 return NULL;
4538
4539 data.sign = sign;
4540 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4541
4542 for (i = 0; i < pwqp->n; ++i) {
4543 if (pwqp->p[i].qp->div->n_row == 0) {
4544 isl_pw_qpolynomial *t;
4545 t = isl_pw_qpolynomial_alloc(
4546 isl_set_copy(pwqp->p[i].set),
4547 isl_qpolynomial_copy(pwqp->p[i].qp));
4548 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4549 continue;
4550 }
4551 data.qp = pwqp->p[i].qp;
4552 if (isl_set_foreach_orthant(pwqp->p[i].set,
4553 &to_polynomial_on_orthant, &data) < 0)
4554 goto error;
4555 }
4556
4557 isl_pw_qpolynomial_free(pwqp);
4558
4559 return data.res;
4560 error:
4561 isl_pw_qpolynomial_free(pwqp);
4562 isl_pw_qpolynomial_free(data.res);
4563 return NULL;
4564 }
4565
4566 static int poly_entry(void **entry, void *user)
4567 {
4568 int *sign = user;
4569 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4570
4571 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4572
4573 return *pwqp ? 0 : -1;
4574 }
4575
4576 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4577 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4578 {
4579 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4580 if (!upwqp)
4581 return NULL;
4582
4583 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4584 &poly_entry, &sign) < 0)
4585 goto error;
4586
4587 return upwqp;
4588 error:
4589 isl_union_pw_qpolynomial_free(upwqp);
4590 return NULL;
4591 }
4592
4593 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4594 __isl_take isl_qpolynomial *qp)
4595 {
4596 int i, k;
4597 isl_dim *dim;
4598 isl_vec *aff = NULL;
4599 isl_basic_map *bmap = NULL;
4600 unsigned pos;
4601 unsigned n_div;
4602
4603 if (!qp)
4604 return NULL;
4605 if (!isl_upoly_is_affine(qp->upoly))
4606 isl_die(qp->dim->ctx, isl_error_invalid,
4607 "input quasi-polynomial not affine", goto error);
4608 aff = isl_qpolynomial_extract_affine(qp);
4609 if (!aff)
4610 goto error;
4611 dim = isl_qpolynomial_get_dim(qp);
4612 dim = isl_dim_from_domain(dim);
4613 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4614 dim = isl_dim_add(dim, isl_dim_out, 1);
4615 n_div = qp->div->n_row;
4616 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4617
4618 for (i = 0; i < n_div; ++i) {
4619 k = isl_basic_map_alloc_div(bmap);
4620 if (k < 0)
4621 goto error;
4622 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4623 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4624 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4625 goto error;
4626 }
4627 k = isl_basic_map_alloc_equality(bmap);
4628 if (k < 0)
4629 goto error;
4630 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4631 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4632 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4633
4634 isl_vec_free(aff);
4635 isl_qpolynomial_free(qp);
4636 bmap = isl_basic_map_finalize(bmap);
4637 return bmap;
4638 error:
4639 isl_vec_free(aff);
4640 isl_qpolynomial_free(qp);
4641 isl_basic_map_free(bmap);
4642 return NULL;
4643 }
Integer set library