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isl_stream_read_obj: read int objects
[isl.git] / isl_polynomial.c
blob4ae1bdfca7131a2c2c40508576563d6a6a2a68cb
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_factorization.h>
13 #include <isl/lp.h>
14 #include <isl/seq.h>
15 #include <isl_union_map_private.h>
16 #include <isl_polynomial_private.h>
17 #include <isl_point_private.h>
18 #include <isl_dim_private.h>
19 #include <isl_map_private.h>
20 #include <isl_mat_private.h>
21 #include <isl_range.h>
22
23 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
24 {
25 switch (type) {
26 case isl_dim_param: return 0;
27 case isl_dim_in: return dim->nparam;
28 case isl_dim_out: return dim->nparam + dim->n_in;
29 default: return 0;
30 }
31 }
32
33 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
34 {
35 if (!up)
36 return -1;
37
38 return up->var < 0;
39 }
40
41 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
42 {
43 if (!up)
44 return NULL;
45
46 isl_assert(up->ctx, up->var < 0, return NULL);
47
48 return (struct isl_upoly_cst *)up;
49 }
50
51 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
52 {
53 if (!up)
54 return NULL;
55
56 isl_assert(up->ctx, up->var >= 0, return NULL);
57
58 return (struct isl_upoly_rec *)up;
59 }
60
61 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
62 __isl_keep struct isl_upoly *up2)
63 {
64 int i;
65 struct isl_upoly_rec *rec1, *rec2;
66
67 if (!up1 || !up2)
68 return -1;
69 if (up1 == up2)
70 return 1;
71 if (up1->var != up2->var)
72 return 0;
73 if (isl_upoly_is_cst(up1)) {
74 struct isl_upoly_cst *cst1, *cst2;
75 cst1 = isl_upoly_as_cst(up1);
76 cst2 = isl_upoly_as_cst(up2);
77 if (!cst1 || !cst2)
78 return -1;
79 return isl_int_eq(cst1->n, cst2->n) &&
80 isl_int_eq(cst1->d, cst2->d);
81 }
82
83 rec1 = isl_upoly_as_rec(up1);
84 rec2 = isl_upoly_as_rec(up2);
85 if (!rec1 || !rec2)
86 return -1;
87
88 if (rec1->n != rec2->n)
89 return 0;
90
91 for (i = 0; i < rec1->n; ++i) {
92 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
93 if (eq < 0 || !eq)
94 return eq;
95 }
96
97 return 1;
98 }
99
100 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
101 {
102 struct isl_upoly_cst *cst;
103
104 if (!up)
105 return -1;
106 if (!isl_upoly_is_cst(up))
107 return 0;
108
109 cst = isl_upoly_as_cst(up);
110 if (!cst)
111 return -1;
112
113 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
114 }
115
116 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
117 {
118 struct isl_upoly_cst *cst;
119
120 if (!up)
121 return 0;
122 if (!isl_upoly_is_cst(up))
123 return 0;
124
125 cst = isl_upoly_as_cst(up);
126 if (!cst)
127 return 0;
128
129 return isl_int_sgn(cst->n);
130 }
131
132 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
133 {
134 struct isl_upoly_cst *cst;
135
136 if (!up)
137 return -1;
138 if (!isl_upoly_is_cst(up))
139 return 0;
140
141 cst = isl_upoly_as_cst(up);
142 if (!cst)
143 return -1;
144
145 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
146 }
147
148 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
149 {
150 struct isl_upoly_cst *cst;
151
152 if (!up)
153 return -1;
154 if (!isl_upoly_is_cst(up))
155 return 0;
156
157 cst = isl_upoly_as_cst(up);
158 if (!cst)
159 return -1;
160
161 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
162 }
163
164 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
165 {
166 struct isl_upoly_cst *cst;
167
168 if (!up)
169 return -1;
170 if (!isl_upoly_is_cst(up))
171 return 0;
172
173 cst = isl_upoly_as_cst(up);
174 if (!cst)
175 return -1;
176
177 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
178 }
179
180 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
181 {
182 struct isl_upoly_cst *cst;
183
184 if (!up)
185 return -1;
186 if (!isl_upoly_is_cst(up))
187 return 0;
188
189 cst = isl_upoly_as_cst(up);
190 if (!cst)
191 return -1;
192
193 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
194 }
195
196 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
197 {
198 struct isl_upoly_cst *cst;
199
200 if (!up)
201 return -1;
202 if (!isl_upoly_is_cst(up))
203 return 0;
204
205 cst = isl_upoly_as_cst(up);
206 if (!cst)
207 return -1;
208
209 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
210 }
211
212 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
213 {
214 struct isl_upoly_cst *cst;
215
216 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
217 if (!cst)
218 return NULL;
219
220 cst->up.ref = 1;
221 cst->up.ctx = ctx;
222 isl_ctx_ref(ctx);
223 cst->up.var = -1;
224
225 isl_int_init(cst->n);
226 isl_int_init(cst->d);
227
228 return cst;
229 }
230
231 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
232 {
233 struct isl_upoly_cst *cst;
234
235 cst = isl_upoly_cst_alloc(ctx);
236 if (!cst)
237 return NULL;
238
239 isl_int_set_si(cst->n, 0);
240 isl_int_set_si(cst->d, 1);
241
242 return &cst->up;
243 }
244
245 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
246 {
247 struct isl_upoly_cst *cst;
248
249 cst = isl_upoly_cst_alloc(ctx);
250 if (!cst)
251 return NULL;
252
253 isl_int_set_si(cst->n, 1);
254 isl_int_set_si(cst->d, 1);
255
256 return &cst->up;
257 }
258
259 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
260 {
261 struct isl_upoly_cst *cst;
262
263 cst = isl_upoly_cst_alloc(ctx);
264 if (!cst)
265 return NULL;
266
267 isl_int_set_si(cst->n, 1);
268 isl_int_set_si(cst->d, 0);
269
270 return &cst->up;
271 }
272
273 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
274 {
275 struct isl_upoly_cst *cst;
276
277 cst = isl_upoly_cst_alloc(ctx);
278 if (!cst)
279 return NULL;
280
281 isl_int_set_si(cst->n, -1);
282 isl_int_set_si(cst->d, 0);
283
284 return &cst->up;
285 }
286
287 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
288 {
289 struct isl_upoly_cst *cst;
290
291 cst = isl_upoly_cst_alloc(ctx);
292 if (!cst)
293 return NULL;
294
295 isl_int_set_si(cst->n, 0);
296 isl_int_set_si(cst->d, 0);
297
298 return &cst->up;
299 }
300
301 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
302 isl_int n, isl_int d)
303 {
304 struct isl_upoly_cst *cst;
305
306 cst = isl_upoly_cst_alloc(ctx);
307 if (!cst)
308 return NULL;
309
310 isl_int_set(cst->n, n);
311 isl_int_set(cst->d, d);
312
313 return &cst->up;
314 }
315
316 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
317 int var, int size)
318 {
319 struct isl_upoly_rec *rec;
320
321 isl_assert(ctx, var >= 0, return NULL);
322 isl_assert(ctx, size >= 0, return NULL);
323 rec = isl_calloc(ctx, struct isl_upoly_rec,
324 sizeof(struct isl_upoly_rec) +
325 (size - 1) * sizeof(struct isl_upoly *));
326 if (!rec)
327 return NULL;
328
329 rec->up.ref = 1;
330 rec->up.ctx = ctx;
331 isl_ctx_ref(ctx);
332 rec->up.var = var;
333
334 rec->n = 0;
335 rec->size = size;
336
337 return rec;
338 }
339
340 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
341 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
342 {
343 qp = isl_qpolynomial_cow(qp);
344 if (!qp || !dim)
345 goto error;
346
347 isl_dim_free(qp->dim);
348 qp->dim = dim;
349
350 return qp;
351 error:
352 isl_qpolynomial_free(qp);
353 isl_dim_free(dim);
354 return NULL;
355 }
356
357 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
358 {
359 return qp ? qp->dim->ctx : NULL;
360 }
361
362 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
363 {
364 return qp ? isl_dim_copy(qp->dim) : NULL;
365 }
366
367 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
368 enum isl_dim_type type)
369 {
370 return qp ? isl_dim_size(qp->dim, type) : 0;
371 }
372
373 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
374 {
375 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
376 }
377
378 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
379 {
380 return qp ? isl_upoly_is_one(qp->upoly) : -1;
381 }
382
383 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
384 {
385 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
386 }
387
388 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
389 {
390 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
391 }
392
393 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
394 {
395 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
396 }
397
398 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
399 {
400 return qp ? isl_upoly_sgn(qp->upoly) : 0;
401 }
402
403 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
404 {
405 isl_int_clear(cst->n);
406 isl_int_clear(cst->d);
407 }
408
409 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
410 {
411 int i;
412
413 for (i = 0; i < rec->n; ++i)
414 isl_upoly_free(rec->p[i]);
415 }
416
417 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
418 {
419 if (!up)
420 return NULL;
421
422 up->ref++;
423 return up;
424 }
425
426 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
427 {
428 struct isl_upoly_cst *cst;
429 struct isl_upoly_cst *dup;
430
431 cst = isl_upoly_as_cst(up);
432 if (!cst)
433 return NULL;
434
435 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
436 if (!dup)
437 return NULL;
438 isl_int_set(dup->n, cst->n);
439 isl_int_set(dup->d, cst->d);
440
441 return &dup->up;
442 }
443
444 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
445 {
446 int i;
447 struct isl_upoly_rec *rec;
448 struct isl_upoly_rec *dup;
449
450 rec = isl_upoly_as_rec(up);
451 if (!rec)
452 return NULL;
453
454 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
455 if (!dup)
456 return NULL;
457
458 for (i = 0; i < rec->n; ++i) {
459 dup->p[i] = isl_upoly_copy(rec->p[i]);
460 if (!dup->p[i])
461 goto error;
462 dup->n++;
463 }
464
465 return &dup->up;
466 error:
467 isl_upoly_free(&dup->up);
468 return NULL;
469 }
470
471 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
472 {
473 struct isl_upoly *dup;
474
475 if (!up)
476 return NULL;
477
478 if (isl_upoly_is_cst(up))
479 return isl_upoly_dup_cst(up);
480 else
481 return isl_upoly_dup_rec(up);
482 }
483
484 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
485 {
486 if (!up)
487 return NULL;
488
489 if (up->ref == 1)
490 return up;
491 up->ref--;
492 return isl_upoly_dup(up);
493 }
494
495 void isl_upoly_free(__isl_take struct isl_upoly *up)
496 {
497 if (!up)
498 return;
499
500 if (--up->ref > 0)
501 return;
502
503 if (up->var < 0)
504 upoly_free_cst((struct isl_upoly_cst *)up);
505 else
506 upoly_free_rec((struct isl_upoly_rec *)up);
507
508 isl_ctx_deref(up->ctx);
509 free(up);
510 }
511
512 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
513 {
514 isl_int gcd;
515
516 isl_int_init(gcd);
517 isl_int_gcd(gcd, cst->n, cst->d);
518 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
519 isl_int_divexact(cst->n, cst->n, gcd);
520 isl_int_divexact(cst->d, cst->d, gcd);
521 }
522 isl_int_clear(gcd);
523 }
524
525 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
526 __isl_take struct isl_upoly *up2)
527 {
528 struct isl_upoly_cst *cst1;
529 struct isl_upoly_cst *cst2;
530
531 up1 = isl_upoly_cow(up1);
532 if (!up1 || !up2)
533 goto error;
534
535 cst1 = isl_upoly_as_cst(up1);
536 cst2 = isl_upoly_as_cst(up2);
537
538 if (isl_int_eq(cst1->d, cst2->d))
539 isl_int_add(cst1->n, cst1->n, cst2->n);
540 else {
541 isl_int_mul(cst1->n, cst1->n, cst2->d);
542 isl_int_addmul(cst1->n, cst2->n, cst1->d);
543 isl_int_mul(cst1->d, cst1->d, cst2->d);
544 }
545
546 isl_upoly_cst_reduce(cst1);
547
548 isl_upoly_free(up2);
549 return up1;
550 error:
551 isl_upoly_free(up1);
552 isl_upoly_free(up2);
553 return NULL;
554 }
555
556 static __isl_give struct isl_upoly *replace_by_zero(
557 __isl_take struct isl_upoly *up)
558 {
559 struct isl_ctx *ctx;
560
561 if (!up)
562 return NULL;
563 ctx = up->ctx;
564 isl_upoly_free(up);
565 return isl_upoly_zero(ctx);
566 }
567
568 static __isl_give struct isl_upoly *replace_by_constant_term(
569 __isl_take struct isl_upoly *up)
570 {
571 struct isl_upoly_rec *rec;
572 struct isl_upoly *cst;
573
574 if (!up)
575 return NULL;
576
577 rec = isl_upoly_as_rec(up);
578 if (!rec)
579 goto error;
580 cst = isl_upoly_copy(rec->p[0]);
581 isl_upoly_free(up);
582 return cst;
583 error:
584 isl_upoly_free(up);
585 return NULL;
586 }
587
588 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
589 __isl_take struct isl_upoly *up2)
590 {
591 int i;
592 struct isl_upoly_rec *rec1, *rec2;
593
594 if (!up1 || !up2)
595 goto error;
596
597 if (isl_upoly_is_nan(up1)) {
598 isl_upoly_free(up2);
599 return up1;
600 }
601
602 if (isl_upoly_is_nan(up2)) {
603 isl_upoly_free(up1);
604 return up2;
605 }
606
607 if (isl_upoly_is_zero(up1)) {
608 isl_upoly_free(up1);
609 return up2;
610 }
611
612 if (isl_upoly_is_zero(up2)) {
613 isl_upoly_free(up2);
614 return up1;
615 }
616
617 if (up1->var < up2->var)
618 return isl_upoly_sum(up2, up1);
619
620 if (up2->var < up1->var) {
621 struct isl_upoly_rec *rec;
622 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
623 isl_upoly_free(up1);
624 return up2;
625 }
626 up1 = isl_upoly_cow(up1);
627 rec = isl_upoly_as_rec(up1);
628 if (!rec)
629 goto error;
630 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
631 if (rec->n == 1)
632 up1 = replace_by_constant_term(up1);
633 return up1;
634 }
635
636 if (isl_upoly_is_cst(up1))
637 return isl_upoly_sum_cst(up1, up2);
638
639 rec1 = isl_upoly_as_rec(up1);
640 rec2 = isl_upoly_as_rec(up2);
641 if (!rec1 || !rec2)
642 goto error;
643
644 if (rec1->n < rec2->n)
645 return isl_upoly_sum(up2, up1);
646
647 up1 = isl_upoly_cow(up1);
648 rec1 = isl_upoly_as_rec(up1);
649 if (!rec1)
650 goto error;
651
652 for (i = rec2->n - 1; i >= 0; --i) {
653 rec1->p[i] = isl_upoly_sum(rec1->p[i],
654 isl_upoly_copy(rec2->p[i]));
655 if (!rec1->p[i])
656 goto error;
657 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
658 isl_upoly_free(rec1->p[i]);
659 rec1->n--;
660 }
661 }
662
663 if (rec1->n == 0)
664 up1 = replace_by_zero(up1);
665 else if (rec1->n == 1)
666 up1 = replace_by_constant_term(up1);
667
668 isl_upoly_free(up2);
669
670 return up1;
671 error:
672 isl_upoly_free(up1);
673 isl_upoly_free(up2);
674 return NULL;
675 }
676
677 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
678 __isl_take struct isl_upoly *up, isl_int v)
679 {
680 struct isl_upoly_cst *cst;
681
682 up = isl_upoly_cow(up);
683 if (!up)
684 return NULL;
685
686 cst = isl_upoly_as_cst(up);
687
688 isl_int_addmul(cst->n, cst->d, v);
689
690 return up;
691 }
692
693 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
694 __isl_take struct isl_upoly *up, isl_int v)
695 {
696 struct isl_upoly_rec *rec;
697
698 if (!up)
699 return NULL;
700
701 if (isl_upoly_is_cst(up))
702 return isl_upoly_cst_add_isl_int(up, v);
703
704 up = isl_upoly_cow(up);
705 rec = isl_upoly_as_rec(up);
706 if (!rec)
707 goto error;
708
709 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
710 if (!rec->p[0])
711 goto error;
712
713 return up;
714 error:
715 isl_upoly_free(up);
716 return NULL;
717 }
718
719 __isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up)
720 {
721 struct isl_upoly_cst *cst;
722
723 if (isl_upoly_is_zero(up))
724 return up;
725
726 up = isl_upoly_cow(up);
727 if (!up)
728 return NULL;
729
730 cst = isl_upoly_as_cst(up);
731
732 isl_int_neg(cst->n, cst->n);
733
734 return up;
735 }
736
737 __isl_give struct isl_upoly *isl_upoly_neg(__isl_take struct isl_upoly *up)
738 {
739 int i;
740 struct isl_upoly_rec *rec;
741
742 if (!up)
743 return NULL;
744
745 if (isl_upoly_is_cst(up))
746 return isl_upoly_neg_cst(up);
747
748 up = isl_upoly_cow(up);
749 rec = isl_upoly_as_rec(up);
750 if (!rec)
751 goto error;
752
753 for (i = 0; i < rec->n; ++i) {
754 rec->p[i] = isl_upoly_neg(rec->p[i]);
755 if (!rec->p[i])
756 goto error;
757 }
758
759 return up;
760 error:
761 isl_upoly_free(up);
762 return NULL;
763 }
764
765 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
766 __isl_take struct isl_upoly *up2)
767 {
768 struct isl_upoly_cst *cst1;
769 struct isl_upoly_cst *cst2;
770
771 up1 = isl_upoly_cow(up1);
772 if (!up1 || !up2)
773 goto error;
774
775 cst1 = isl_upoly_as_cst(up1);
776 cst2 = isl_upoly_as_cst(up2);
777
778 isl_int_mul(cst1->n, cst1->n, cst2->n);
779 isl_int_mul(cst1->d, cst1->d, cst2->d);
780
781 isl_upoly_cst_reduce(cst1);
782
783 isl_upoly_free(up2);
784 return up1;
785 error:
786 isl_upoly_free(up1);
787 isl_upoly_free(up2);
788 return NULL;
789 }
790
791 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
792 __isl_take struct isl_upoly *up2)
793 {
794 struct isl_upoly_rec *rec1;
795 struct isl_upoly_rec *rec2;
796 struct isl_upoly_rec *res;
797 int i, j;
798 int size;
799
800 rec1 = isl_upoly_as_rec(up1);
801 rec2 = isl_upoly_as_rec(up2);
802 if (!rec1 || !rec2)
803 goto error;
804 size = rec1->n + rec2->n - 1;
805 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
806 if (!res)
807 goto error;
808
809 for (i = 0; i < rec1->n; ++i) {
810 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
811 isl_upoly_copy(rec1->p[i]));
812 if (!res->p[i])
813 goto error;
814 res->n++;
815 }
816 for (; i < size; ++i) {
817 res->p[i] = isl_upoly_zero(up1->ctx);
818 if (!res->p[i])
819 goto error;
820 res->n++;
821 }
822 for (i = 0; i < rec1->n; ++i) {
823 for (j = 1; j < rec2->n; ++j) {
824 struct isl_upoly *up;
825 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
826 isl_upoly_copy(rec1->p[i]));
827 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
828 if (!res->p[i + j])
829 goto error;
830 }
831 }
832
833 isl_upoly_free(up1);
834 isl_upoly_free(up2);
835
836 return &res->up;
837 error:
838 isl_upoly_free(up1);
839 isl_upoly_free(up2);
840 isl_upoly_free(&res->up);
841 return NULL;
842 }
843
844 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
845 __isl_take struct isl_upoly *up2)
846 {
847 if (!up1 || !up2)
848 goto error;
849
850 if (isl_upoly_is_nan(up1)) {
851 isl_upoly_free(up2);
852 return up1;
853 }
854
855 if (isl_upoly_is_nan(up2)) {
856 isl_upoly_free(up1);
857 return up2;
858 }
859
860 if (isl_upoly_is_zero(up1)) {
861 isl_upoly_free(up2);
862 return up1;
863 }
864
865 if (isl_upoly_is_zero(up2)) {
866 isl_upoly_free(up1);
867 return up2;
868 }
869
870 if (isl_upoly_is_one(up1)) {
871 isl_upoly_free(up1);
872 return up2;
873 }
874
875 if (isl_upoly_is_one(up2)) {
876 isl_upoly_free(up2);
877 return up1;
878 }
879
880 if (up1->var < up2->var)
881 return isl_upoly_mul(up2, up1);
882
883 if (up2->var < up1->var) {
884 int i;
885 struct isl_upoly_rec *rec;
886 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
887 isl_ctx *ctx = up1->ctx;
888 isl_upoly_free(up1);
889 isl_upoly_free(up2);
890 return isl_upoly_nan(ctx);
891 }
892 up1 = isl_upoly_cow(up1);
893 rec = isl_upoly_as_rec(up1);
894 if (!rec)
895 goto error;
896
897 for (i = 0; i < rec->n; ++i) {
898 rec->p[i] = isl_upoly_mul(rec->p[i],
899 isl_upoly_copy(up2));
900 if (!rec->p[i])
901 goto error;
902 }
903 isl_upoly_free(up2);
904 return up1;
905 }
906
907 if (isl_upoly_is_cst(up1))
908 return isl_upoly_mul_cst(up1, up2);
909
910 return isl_upoly_mul_rec(up1, up2);
911 error:
912 isl_upoly_free(up1);
913 isl_upoly_free(up2);
914 return NULL;
915 }
916
917 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
918 unsigned power)
919 {
920 struct isl_upoly *res;
921
922 if (!up)
923 return NULL;
924 if (power == 1)
925 return up;
926
927 if (power % 2)
928 res = isl_upoly_copy(up);
929 else
930 res = isl_upoly_one(up->ctx);
931
932 while (power >>= 1) {
933 up = isl_upoly_mul(up, isl_upoly_copy(up));
934 if (power % 2)
935 res = isl_upoly_mul(res, isl_upoly_copy(up));
936 }
937
938 isl_upoly_free(up);
939 return res;
940 }
941
942 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
943 unsigned n_div, __isl_take struct isl_upoly *up)
944 {
945 struct isl_qpolynomial *qp = NULL;
946 unsigned total;
947
948 if (!dim || !up)
949 goto error;
950
951 total = isl_dim_total(dim);
952
953 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
954 if (!qp)
955 goto error;
956
957 qp->ref = 1;
958 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
959 if (!qp->div)
960 goto error;
961
962 qp->dim = dim;
963 qp->upoly = up;
964
965 return qp;
966 error:
967 isl_dim_free(dim);
968 isl_upoly_free(up);
969 isl_qpolynomial_free(qp);
970 return NULL;
971 }
972
973 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
974 {
975 if (!qp)
976 return NULL;
977
978 qp->ref++;
979 return qp;
980 }
981
982 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
983 {
984 struct isl_qpolynomial *dup;
985
986 if (!qp)
987 return NULL;
988
989 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
990 isl_upoly_copy(qp->upoly));
991 if (!dup)
992 return NULL;
993 isl_mat_free(dup->div);
994 dup->div = isl_mat_copy(qp->div);
995 if (!dup->div)
996 goto error;
997
998 return dup;
999 error:
1000 isl_qpolynomial_free(dup);
1001 return NULL;
1002 }
1003
1004 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1005 {
1006 if (!qp)
1007 return NULL;
1008
1009 if (qp->ref == 1)
1010 return qp;
1011 qp->ref--;
1012 return isl_qpolynomial_dup(qp);
1013 }
1014
1015 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1016 {
1017 if (!qp)
1018 return;
1019
1020 if (--qp->ref > 0)
1021 return;
1022
1023 isl_dim_free(qp->dim);
1024 isl_mat_free(qp->div);
1025 isl_upoly_free(qp->upoly);
1026
1027 free(qp);
1028 }
1029
1030 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1031 {
1032 int i;
1033 struct isl_upoly *up;
1034 struct isl_upoly_rec *rec;
1035 struct isl_upoly_cst *cst;
1036
1037 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1038 if (!rec)
1039 return NULL;
1040 for (i = 0; i < 1 + power; ++i) {
1041 rec->p[i] = isl_upoly_zero(ctx);
1042 if (!rec->p[i])
1043 goto error;
1044 rec->n++;
1045 }
1046 cst = isl_upoly_as_cst(rec->p[power]);
1047 isl_int_set_si(cst->n, 1);
1048
1049 return &rec->up;
1050 error:
1051 isl_upoly_free(&rec->up);
1052 return NULL;
1053 }
1054
1055 /* r array maps original positions to new positions.
1056 */
1057 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1058 int *r)
1059 {
1060 int i;
1061 struct isl_upoly_rec *rec;
1062 struct isl_upoly *base;
1063 struct isl_upoly *res;
1064
1065 if (isl_upoly_is_cst(up))
1066 return up;
1067
1068 rec = isl_upoly_as_rec(up);
1069 if (!rec)
1070 goto error;
1071
1072 isl_assert(up->ctx, rec->n >= 1, goto error);
1073
1074 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1075 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1076
1077 for (i = rec->n - 2; i >= 0; --i) {
1078 res = isl_upoly_mul(res, isl_upoly_copy(base));
1079 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1080 }
1081
1082 isl_upoly_free(base);
1083 isl_upoly_free(up);
1084
1085 return res;
1086 error:
1087 isl_upoly_free(up);
1088 return NULL;
1089 }
1090
1091 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1092 {
1093 int n_row, n_col;
1094 int equal;
1095
1096 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1097 div1->n_col >= div2->n_col, return -1);
1098
1099 if (div1->n_row == div2->n_row)
1100 return isl_mat_is_equal(div1, div2);
1101
1102 n_row = div1->n_row;
1103 n_col = div1->n_col;
1104 div1->n_row = div2->n_row;
1105 div1->n_col = div2->n_col;
1106
1107 equal = isl_mat_is_equal(div1, div2);
1108
1109 div1->n_row = n_row;
1110 div1->n_col = n_col;
1111
1112 return equal;
1113 }
1114
1115 static void expand_row(__isl_keep isl_mat *dst, int d,
1116 __isl_keep isl_mat *src, int s, int *exp)
1117 {
1118 int i;
1119 unsigned c = src->n_col - src->n_row;
1120
1121 isl_seq_cpy(dst->row[d], src->row[s], c);
1122 isl_seq_clr(dst->row[d] + c, dst->n_col - c);
1123
1124 for (i = 0; i < s; ++i)
1125 isl_int_set(dst->row[d][c + exp[i]], src->row[s][c + i]);
1126 }
1127
1128 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1129 {
1130 int li, lj;
1131
1132 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1133 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1134
1135 if (li != lj)
1136 return li - lj;
1137
1138 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1139 }
1140
1141 struct isl_div_sort_info {
1142 isl_mat *div;
1143 int row;
1144 };
1145
1146 static int div_sort_cmp(const void *p1, const void *p2)
1147 {
1148 const struct isl_div_sort_info *i1, *i2;
1149 i1 = (const struct isl_div_sort_info *) p1;
1150 i2 = (const struct isl_div_sort_info *) p2;
1151
1152 return cmp_row(i1->div, i1->row, i2->row);
1153 }
1154
1155 /* Sort divs and remove duplicates.
1156 */
1157 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1158 {
1159 int i;
1160 int skip;
1161 int len;
1162 struct isl_div_sort_info *array = NULL;
1163 int *pos = NULL, *at = NULL;
1164 int *reordering = NULL;
1165 unsigned div_pos;
1166
1167 if (!qp)
1168 return NULL;
1169 if (qp->div->n_row <= 1)
1170 return qp;
1171
1172 div_pos = isl_dim_total(qp->dim);
1173
1174 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1175 qp->div->n_row);
1176 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1177 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1178 len = qp->div->n_col - 2;
1179 reordering = isl_alloc_array(qp->div->ctx, int, len);
1180 if (!array || !pos || !at || !reordering)
1181 goto error;
1182
1183 for (i = 0; i < qp->div->n_row; ++i) {
1184 array[i].div = qp->div;
1185 array[i].row = i;
1186 pos[i] = i;
1187 at[i] = i;
1188 }
1189
1190 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1191 div_sort_cmp);
1192
1193 for (i = 0; i < div_pos; ++i)
1194 reordering[i] = i;
1195
1196 for (i = 0; i < qp->div->n_row; ++i) {
1197 if (pos[array[i].row] == i)
1198 continue;
1199 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1200 pos[at[i]] = pos[array[i].row];
1201 at[pos[array[i].row]] = at[i];
1202 at[i] = array[i].row;
1203 pos[array[i].row] = i;
1204 }
1205
1206 skip = 0;
1207 for (i = 0; i < len - div_pos; ++i) {
1208 if (i > 0 &&
1209 isl_seq_eq(qp->div->row[i - skip - 1],
1210 qp->div->row[i - skip], qp->div->n_col)) {
1211 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1212 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1213 2 + div_pos + i - skip);
1214 qp->div = isl_mat_drop_cols(qp->div,
1215 2 + div_pos + i - skip, 1);
1216 skip++;
1217 }
1218 reordering[div_pos + array[i].row] = div_pos + i - skip;
1219 }
1220
1221 qp->upoly = reorder(qp->upoly, reordering);
1222
1223 if (!qp->upoly || !qp->div)
1224 goto error;
1225
1226 free(at);
1227 free(pos);
1228 free(array);
1229 free(reordering);
1230
1231 return qp;
1232 error:
1233 free(at);
1234 free(pos);
1235 free(array);
1236 free(reordering);
1237 isl_qpolynomial_free(qp);
1238 return NULL;
1239 }
1240
1241 static __isl_give isl_mat *merge_divs(__isl_keep isl_mat *div1,
1242 __isl_keep isl_mat *div2, int *exp1, int *exp2)
1243 {
1244 int i, j, k;
1245 isl_mat *div = NULL;
1246 unsigned d = div1->n_col - div1->n_row;
1247
1248 div = isl_mat_alloc(div1->ctx, 1 + div1->n_row + div2->n_row,
1249 d + div1->n_row + div2->n_row);
1250 if (!div)
1251 return NULL;
1252
1253 for (i = 0, j = 0, k = 0; i < div1->n_row && j < div2->n_row; ++k) {
1254 int cmp;
1255
1256 expand_row(div, k, div1, i, exp1);
1257 expand_row(div, k + 1, div2, j, exp2);
1258
1259 cmp = cmp_row(div, k, k + 1);
1260 if (cmp == 0) {
1261 exp1[i++] = k;
1262 exp2[j++] = k;
1263 } else if (cmp < 0) {
1264 exp1[i++] = k;
1265 } else {
1266 exp2[j++] = k;
1267 isl_seq_cpy(div->row[k], div->row[k + 1], div->n_col);
1268 }
1269 }
1270 for (; i < div1->n_row; ++i, ++k) {
1271 expand_row(div, k, div1, i, exp1);
1272 exp1[i] = k;
1273 }
1274 for (; j < div2->n_row; ++j, ++k) {
1275 expand_row(div, k, div2, j, exp2);
1276 exp2[j] = k;
1277 }
1278
1279 div->n_row = k;
1280 div->n_col = d + k;
1281
1282 return div;
1283 }
1284
1285 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1286 int *exp, int first)
1287 {
1288 int i;
1289 struct isl_upoly_rec *rec;
1290
1291 if (isl_upoly_is_cst(up))
1292 return up;
1293
1294 if (up->var < first)
1295 return up;
1296
1297 if (exp[up->var - first] == up->var - first)
1298 return up;
1299
1300 up = isl_upoly_cow(up);
1301 if (!up)
1302 goto error;
1303
1304 up->var = exp[up->var - first] + first;
1305
1306 rec = isl_upoly_as_rec(up);
1307 if (!rec)
1308 goto error;
1309
1310 for (i = 0; i < rec->n; ++i) {
1311 rec->p[i] = expand(rec->p[i], exp, first);
1312 if (!rec->p[i])
1313 goto error;
1314 }
1315
1316 return up;
1317 error:
1318 isl_upoly_free(up);
1319 return NULL;
1320 }
1321
1322 static __isl_give isl_qpolynomial *with_merged_divs(
1323 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1324 __isl_take isl_qpolynomial *qp2),
1325 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1326 {
1327 int *exp1 = NULL;
1328 int *exp2 = NULL;
1329 isl_mat *div = NULL;
1330
1331 qp1 = isl_qpolynomial_cow(qp1);
1332 qp2 = isl_qpolynomial_cow(qp2);
1333
1334 if (!qp1 || !qp2)
1335 goto error;
1336
1337 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1338 qp1->div->n_col >= qp2->div->n_col, goto error);
1339
1340 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1341 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1342 if (!exp1 || !exp2)
1343 goto error;
1344
1345 div = merge_divs(qp1->div, qp2->div, exp1, exp2);
1346 if (!div)
1347 goto error;
1348
1349 isl_mat_free(qp1->div);
1350 qp1->div = isl_mat_copy(div);
1351 isl_mat_free(qp2->div);
1352 qp2->div = isl_mat_copy(div);
1353
1354 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1355 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1356
1357 if (!qp1->upoly || !qp2->upoly)
1358 goto error;
1359
1360 isl_mat_free(div);
1361 free(exp1);
1362 free(exp2);
1363
1364 return fn(qp1, qp2);
1365 error:
1366 isl_mat_free(div);
1367 free(exp1);
1368 free(exp2);
1369 isl_qpolynomial_free(qp1);
1370 isl_qpolynomial_free(qp2);
1371 return NULL;
1372 }
1373
1374 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1375 __isl_take isl_qpolynomial *qp2)
1376 {
1377 qp1 = isl_qpolynomial_cow(qp1);
1378
1379 if (!qp1 || !qp2)
1380 goto error;
1381
1382 if (qp1->div->n_row < qp2->div->n_row)
1383 return isl_qpolynomial_add(qp2, qp1);
1384
1385 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1386 if (!compatible_divs(qp1->div, qp2->div))
1387 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1388
1389 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1390 if (!qp1->upoly)
1391 goto error;
1392
1393 isl_qpolynomial_free(qp2);
1394
1395 return qp1;
1396 error:
1397 isl_qpolynomial_free(qp1);
1398 isl_qpolynomial_free(qp2);
1399 return NULL;
1400 }
1401
1402 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1403 __isl_keep isl_set *dom,
1404 __isl_take isl_qpolynomial *qp1,
1405 __isl_take isl_qpolynomial *qp2)
1406 {
1407 qp1 = isl_qpolynomial_add(qp1, qp2);
1408 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1409 return qp1;
1410 }
1411
1412 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1413 __isl_take isl_qpolynomial *qp2)
1414 {
1415 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1416 }
1417
1418 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1419 __isl_take isl_qpolynomial *qp, isl_int v)
1420 {
1421 if (isl_int_is_zero(v))
1422 return qp;
1423
1424 qp = isl_qpolynomial_cow(qp);
1425 if (!qp)
1426 return NULL;
1427
1428 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1429 if (!qp->upoly)
1430 goto error;
1431
1432 return qp;
1433 error:
1434 isl_qpolynomial_free(qp);
1435 return NULL;
1436
1437 }
1438
1439 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1440 {
1441 qp = isl_qpolynomial_cow(qp);
1442
1443 if (!qp)
1444 return NULL;
1445
1446 qp->upoly = isl_upoly_neg(qp->upoly);
1447 if (!qp->upoly)
1448 goto error;
1449
1450 return qp;
1451 error:
1452 isl_qpolynomial_free(qp);
1453 return NULL;
1454 }
1455
1456 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1457 __isl_take isl_qpolynomial *qp2)
1458 {
1459 qp1 = isl_qpolynomial_cow(qp1);
1460
1461 if (!qp1 || !qp2)
1462 goto error;
1463
1464 if (qp1->div->n_row < qp2->div->n_row)
1465 return isl_qpolynomial_mul(qp2, qp1);
1466
1467 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1468 if (!compatible_divs(qp1->div, qp2->div))
1469 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1470
1471 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1472 if (!qp1->upoly)
1473 goto error;
1474
1475 isl_qpolynomial_free(qp2);
1476
1477 return qp1;
1478 error:
1479 isl_qpolynomial_free(qp1);
1480 isl_qpolynomial_free(qp2);
1481 return NULL;
1482 }
1483
1484 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1485 unsigned power)
1486 {
1487 qp = isl_qpolynomial_cow(qp);
1488
1489 if (!qp)
1490 return NULL;
1491
1492 qp->upoly = isl_upoly_pow(qp->upoly, power);
1493 if (!qp->upoly)
1494 goto error;
1495
1496 return qp;
1497 error:
1498 isl_qpolynomial_free(qp);
1499 return NULL;
1500 }
1501
1502 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1503 {
1504 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1505 }
1506
1507 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1508 {
1509 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1510 }
1511
1512 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1513 {
1514 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1515 }
1516
1517 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1518 {
1519 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1520 }
1521
1522 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1523 {
1524 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1525 }
1526
1527 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1528 isl_int v)
1529 {
1530 struct isl_qpolynomial *qp;
1531 struct isl_upoly_cst *cst;
1532
1533 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1534 if (!qp)
1535 return NULL;
1536
1537 cst = isl_upoly_as_cst(qp->upoly);
1538 isl_int_set(cst->n, v);
1539
1540 return qp;
1541 }
1542
1543 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1544 isl_int *n, isl_int *d)
1545 {
1546 struct isl_upoly_cst *cst;
1547
1548 if (!qp)
1549 return -1;
1550
1551 if (!isl_upoly_is_cst(qp->upoly))
1552 return 0;
1553
1554 cst = isl_upoly_as_cst(qp->upoly);
1555 if (!cst)
1556 return -1;
1557
1558 if (n)
1559 isl_int_set(*n, cst->n);
1560 if (d)
1561 isl_int_set(*d, cst->d);
1562
1563 return 1;
1564 }
1565
1566 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1567 {
1568 int is_cst;
1569 struct isl_upoly_rec *rec;
1570
1571 if (!up)
1572 return -1;
1573
1574 if (up->var < 0)
1575 return 1;
1576
1577 rec = isl_upoly_as_rec(up);
1578 if (!rec)
1579 return -1;
1580
1581 if (rec->n > 2)
1582 return 0;
1583
1584 isl_assert(up->ctx, rec->n > 1, return -1);
1585
1586 is_cst = isl_upoly_is_cst(rec->p[1]);
1587 if (is_cst < 0)
1588 return -1;
1589 if (!is_cst)
1590 return 0;
1591
1592 return isl_upoly_is_affine(rec->p[0]);
1593 }
1594
1595 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1596 {
1597 if (!qp)
1598 return -1;
1599
1600 if (qp->div->n_row > 0)
1601 return 0;
1602
1603 return isl_upoly_is_affine(qp->upoly);
1604 }
1605
1606 static void update_coeff(__isl_keep isl_vec *aff,
1607 __isl_keep struct isl_upoly_cst *cst, int pos)
1608 {
1609 isl_int gcd;
1610 isl_int f;
1611
1612 if (isl_int_is_zero(cst->n))
1613 return;
1614
1615 isl_int_init(gcd);
1616 isl_int_init(f);
1617 isl_int_gcd(gcd, cst->d, aff->el[0]);
1618 isl_int_divexact(f, cst->d, gcd);
1619 isl_int_divexact(gcd, aff->el[0], gcd);
1620 isl_seq_scale(aff->el, aff->el, f, aff->size);
1621 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1622 isl_int_clear(gcd);
1623 isl_int_clear(f);
1624 }
1625
1626 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1627 __isl_keep isl_vec *aff)
1628 {
1629 struct isl_upoly_cst *cst;
1630 struct isl_upoly_rec *rec;
1631
1632 if (!up || !aff)
1633 return -1;
1634
1635 if (up->var < 0) {
1636 struct isl_upoly_cst *cst;
1637
1638 cst = isl_upoly_as_cst(up);
1639 if (!cst)
1640 return -1;
1641 update_coeff(aff, cst, 0);
1642 return 0;
1643 }
1644
1645 rec = isl_upoly_as_rec(up);
1646 if (!rec)
1647 return -1;
1648 isl_assert(up->ctx, rec->n == 2, return -1);
1649
1650 cst = isl_upoly_as_cst(rec->p[1]);
1651 if (!cst)
1652 return -1;
1653 update_coeff(aff, cst, 1 + up->var);
1654
1655 return isl_upoly_update_affine(rec->p[0], aff);
1656 }
1657
1658 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1659 __isl_keep isl_qpolynomial *qp)
1660 {
1661 isl_vec *aff;
1662 unsigned d;
1663
1664 if (!qp)
1665 return NULL;
1666
1667 isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
1668 d = isl_dim_total(qp->dim);
1669 aff = isl_vec_alloc(qp->div->ctx, 2 + d);
1670 if (!aff)
1671 return NULL;
1672
1673 isl_seq_clr(aff->el + 1, 1 + d);
1674 isl_int_set_si(aff->el[0], 1);
1675
1676 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1677 goto error;
1678
1679 return aff;
1680 error:
1681 isl_vec_free(aff);
1682 return NULL;
1683 }
1684
1685 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1686 __isl_keep isl_qpolynomial *qp2)
1687 {
1688 if (!qp1 || !qp2)
1689 return -1;
1690
1691 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1692 }
1693
1694 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1695 {
1696 int i;
1697 struct isl_upoly_rec *rec;
1698
1699 if (isl_upoly_is_cst(up)) {
1700 struct isl_upoly_cst *cst;
1701 cst = isl_upoly_as_cst(up);
1702 if (!cst)
1703 return;
1704 isl_int_lcm(*d, *d, cst->d);
1705 return;
1706 }
1707
1708 rec = isl_upoly_as_rec(up);
1709 if (!rec)
1710 return;
1711
1712 for (i = 0; i < rec->n; ++i)
1713 upoly_update_den(rec->p[i], d);
1714 }
1715
1716 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1717 {
1718 isl_int_set_si(*d, 1);
1719 if (!qp)
1720 return;
1721 upoly_update_den(qp->upoly, d);
1722 }
1723
1724 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1725 int pos, int power)
1726 {
1727 struct isl_ctx *ctx;
1728
1729 if (!dim)
1730 return NULL;
1731
1732 ctx = dim->ctx;
1733
1734 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1735 }
1736
1737 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1738 enum isl_dim_type type, unsigned pos)
1739 {
1740 if (!dim)
1741 return NULL;
1742
1743 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1744 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1745
1746 if (type == isl_dim_set)
1747 pos += isl_dim_size(dim, isl_dim_param);
1748
1749 return isl_qpolynomial_var_pow(dim, pos, 1);
1750 error:
1751 isl_dim_free(dim);
1752 return NULL;
1753 }
1754
1755 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1756 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1757 {
1758 int i;
1759 struct isl_upoly_rec *rec;
1760 struct isl_upoly *base, *res;
1761
1762 if (!up)
1763 return NULL;
1764
1765 if (isl_upoly_is_cst(up))
1766 return up;
1767
1768 if (up->var < first)
1769 return up;
1770
1771 rec = isl_upoly_as_rec(up);
1772 if (!rec)
1773 goto error;
1774
1775 isl_assert(up->ctx, rec->n >= 1, goto error);
1776
1777 if (up->var >= first + n)
1778 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1779 else
1780 base = isl_upoly_copy(subs[up->var - first]);
1781
1782 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1783 for (i = rec->n - 2; i >= 0; --i) {
1784 struct isl_upoly *t;
1785 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1786 res = isl_upoly_mul(res, isl_upoly_copy(base));
1787 res = isl_upoly_sum(res, t);
1788 }
1789
1790 isl_upoly_free(base);
1791 isl_upoly_free(up);
1792
1793 return res;
1794 error:
1795 isl_upoly_free(up);
1796 return NULL;
1797 }
1798
1799 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1800 isl_int denom, unsigned len)
1801 {
1802 int i;
1803 struct isl_upoly *up;
1804
1805 isl_assert(ctx, len >= 1, return NULL);
1806
1807 up = isl_upoly_rat_cst(ctx, f[0], denom);
1808 for (i = 0; i < len - 1; ++i) {
1809 struct isl_upoly *t;
1810 struct isl_upoly *c;
1811
1812 if (isl_int_is_zero(f[1 + i]))
1813 continue;
1814
1815 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1816 t = isl_upoly_var_pow(ctx, i, 1);
1817 t = isl_upoly_mul(c, t);
1818 up = isl_upoly_sum(up, t);
1819 }
1820
1821 return up;
1822 }
1823
1824 /* Remove common factor of non-constant terms and denominator.
1825 */
1826 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1827 {
1828 isl_ctx *ctx = qp->div->ctx;
1829 unsigned total = qp->div->n_col - 2;
1830
1831 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1832 isl_int_gcd(ctx->normalize_gcd,
1833 ctx->normalize_gcd, qp->div->row[div][0]);
1834 if (isl_int_is_one(ctx->normalize_gcd))
1835 return;
1836
1837 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1838 ctx->normalize_gcd, total);
1839 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1840 ctx->normalize_gcd);
1841 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1842 ctx->normalize_gcd);
1843 }
1844
1845 /* Replace the integer division identified by "div" by the polynomial "s".
1846 * The integer division is assumed not to appear in the definition
1847 * of any other integer divisions.
1848 */
1849 static __isl_give isl_qpolynomial *substitute_div(
1850 __isl_take isl_qpolynomial *qp,
1851 int div, __isl_take struct isl_upoly *s)
1852 {
1853 int i;
1854 int total;
1855 int *reordering;
1856
1857 if (!qp || !s)
1858 goto error;
1859
1860 qp = isl_qpolynomial_cow(qp);
1861 if (!qp)
1862 goto error;
1863
1864 total = isl_dim_total(qp->dim);
1865 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1866 if (!qp->upoly)
1867 goto error;
1868
1869 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1870 if (!reordering)
1871 goto error;
1872 for (i = 0; i < total + div; ++i)
1873 reordering[i] = i;
1874 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1875 reordering[i] = i - 1;
1876 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1877 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1878 qp->upoly = reorder(qp->upoly, reordering);
1879 free(reordering);
1880
1881 if (!qp->upoly || !qp->div)
1882 goto error;
1883
1884 isl_upoly_free(s);
1885 return qp;
1886 error:
1887 isl_qpolynomial_free(qp);
1888 isl_upoly_free(s);
1889 return NULL;
1890 }
1891
1892 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1893 * divisions because d is equal to 1 by their definition, i.e., e.
1894 */
1895 static __isl_give isl_qpolynomial *substitute_non_divs(
1896 __isl_take isl_qpolynomial *qp)
1897 {
1898 int i, j;
1899 int total;
1900 struct isl_upoly *s;
1901
1902 if (!qp)
1903 return NULL;
1904
1905 total = isl_dim_total(qp->dim);
1906 for (i = 0; qp && i < qp->div->n_row; ++i) {
1907 if (!isl_int_is_one(qp->div->row[i][0]))
1908 continue;
1909 for (j = i + 1; j < qp->div->n_row; ++j) {
1910 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1911 continue;
1912 isl_seq_combine(qp->div->row[j] + 1,
1913 qp->div->ctx->one, qp->div->row[j] + 1,
1914 qp->div->row[j][2 + total + i],
1915 qp->div->row[i] + 1, 1 + total + i);
1916 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1917 normalize_div(qp, j);
1918 }
1919 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1920 qp->div->row[i][0], qp->div->n_col - 1);
1921 qp = substitute_div(qp, i, s);
1922 --i;
1923 }
1924
1925 return qp;
1926 }
1927
1928 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1929 * with d the denominator. When replacing the coefficient e of x by
1930 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1931 * inside the division, so we need to add floor(e/d) * x outside.
1932 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1933 * to adjust the coefficient of x in each later div that depends on the
1934 * current div "div" and also in the affine expression "aff"
1935 * (if it too depends on "div").
1936 */
1937 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1938 __isl_keep isl_vec *aff)
1939 {
1940 int i, j;
1941 isl_int v;
1942 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1943
1944 isl_int_init(v);
1945 for (i = 0; i < 1 + total + div; ++i) {
1946 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1947 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1948 continue;
1949 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1950 isl_int_fdiv_r(qp->div->row[div][1 + i],
1951 qp->div->row[div][1 + i], qp->div->row[div][0]);
1952 if (!isl_int_is_zero(aff->el[1 + total + div]))
1953 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1954 for (j = div + 1; j < qp->div->n_row; ++j) {
1955 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1956 continue;
1957 isl_int_addmul(qp->div->row[j][1 + i],
1958 v, qp->div->row[j][2 + total + div]);
1959 }
1960 }
1961 isl_int_clear(v);
1962 }
1963
1964 /* Check if the last non-zero coefficient is bigger that half of the
1965 * denominator. If so, we will invert the div to further reduce the number
1966 * of distinct divs that may appear.
1967 * If the last non-zero coefficient is exactly half the denominator,
1968 * then we continue looking for earlier coefficients that are bigger
1969 * than half the denominator.
1970 */
1971 static int needs_invert(__isl_keep isl_mat *div, int row)
1972 {
1973 int i;
1974 int cmp;
1975
1976 for (i = div->n_col - 1; i >= 1; --i) {
1977 if (isl_int_is_zero(div->row[row][i]))
1978 continue;
1979 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1980 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1981 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1982 if (cmp)
1983 return cmp > 0;
1984 if (i == 1)
1985 return 1;
1986 }
1987
1988 return 0;
1989 }
1990
1991 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1992 * We only invert the coefficients of e (and the coefficient of q in
1993 * later divs and in "aff"). After calling this function, the
1994 * coefficients of e should be reduced again.
1995 */
1996 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1997 __isl_keep isl_vec *aff)
1998 {
1999 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2000
2001 isl_seq_neg(qp->div->row[div] + 1,
2002 qp->div->row[div] + 1, qp->div->n_col - 1);
2003 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2004 isl_int_add(qp->div->row[div][1],
2005 qp->div->row[div][1], qp->div->row[div][0]);
2006 if (!isl_int_is_zero(aff->el[1 + total + div]))
2007 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2008 isl_mat_col_mul(qp->div, 2 + total + div,
2009 qp->div->ctx->negone, 2 + total + div);
2010 }
2011
2012 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2013 * in the interval [0, d-1], with d the denominator and such that the
2014 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2015 *
2016 * After the reduction, some divs may have become redundant or identical,
2017 * so we call substitute_non_divs and sort_divs. If these functions
2018 * eliminate divs of merge * two or more divs into one, the coefficients
2019 * of the enclosing divs may have to be reduced again, so we call
2020 * ourselves recursively if the number of divs decreases.
2021 */
2022 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2023 {
2024 int i, j;
2025 isl_vec *aff = NULL;
2026 struct isl_upoly *s;
2027 unsigned n_div;
2028
2029 if (!qp)
2030 return NULL;
2031
2032 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2033 aff = isl_vec_clr(aff);
2034 if (!aff)
2035 goto error;
2036
2037 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2038
2039 for (i = 0; i < qp->div->n_row; ++i) {
2040 normalize_div(qp, i);
2041 reduce_div(qp, i, aff);
2042 if (needs_invert(qp->div, i)) {
2043 invert_div(qp, i, aff);
2044 reduce_div(qp, i, aff);
2045 }
2046 }
2047
2048 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2049 qp->div->ctx->one, aff->size);
2050 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2051 isl_upoly_free(s);
2052 if (!qp->upoly)
2053 goto error;
2054
2055 isl_vec_free(aff);
2056
2057 n_div = qp->div->n_row;
2058 qp = substitute_non_divs(qp);
2059 qp = sort_divs(qp);
2060 if (qp && qp->div->n_row < n_div)
2061 return reduce_divs(qp);
2062
2063 return qp;
2064 error:
2065 isl_qpolynomial_free(qp);
2066 isl_vec_free(aff);
2067 return NULL;
2068 }
2069
2070 /* Assumes each div only depends on earlier divs.
2071 */
2072 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2073 int power)
2074 {
2075 struct isl_qpolynomial *qp = NULL;
2076 struct isl_upoly_rec *rec;
2077 struct isl_upoly_cst *cst;
2078 int i, d;
2079 int pos;
2080
2081 if (!div)
2082 return NULL;
2083
2084 d = div->line - div->bmap->div;
2085
2086 pos = isl_dim_total(div->bmap->dim) + d;
2087 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2088 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2089 div->bmap->n_div, &rec->up);
2090 if (!qp)
2091 goto error;
2092
2093 for (i = 0; i < div->bmap->n_div; ++i)
2094 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2095
2096 for (i = 0; i < 1 + power; ++i) {
2097 rec->p[i] = isl_upoly_zero(div->ctx);
2098 if (!rec->p[i])
2099 goto error;
2100 rec->n++;
2101 }
2102 cst = isl_upoly_as_cst(rec->p[power]);
2103 isl_int_set_si(cst->n, 1);
2104
2105 isl_div_free(div);
2106
2107 qp = reduce_divs(qp);
2108
2109 return qp;
2110 error:
2111 isl_qpolynomial_free(qp);
2112 isl_div_free(div);
2113 return NULL;
2114 }
2115
2116 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2117 {
2118 return isl_qpolynomial_div_pow(div, 1);
2119 }
2120
2121 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2122 const isl_int n, const isl_int d)
2123 {
2124 struct isl_qpolynomial *qp;
2125 struct isl_upoly_cst *cst;
2126
2127 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2128 if (!qp)
2129 return NULL;
2130
2131 cst = isl_upoly_as_cst(qp->upoly);
2132 isl_int_set(cst->n, n);
2133 isl_int_set(cst->d, d);
2134
2135 return qp;
2136 }
2137
2138 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2139 {
2140 struct isl_upoly_rec *rec;
2141 int i;
2142
2143 if (!up)
2144 return -1;
2145
2146 if (isl_upoly_is_cst(up))
2147 return 0;
2148
2149 if (up->var < d)
2150 active[up->var] = 1;
2151
2152 rec = isl_upoly_as_rec(up);
2153 for (i = 0; i < rec->n; ++i)
2154 if (up_set_active(rec->p[i], active, d) < 0)
2155 return -1;
2156
2157 return 0;
2158 }
2159
2160 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2161 {
2162 int i, j;
2163 int d = isl_dim_total(qp->dim);
2164
2165 if (!qp || !active)
2166 return -1;
2167
2168 for (i = 0; i < d; ++i)
2169 for (j = 0; j < qp->div->n_row; ++j) {
2170 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2171 continue;
2172 active[i] = 1;
2173 break;
2174 }
2175
2176 return up_set_active(qp->upoly, active, d);
2177 }
2178
2179 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2180 enum isl_dim_type type, unsigned first, unsigned n)
2181 {
2182 int i;
2183 int *active = NULL;
2184 int involves = 0;
2185
2186 if (!qp)
2187 return -1;
2188 if (n == 0)
2189 return 0;
2190
2191 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2192 return -1);
2193 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2194 type == isl_dim_set, return -1);
2195
2196 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
2197 if (set_active(qp, active) < 0)
2198 goto error;
2199
2200 if (type == isl_dim_set)
2201 first += isl_dim_size(qp->dim, isl_dim_param);
2202 for (i = 0; i < n; ++i)
2203 if (active[first + i]) {
2204 involves = 1;
2205 break;
2206 }
2207
2208 free(active);
2209
2210 return involves;
2211 error:
2212 free(active);
2213 return -1;
2214 }
2215
2216 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2217 unsigned first, unsigned n)
2218 {
2219 int i;
2220 struct isl_upoly_rec *rec;
2221
2222 if (!up)
2223 return NULL;
2224 if (n == 0 || up->var < 0 || up->var < first)
2225 return up;
2226 if (up->var < first + n) {
2227 up = replace_by_constant_term(up);
2228 return isl_upoly_drop(up, first, n);
2229 }
2230 up = isl_upoly_cow(up);
2231 if (!up)
2232 return NULL;
2233 up->var -= n;
2234 rec = isl_upoly_as_rec(up);
2235 if (!rec)
2236 goto error;
2237
2238 for (i = 0; i < rec->n; ++i) {
2239 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2240 if (!rec->p[i])
2241 goto error;
2242 }
2243
2244 return up;
2245 error:
2246 isl_upoly_free(up);
2247 return NULL;
2248 }
2249
2250 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2251 __isl_take isl_qpolynomial *qp,
2252 enum isl_dim_type type, unsigned pos, const char *s)
2253 {
2254 qp = isl_qpolynomial_cow(qp);
2255 if (!qp)
2256 return NULL;
2257 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2258 if (!qp->dim)
2259 goto error;
2260 return qp;
2261 error:
2262 isl_qpolynomial_free(qp);
2263 return NULL;
2264 }
2265
2266 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2267 __isl_take isl_qpolynomial *qp,
2268 enum isl_dim_type type, unsigned first, unsigned n)
2269 {
2270 if (!qp)
2271 return NULL;
2272 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
2273 return qp;
2274
2275 qp = isl_qpolynomial_cow(qp);
2276 if (!qp)
2277 return NULL;
2278
2279 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2280 goto error);
2281 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2282 type == isl_dim_set, goto error);
2283
2284 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2285 if (!qp->dim)
2286 goto error;
2287
2288 if (type == isl_dim_set)
2289 first += isl_dim_size(qp->dim, isl_dim_param);
2290
2291 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2292 if (!qp->div)
2293 goto error;
2294
2295 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2296 if (!qp->upoly)
2297 goto error;
2298
2299 return qp;
2300 error:
2301 isl_qpolynomial_free(qp);
2302 return NULL;
2303 }
2304
2305 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2306 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2307 {
2308 int i, j, k;
2309 isl_int denom;
2310 unsigned total;
2311 unsigned n_div;
2312 struct isl_upoly *up;
2313
2314 if (!eq)
2315 goto error;
2316 if (eq->n_eq == 0) {
2317 isl_basic_set_free(eq);
2318 return qp;
2319 }
2320
2321 qp = isl_qpolynomial_cow(qp);
2322 if (!qp)
2323 goto error;
2324 qp->div = isl_mat_cow(qp->div);
2325 if (!qp->div)
2326 goto error;
2327
2328 total = 1 + isl_dim_total(eq->dim);
2329 n_div = eq->n_div;
2330 isl_int_init(denom);
2331 for (i = 0; i < eq->n_eq; ++i) {
2332 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2333 if (j < 0 || j == 0 || j >= total)
2334 continue;
2335
2336 for (k = 0; k < qp->div->n_row; ++k) {
2337 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2338 continue;
2339 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2340 &qp->div->row[k][0]);
2341 normalize_div(qp, k);
2342 }
2343
2344 if (isl_int_is_pos(eq->eq[i][j]))
2345 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2346 isl_int_abs(denom, eq->eq[i][j]);
2347 isl_int_set_si(eq->eq[i][j], 0);
2348
2349 up = isl_upoly_from_affine(qp->dim->ctx,
2350 eq->eq[i], denom, total);
2351 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2352 isl_upoly_free(up);
2353 }
2354 isl_int_clear(denom);
2355
2356 if (!qp->upoly)
2357 goto error;
2358
2359 isl_basic_set_free(eq);
2360
2361 qp = substitute_non_divs(qp);
2362 qp = sort_divs(qp);
2363
2364 return qp;
2365 error:
2366 isl_basic_set_free(eq);
2367 isl_qpolynomial_free(qp);
2368 return NULL;
2369 }
2370
2371 static __isl_give isl_basic_set *add_div_constraints(
2372 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2373 {
2374 int i;
2375 unsigned total;
2376
2377 if (!bset || !div)
2378 goto error;
2379
2380 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2381 if (!bset)
2382 goto error;
2383 total = isl_basic_set_total_dim(bset);
2384 for (i = 0; i < div->n_row; ++i)
2385 if (isl_basic_set_add_div_constraints_var(bset,
2386 total - div->n_row + i, div->row[i]) < 0)
2387 goto error;
2388
2389 isl_mat_free(div);
2390 return bset;
2391 error:
2392 isl_mat_free(div);
2393 isl_basic_set_free(bset);
2394 return NULL;
2395 }
2396
2397 /* Look for equalities among the variables shared by context and qp
2398 * and the integer divisions of qp, if any.
2399 * The equalities are then used to eliminate variables and/or integer
2400 * divisions from qp.
2401 */
2402 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2403 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2404 {
2405 isl_basic_set *aff;
2406
2407 if (!qp)
2408 goto error;
2409 if (qp->div->n_row > 0) {
2410 isl_basic_set *bset;
2411 context = isl_set_add_dims(context, isl_dim_set,
2412 qp->div->n_row);
2413 bset = isl_basic_set_universe(isl_set_get_dim(context));
2414 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2415 context = isl_set_intersect(context,
2416 isl_set_from_basic_set(bset));
2417 }
2418
2419 aff = isl_set_affine_hull(context);
2420 return isl_qpolynomial_substitute_equalities(qp, aff);
2421 error:
2422 isl_qpolynomial_free(qp);
2423 isl_set_free(context);
2424 return NULL;
2425 }
2426
2427 #undef PW
2428 #define PW isl_pw_qpolynomial
2429 #undef EL
2430 #define EL isl_qpolynomial
2431 #undef IS_ZERO
2432 #define IS_ZERO is_zero
2433 #undef FIELD
2434 #define FIELD qp
2435
2436 #include <isl_pw_templ.c>
2437
2438 #undef UNION
2439 #define UNION isl_union_pw_qpolynomial
2440 #undef PART
2441 #define PART isl_pw_qpolynomial
2442 #undef PARTS
2443 #define PARTS pw_qpolynomial
2444
2445 #include <isl_union_templ.c>
2446
2447 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2448 {
2449 if (!pwqp)
2450 return -1;
2451
2452 if (pwqp->n != -1)
2453 return 0;
2454
2455 if (!isl_set_fast_is_universe(pwqp->p[0].set))
2456 return 0;
2457
2458 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2459 }
2460
2461 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2462 __isl_take isl_pw_qpolynomial *pwqp1,
2463 __isl_take isl_pw_qpolynomial *pwqp2)
2464 {
2465 int i, j, n;
2466 struct isl_pw_qpolynomial *res;
2467 isl_set *set;
2468
2469 if (!pwqp1 || !pwqp2)
2470 goto error;
2471
2472 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2473 goto error);
2474
2475 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2476 isl_pw_qpolynomial_free(pwqp2);
2477 return pwqp1;
2478 }
2479
2480 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2481 isl_pw_qpolynomial_free(pwqp1);
2482 return pwqp2;
2483 }
2484
2485 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2486 isl_pw_qpolynomial_free(pwqp1);
2487 return pwqp2;
2488 }
2489
2490 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2491 isl_pw_qpolynomial_free(pwqp2);
2492 return pwqp1;
2493 }
2494
2495 n = pwqp1->n * pwqp2->n;
2496 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2497
2498 for (i = 0; i < pwqp1->n; ++i) {
2499 for (j = 0; j < pwqp2->n; ++j) {
2500 struct isl_set *common;
2501 struct isl_qpolynomial *prod;
2502 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2503 isl_set_copy(pwqp2->p[j].set));
2504 if (isl_set_fast_is_empty(common)) {
2505 isl_set_free(common);
2506 continue;
2507 }
2508
2509 prod = isl_qpolynomial_mul(
2510 isl_qpolynomial_copy(pwqp1->p[i].qp),
2511 isl_qpolynomial_copy(pwqp2->p[j].qp));
2512
2513 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2514 }
2515 }
2516
2517 isl_pw_qpolynomial_free(pwqp1);
2518 isl_pw_qpolynomial_free(pwqp2);
2519
2520 return res;
2521 error:
2522 isl_pw_qpolynomial_free(pwqp1);
2523 isl_pw_qpolynomial_free(pwqp2);
2524 return NULL;
2525 }
2526
2527 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2528 __isl_take isl_pw_qpolynomial *pwqp)
2529 {
2530 int i;
2531
2532 if (!pwqp)
2533 return NULL;
2534
2535 if (isl_pw_qpolynomial_is_zero(pwqp))
2536 return pwqp;
2537
2538 pwqp = isl_pw_qpolynomial_cow(pwqp);
2539 if (!pwqp)
2540 return NULL;
2541
2542 for (i = 0; i < pwqp->n; ++i) {
2543 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2544 if (!pwqp->p[i].qp)
2545 goto error;
2546 }
2547
2548 return pwqp;
2549 error:
2550 isl_pw_qpolynomial_free(pwqp);
2551 return NULL;
2552 }
2553
2554 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2555 __isl_take isl_pw_qpolynomial *pwqp1,
2556 __isl_take isl_pw_qpolynomial *pwqp2)
2557 {
2558 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2559 }
2560
2561 __isl_give struct isl_upoly *isl_upoly_eval(
2562 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2563 {
2564 int i;
2565 struct isl_upoly_rec *rec;
2566 struct isl_upoly *res;
2567 struct isl_upoly *base;
2568
2569 if (isl_upoly_is_cst(up)) {
2570 isl_vec_free(vec);
2571 return up;
2572 }
2573
2574 rec = isl_upoly_as_rec(up);
2575 if (!rec)
2576 goto error;
2577
2578 isl_assert(up->ctx, rec->n >= 1, goto error);
2579
2580 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2581
2582 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2583 isl_vec_copy(vec));
2584
2585 for (i = rec->n - 2; i >= 0; --i) {
2586 res = isl_upoly_mul(res, isl_upoly_copy(base));
2587 res = isl_upoly_sum(res,
2588 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2589 isl_vec_copy(vec)));
2590 }
2591
2592 isl_upoly_free(base);
2593 isl_upoly_free(up);
2594 isl_vec_free(vec);
2595 return res;
2596 error:
2597 isl_upoly_free(up);
2598 isl_vec_free(vec);
2599 return NULL;
2600 }
2601
2602 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2603 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2604 {
2605 isl_vec *ext;
2606 struct isl_upoly *up;
2607 isl_dim *dim;
2608
2609 if (!qp || !pnt)
2610 goto error;
2611 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2612
2613 if (qp->div->n_row == 0)
2614 ext = isl_vec_copy(pnt->vec);
2615 else {
2616 int i;
2617 unsigned dim = isl_dim_total(qp->dim);
2618 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2619 if (!ext)
2620 goto error;
2621
2622 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2623 for (i = 0; i < qp->div->n_row; ++i) {
2624 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2625 1 + dim + i, &ext->el[1+dim+i]);
2626 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2627 qp->div->row[i][0]);
2628 }
2629 }
2630
2631 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2632 if (!up)
2633 goto error;
2634
2635 dim = isl_dim_copy(qp->dim);
2636 isl_qpolynomial_free(qp);
2637 isl_point_free(pnt);
2638
2639 return isl_qpolynomial_alloc(dim, 0, up);
2640 error:
2641 isl_qpolynomial_free(qp);
2642 isl_point_free(pnt);
2643 return NULL;
2644 }
2645
2646 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2647 __isl_keep struct isl_upoly_cst *cst2)
2648 {
2649 int cmp;
2650 isl_int t;
2651 isl_int_init(t);
2652 isl_int_mul(t, cst1->n, cst2->d);
2653 isl_int_submul(t, cst2->n, cst1->d);
2654 cmp = isl_int_sgn(t);
2655 isl_int_clear(t);
2656 return cmp;
2657 }
2658
2659 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2660 __isl_keep isl_qpolynomial *qp2)
2661 {
2662 struct isl_upoly_cst *cst1, *cst2;
2663
2664 if (!qp1 || !qp2)
2665 return -1;
2666 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2667 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2668 if (isl_qpolynomial_is_nan(qp1))
2669 return -1;
2670 if (isl_qpolynomial_is_nan(qp2))
2671 return -1;
2672 cst1 = isl_upoly_as_cst(qp1->upoly);
2673 cst2 = isl_upoly_as_cst(qp2->upoly);
2674
2675 return isl_upoly_cmp(cst1, cst2) <= 0;
2676 }
2677
2678 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2679 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2680 {
2681 struct isl_upoly_cst *cst1, *cst2;
2682 int cmp;
2683
2684 if (!qp1 || !qp2)
2685 goto error;
2686 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2687 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2688 cst1 = isl_upoly_as_cst(qp1->upoly);
2689 cst2 = isl_upoly_as_cst(qp2->upoly);
2690 cmp = isl_upoly_cmp(cst1, cst2);
2691
2692 if (cmp <= 0) {
2693 isl_qpolynomial_free(qp2);
2694 } else {
2695 isl_qpolynomial_free(qp1);
2696 qp1 = qp2;
2697 }
2698 return qp1;
2699 error:
2700 isl_qpolynomial_free(qp1);
2701 isl_qpolynomial_free(qp2);
2702 return NULL;
2703 }
2704
2705 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2706 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2707 {
2708 struct isl_upoly_cst *cst1, *cst2;
2709 int cmp;
2710
2711 if (!qp1 || !qp2)
2712 goto error;
2713 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2714 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2715 cst1 = isl_upoly_as_cst(qp1->upoly);
2716 cst2 = isl_upoly_as_cst(qp2->upoly);
2717 cmp = isl_upoly_cmp(cst1, cst2);
2718
2719 if (cmp >= 0) {
2720 isl_qpolynomial_free(qp2);
2721 } else {
2722 isl_qpolynomial_free(qp1);
2723 qp1 = qp2;
2724 }
2725 return qp1;
2726 error:
2727 isl_qpolynomial_free(qp1);
2728 isl_qpolynomial_free(qp2);
2729 return NULL;
2730 }
2731
2732 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2733 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2734 unsigned first, unsigned n)
2735 {
2736 unsigned total;
2737 unsigned g_pos;
2738 int *exp;
2739
2740 if (n == 0)
2741 return qp;
2742
2743 qp = isl_qpolynomial_cow(qp);
2744 if (!qp)
2745 return NULL;
2746
2747 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2748 goto error);
2749
2750 g_pos = pos(qp->dim, type) + first;
2751
2752 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2753 if (!qp->div)
2754 goto error;
2755
2756 total = qp->div->n_col - 2;
2757 if (total > g_pos) {
2758 int i;
2759 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2760 if (!exp)
2761 goto error;
2762 for (i = 0; i < total - g_pos; ++i)
2763 exp[i] = i + n;
2764 qp->upoly = expand(qp->upoly, exp, g_pos);
2765 free(exp);
2766 if (!qp->upoly)
2767 goto error;
2768 }
2769
2770 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2771 if (!qp->dim)
2772 goto error;
2773
2774 return qp;
2775 error:
2776 isl_qpolynomial_free(qp);
2777 return NULL;
2778 }
2779
2780 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2781 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2782 {
2783 unsigned pos;
2784
2785 pos = isl_qpolynomial_dim(qp, type);
2786
2787 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2788 }
2789
2790 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2791 __isl_take isl_pw_qpolynomial *pwqp,
2792 enum isl_dim_type type, unsigned n)
2793 {
2794 unsigned pos;
2795
2796 pos = isl_pw_qpolynomial_dim(pwqp, type);
2797
2798 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2799 }
2800
2801 static int *reordering_move(isl_ctx *ctx,
2802 unsigned len, unsigned dst, unsigned src, unsigned n)
2803 {
2804 int i;
2805 int *reordering;
2806
2807 reordering = isl_alloc_array(ctx, int, len);
2808 if (!reordering)
2809 return NULL;
2810
2811 if (dst <= src) {
2812 for (i = 0; i < dst; ++i)
2813 reordering[i] = i;
2814 for (i = 0; i < n; ++i)
2815 reordering[src + i] = dst + i;
2816 for (i = 0; i < src - dst; ++i)
2817 reordering[dst + i] = dst + n + i;
2818 for (i = 0; i < len - src - n; ++i)
2819 reordering[src + n + i] = src + n + i;
2820 } else {
2821 for (i = 0; i < src; ++i)
2822 reordering[i] = i;
2823 for (i = 0; i < n; ++i)
2824 reordering[src + i] = dst + i;
2825 for (i = 0; i < dst - src; ++i)
2826 reordering[src + n + i] = src + i;
2827 for (i = 0; i < len - dst - n; ++i)
2828 reordering[dst + n + i] = dst + n + i;
2829 }
2830
2831 return reordering;
2832 }
2833
2834 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2835 __isl_take isl_qpolynomial *qp,
2836 enum isl_dim_type dst_type, unsigned dst_pos,
2837 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2838 {
2839 unsigned g_dst_pos;
2840 unsigned g_src_pos;
2841 int *reordering;
2842
2843 qp = isl_qpolynomial_cow(qp);
2844 if (!qp)
2845 return NULL;
2846
2847 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2848 goto error);
2849
2850 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2851 g_src_pos = pos(qp->dim, src_type) + src_pos;
2852 if (dst_type > src_type)
2853 g_dst_pos -= n;
2854
2855 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2856 if (!qp->div)
2857 goto error;
2858 qp = sort_divs(qp);
2859 if (!qp)
2860 goto error;
2861
2862 reordering = reordering_move(qp->dim->ctx,
2863 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2864 if (!reordering)
2865 goto error;
2866
2867 qp->upoly = reorder(qp->upoly, reordering);
2868 free(reordering);
2869 if (!qp->upoly)
2870 goto error;
2871
2872 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2873 if (!qp->dim)
2874 goto error;
2875
2876 return qp;
2877 error:
2878 isl_qpolynomial_free(qp);
2879 return NULL;
2880 }
2881
2882 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2883 isl_int *f, isl_int denom)
2884 {
2885 struct isl_upoly *up;
2886
2887 if (!dim)
2888 return NULL;
2889
2890 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2891
2892 return isl_qpolynomial_alloc(dim, 0, up);
2893 }
2894
2895 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2896 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2897 {
2898 isl_int denom;
2899 isl_dim *dim;
2900 struct isl_upoly *up;
2901 isl_qpolynomial *qp;
2902 int sgn;
2903
2904 if (!c)
2905 return NULL;
2906
2907 isl_int_init(denom);
2908
2909 isl_constraint_get_coefficient(c, type, pos, &denom);
2910 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2911 sgn = isl_int_sgn(denom);
2912 isl_int_abs(denom, denom);
2913 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2914 1 + isl_constraint_dim(c, isl_dim_all));
2915 if (sgn < 0)
2916 isl_int_neg(denom, denom);
2917 isl_constraint_set_coefficient(c, type, pos, denom);
2918
2919 dim = isl_dim_copy(c->bmap->dim);
2920
2921 isl_int_clear(denom);
2922 isl_constraint_free(c);
2923
2924 qp = isl_qpolynomial_alloc(dim, 0, up);
2925 if (sgn > 0)
2926 qp = isl_qpolynomial_neg(qp);
2927 return qp;
2928 }
2929
2930 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2931 * in "qp" by subs[i].
2932 */
2933 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2934 __isl_take isl_qpolynomial *qp,
2935 enum isl_dim_type type, unsigned first, unsigned n,
2936 __isl_keep isl_qpolynomial **subs)
2937 {
2938 int i;
2939 struct isl_upoly **ups;
2940
2941 if (n == 0)
2942 return qp;
2943
2944 qp = isl_qpolynomial_cow(qp);
2945 if (!qp)
2946 return NULL;
2947 for (i = 0; i < n; ++i)
2948 if (!subs[i])
2949 goto error;
2950
2951 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2952 goto error);
2953
2954 for (i = 0; i < n; ++i)
2955 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2956 goto error);
2957
2958 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2959 for (i = 0; i < n; ++i)
2960 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2961
2962 first += pos(qp->dim, type);
2963
2964 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2965 if (!ups)
2966 goto error;
2967 for (i = 0; i < n; ++i)
2968 ups[i] = subs[i]->upoly;
2969
2970 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2971
2972 free(ups);
2973
2974 if (!qp->upoly)
2975 goto error;
2976
2977 return qp;
2978 error:
2979 isl_qpolynomial_free(qp);
2980 return NULL;
2981 }
2982
2983 /* Extend "bset" with extra set dimensions for each integer division
2984 * in "qp" and then call "fn" with the extended bset and the polynomial
2985 * that results from replacing each of the integer divisions by the
2986 * corresponding extra set dimension.
2987 */
2988 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2989 __isl_keep isl_basic_set *bset,
2990 int (*fn)(__isl_take isl_basic_set *bset,
2991 __isl_take isl_qpolynomial *poly, void *user), void *user)
2992 {
2993 isl_dim *dim;
2994 isl_mat *div;
2995 isl_qpolynomial *poly;
2996
2997 if (!qp || !bset)
2998 goto error;
2999 if (qp->div->n_row == 0)
3000 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3001 user);
3002
3003 div = isl_mat_copy(qp->div);
3004 dim = isl_dim_copy(qp->dim);
3005 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3006 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3007 bset = isl_basic_set_copy(bset);
3008 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3009 bset = add_div_constraints(bset, div);
3010
3011 return fn(bset, poly, user);
3012 error:
3013 return -1;
3014 }
3015
3016 /* Return total degree in variables first (inclusive) up to last (exclusive).
3017 */
3018 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3019 {
3020 int deg = -1;
3021 int i;
3022 struct isl_upoly_rec *rec;
3023
3024 if (!up)
3025 return -2;
3026 if (isl_upoly_is_zero(up))
3027 return -1;
3028 if (isl_upoly_is_cst(up) || up->var < first)
3029 return 0;
3030
3031 rec = isl_upoly_as_rec(up);
3032 if (!rec)
3033 return -2;
3034
3035 for (i = 0; i < rec->n; ++i) {
3036 int d;
3037
3038 if (isl_upoly_is_zero(rec->p[i]))
3039 continue;
3040 d = isl_upoly_degree(rec->p[i], first, last);
3041 if (up->var < last)
3042 d += i;
3043 if (d > deg)
3044 deg = d;
3045 }
3046
3047 return deg;
3048 }
3049
3050 /* Return total degree in set variables.
3051 */
3052 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3053 {
3054 unsigned ovar;
3055 unsigned nvar;
3056
3057 if (!poly)
3058 return -2;
3059
3060 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3061 nvar = isl_dim_size(poly->dim, isl_dim_set);
3062 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3063 }
3064
3065 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3066 unsigned pos, int deg)
3067 {
3068 int i;
3069 struct isl_upoly_rec *rec;
3070
3071 if (!up)
3072 return NULL;
3073
3074 if (isl_upoly_is_cst(up) || up->var < pos) {
3075 if (deg == 0)
3076 return isl_upoly_copy(up);
3077 else
3078 return isl_upoly_zero(up->ctx);
3079 }
3080
3081 rec = isl_upoly_as_rec(up);
3082 if (!rec)
3083 return NULL;
3084
3085 if (up->var == pos) {
3086 if (deg < rec->n)
3087 return isl_upoly_copy(rec->p[deg]);
3088 else
3089 return isl_upoly_zero(up->ctx);
3090 }
3091
3092 up = isl_upoly_copy(up);
3093 up = isl_upoly_cow(up);
3094 rec = isl_upoly_as_rec(up);
3095 if (!rec)
3096 goto error;
3097
3098 for (i = 0; i < rec->n; ++i) {
3099 struct isl_upoly *t;
3100 t = isl_upoly_coeff(rec->p[i], pos, deg);
3101 if (!t)
3102 goto error;
3103 isl_upoly_free(rec->p[i]);
3104 rec->p[i] = t;
3105 }
3106
3107 return up;
3108 error:
3109 isl_upoly_free(up);
3110 return NULL;
3111 }
3112
3113 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3114 */
3115 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3116 __isl_keep isl_qpolynomial *qp,
3117 enum isl_dim_type type, unsigned t_pos, int deg)
3118 {
3119 unsigned g_pos;
3120 struct isl_upoly *up;
3121 isl_qpolynomial *c;
3122
3123 if (!qp)
3124 return NULL;
3125
3126 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3127 return NULL);
3128
3129 g_pos = pos(qp->dim, type) + t_pos;
3130 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3131
3132 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3133 if (!c)
3134 return NULL;
3135 isl_mat_free(c->div);
3136 c->div = isl_mat_copy(qp->div);
3137 if (!c->div)
3138 goto error;
3139 return c;
3140 error:
3141 isl_qpolynomial_free(c);
3142 return NULL;
3143 }
3144
3145 /* Homogenize the polynomial in the variables first (inclusive) up to
3146 * last (exclusive) by inserting powers of variable first.
3147 * Variable first is assumed not to appear in the input.
3148 */
3149 __isl_give struct isl_upoly *isl_upoly_homogenize(
3150 __isl_take struct isl_upoly *up, int deg, int target,
3151 int first, int last)
3152 {
3153 int i;
3154 struct isl_upoly_rec *rec;
3155
3156 if (!up)
3157 return NULL;
3158 if (isl_upoly_is_zero(up))
3159 return up;
3160 if (deg == target)
3161 return up;
3162 if (isl_upoly_is_cst(up) || up->var < first) {
3163 struct isl_upoly *hom;
3164
3165 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3166 if (!hom)
3167 goto error;
3168 rec = isl_upoly_as_rec(hom);
3169 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3170
3171 return hom;
3172 }
3173
3174 up = isl_upoly_cow(up);
3175 rec = isl_upoly_as_rec(up);
3176 if (!rec)
3177 goto error;
3178
3179 for (i = 0; i < rec->n; ++i) {
3180 if (isl_upoly_is_zero(rec->p[i]))
3181 continue;
3182 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3183 up->var < last ? deg + i : i, target,
3184 first, last);
3185 if (!rec->p[i])
3186 goto error;
3187 }
3188
3189 return up;
3190 error:
3191 isl_upoly_free(up);
3192 return NULL;
3193 }
3194
3195 /* Homogenize the polynomial in the set variables by introducing
3196 * powers of an extra set variable at position 0.
3197 */
3198 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3199 __isl_take isl_qpolynomial *poly)
3200 {
3201 unsigned ovar;
3202 unsigned nvar;
3203 int deg = isl_qpolynomial_degree(poly);
3204
3205 if (deg < -1)
3206 goto error;
3207
3208 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3209 poly = isl_qpolynomial_cow(poly);
3210 if (!poly)
3211 goto error;
3212
3213 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3214 nvar = isl_dim_size(poly->dim, isl_dim_set);
3215 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3216 ovar, ovar + nvar);
3217 if (!poly->upoly)
3218 goto error;
3219
3220 return poly;
3221 error:
3222 isl_qpolynomial_free(poly);
3223 return NULL;
3224 }
3225
3226 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3227 __isl_take isl_mat *div)
3228 {
3229 isl_term *term;
3230 int n;
3231
3232 if (!dim || !div)
3233 goto error;
3234
3235 n = isl_dim_total(dim) + div->n_row;
3236
3237 term = isl_calloc(dim->ctx, struct isl_term,
3238 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3239 if (!term)
3240 goto error;
3241
3242 term->ref = 1;
3243 term->dim = dim;
3244 term->div = div;
3245 isl_int_init(term->n);
3246 isl_int_init(term->d);
3247
3248 return term;
3249 error:
3250 isl_dim_free(dim);
3251 isl_mat_free(div);
3252 return NULL;
3253 }
3254
3255 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3256 {
3257 if (!term)
3258 return NULL;
3259
3260 term->ref++;
3261 return term;
3262 }
3263
3264 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3265 {
3266 int i;
3267 isl_term *dup;
3268 unsigned total;
3269
3270 if (term)
3271 return NULL;
3272
3273 total = isl_dim_total(term->dim) + term->div->n_row;
3274
3275 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3276 if (!dup)
3277 return NULL;
3278
3279 isl_int_set(dup->n, term->n);
3280 isl_int_set(dup->d, term->d);
3281
3282 for (i = 0; i < total; ++i)
3283 dup->pow[i] = term->pow[i];
3284
3285 return dup;
3286 }
3287
3288 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3289 {
3290 if (!term)
3291 return NULL;
3292
3293 if (term->ref == 1)
3294 return term;
3295 term->ref--;
3296 return isl_term_dup(term);
3297 }
3298
3299 void isl_term_free(__isl_take isl_term *term)
3300 {
3301 if (!term)
3302 return;
3303
3304 if (--term->ref > 0)
3305 return;
3306
3307 isl_dim_free(term->dim);
3308 isl_mat_free(term->div);
3309 isl_int_clear(term->n);
3310 isl_int_clear(term->d);
3311 free(term);
3312 }
3313
3314 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3315 {
3316 if (!term)
3317 return 0;
3318
3319 switch (type) {
3320 case isl_dim_param:
3321 case isl_dim_in:
3322 case isl_dim_out: return isl_dim_size(term->dim, type);
3323 case isl_dim_div: return term->div->n_row;
3324 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3325 default: return 0;
3326 }
3327 }
3328
3329 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3330 {
3331 return term ? term->dim->ctx : NULL;
3332 }
3333
3334 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3335 {
3336 if (!term)
3337 return;
3338 isl_int_set(*n, term->n);
3339 }
3340
3341 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3342 {
3343 if (!term)
3344 return;
3345 isl_int_set(*d, term->d);
3346 }
3347
3348 int isl_term_get_exp(__isl_keep isl_term *term,
3349 enum isl_dim_type type, unsigned pos)
3350 {
3351 if (!term)
3352 return -1;
3353
3354 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3355
3356 if (type >= isl_dim_set)
3357 pos += isl_dim_size(term->dim, isl_dim_param);
3358 if (type >= isl_dim_div)
3359 pos += isl_dim_size(term->dim, isl_dim_set);
3360
3361 return term->pow[pos];
3362 }
3363
3364 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3365 {
3366 isl_basic_map *bmap;
3367 unsigned total;
3368 int k;
3369
3370 if (!term)
3371 return NULL;
3372
3373 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3374 return NULL);
3375
3376 total = term->div->n_col - term->div->n_row - 2;
3377 /* No nested divs for now */
3378 isl_assert(term->dim->ctx,
3379 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3380 term->div->n_row) == -1,
3381 return NULL);
3382
3383 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3384 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3385 goto error;
3386
3387 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3388
3389 return isl_basic_map_div(bmap, k);
3390 error:
3391 isl_basic_map_free(bmap);
3392 return NULL;
3393 }
3394
3395 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3396 int (*fn)(__isl_take isl_term *term, void *user),
3397 __isl_take isl_term *term, void *user)
3398 {
3399 int i;
3400 struct isl_upoly_rec *rec;
3401
3402 if (!up || !term)
3403 goto error;
3404
3405 if (isl_upoly_is_zero(up))
3406 return term;
3407
3408 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3409 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3410 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3411
3412 if (isl_upoly_is_cst(up)) {
3413 struct isl_upoly_cst *cst;
3414 cst = isl_upoly_as_cst(up);
3415 if (!cst)
3416 goto error;
3417 term = isl_term_cow(term);
3418 if (!term)
3419 goto error;
3420 isl_int_set(term->n, cst->n);
3421 isl_int_set(term->d, cst->d);
3422 if (fn(isl_term_copy(term), user) < 0)
3423 goto error;
3424 return term;
3425 }
3426
3427 rec = isl_upoly_as_rec(up);
3428 if (!rec)
3429 goto error;
3430
3431 for (i = 0; i < rec->n; ++i) {
3432 term = isl_term_cow(term);
3433 if (!term)
3434 goto error;
3435 term->pow[up->var] = i;
3436 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3437 if (!term)
3438 goto error;
3439 }
3440 term->pow[up->var] = 0;
3441
3442 return term;
3443 error:
3444 isl_term_free(term);
3445 return NULL;
3446 }
3447
3448 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3449 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3450 {
3451 isl_term *term;
3452
3453 if (!qp)
3454 return -1;
3455
3456 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3457 if (!term)
3458 return -1;
3459
3460 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3461
3462 isl_term_free(term);
3463
3464 return term ? 0 : -1;
3465 }
3466
3467 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3468 {
3469 struct isl_upoly *up;
3470 isl_qpolynomial *qp;
3471 int i, n;
3472
3473 if (!term)
3474 return NULL;
3475
3476 n = isl_dim_total(term->dim) + term->div->n_row;
3477
3478 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3479 for (i = 0; i < n; ++i) {
3480 if (!term->pow[i])
3481 continue;
3482 up = isl_upoly_mul(up,
3483 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3484 }
3485
3486 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3487 if (!qp)
3488 goto error;
3489 isl_mat_free(qp->div);
3490 qp->div = isl_mat_copy(term->div);
3491 if (!qp->div)
3492 goto error;
3493
3494 isl_term_free(term);
3495 return qp;
3496 error:
3497 isl_qpolynomial_free(qp);
3498 isl_term_free(term);
3499 return NULL;
3500 }
3501
3502 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3503 __isl_take isl_dim *dim)
3504 {
3505 int i;
3506 int extra;
3507 unsigned total;
3508
3509 if (!qp || !dim)
3510 goto error;
3511
3512 if (isl_dim_equal(qp->dim, dim)) {
3513 isl_dim_free(dim);
3514 return qp;
3515 }
3516
3517 qp = isl_qpolynomial_cow(qp);
3518 if (!qp)
3519 goto error;
3520
3521 extra = isl_dim_size(dim, isl_dim_set) -
3522 isl_dim_size(qp->dim, isl_dim_set);
3523 total = isl_dim_total(qp->dim);
3524 if (qp->div->n_row) {
3525 int *exp;
3526
3527 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3528 if (!exp)
3529 goto error;
3530 for (i = 0; i < qp->div->n_row; ++i)
3531 exp[i] = extra + i;
3532 qp->upoly = expand(qp->upoly, exp, total);
3533 free(exp);
3534 if (!qp->upoly)
3535 goto error;
3536 }
3537 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3538 if (!qp->div)
3539 goto error;
3540 for (i = 0; i < qp->div->n_row; ++i)
3541 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3542
3543 isl_dim_free(qp->dim);
3544 qp->dim = dim;
3545
3546 return qp;
3547 error:
3548 isl_dim_free(dim);
3549 isl_qpolynomial_free(qp);
3550 return NULL;
3551 }
3552
3553 /* For each parameter or variable that does not appear in qp,
3554 * first eliminate the variable from all constraints and then set it to zero.
3555 */
3556 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3557 __isl_keep isl_qpolynomial *qp)
3558 {
3559 int *active = NULL;
3560 int i;
3561 int d;
3562 unsigned nparam;
3563 unsigned nvar;
3564
3565 if (!set || !qp)
3566 goto error;
3567
3568 d = isl_dim_total(set->dim);
3569 active = isl_calloc_array(set->ctx, int, d);
3570 if (set_active(qp, active) < 0)
3571 goto error;
3572
3573 for (i = 0; i < d; ++i)
3574 if (!active[i])
3575 break;
3576
3577 if (i == d) {
3578 free(active);
3579 return set;
3580 }
3581
3582 nparam = isl_dim_size(set->dim, isl_dim_param);
3583 nvar = isl_dim_size(set->dim, isl_dim_set);
3584 for (i = 0; i < nparam; ++i) {
3585 if (active[i])
3586 continue;
3587 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3588 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3589 }
3590 for (i = 0; i < nvar; ++i) {
3591 if (active[nparam + i])
3592 continue;
3593 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3594 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3595 }
3596
3597 free(active);
3598
3599 return set;
3600 error:
3601 free(active);
3602 isl_set_free(set);
3603 return NULL;
3604 }
3605
3606 struct isl_opt_data {
3607 isl_qpolynomial *qp;
3608 int first;
3609 isl_qpolynomial *opt;
3610 int max;
3611 };
3612
3613 static int opt_fn(__isl_take isl_point *pnt, void *user)
3614 {
3615 struct isl_opt_data *data = (struct isl_opt_data *)user;
3616 isl_qpolynomial *val;
3617
3618 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3619 if (data->first) {
3620 data->first = 0;
3621 data->opt = val;
3622 } else if (data->max) {
3623 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3624 } else {
3625 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3626 }
3627
3628 return 0;
3629 }
3630
3631 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3632 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3633 {
3634 struct isl_opt_data data = { NULL, 1, NULL, max };
3635
3636 if (!set || !qp)
3637 goto error;
3638
3639 if (isl_upoly_is_cst(qp->upoly)) {
3640 isl_set_free(set);
3641 return qp;
3642 }
3643
3644 set = fix_inactive(set, qp);
3645
3646 data.qp = qp;
3647 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3648 goto error;
3649
3650 if (data.first)
3651 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3652
3653 isl_set_free(set);
3654 isl_qpolynomial_free(qp);
3655 return data.opt;
3656 error:
3657 isl_set_free(set);
3658 isl_qpolynomial_free(qp);
3659 isl_qpolynomial_free(data.opt);
3660 return NULL;
3661 }
3662
3663 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3664 __isl_take isl_morph *morph)
3665 {
3666 int i;
3667 int n_sub;
3668 isl_ctx *ctx;
3669 struct isl_upoly *up;
3670 unsigned n_div;
3671 struct isl_upoly **subs;
3672 isl_mat *mat;
3673
3674 qp = isl_qpolynomial_cow(qp);
3675 if (!qp || !morph)
3676 goto error;
3677
3678 ctx = qp->dim->ctx;
3679 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3680
3681 n_sub = morph->inv->n_row - 1;
3682 if (morph->inv->n_row != morph->inv->n_col)
3683 n_sub += qp->div->n_row;
3684 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3685 if (!subs)
3686 goto error;
3687
3688 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3689 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3690 morph->inv->row[0][0], morph->inv->n_col);
3691 if (morph->inv->n_row != morph->inv->n_col)
3692 for (i = 0; i < qp->div->n_row; ++i)
3693 subs[morph->inv->n_row - 1 + i] =
3694 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3695
3696 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3697
3698 for (i = 0; i < n_sub; ++i)
3699 isl_upoly_free(subs[i]);
3700 free(subs);
3701
3702 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3703 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3704 qp->div = isl_mat_product(qp->div, mat);
3705 isl_dim_free(qp->dim);
3706 qp->dim = isl_dim_copy(morph->ran->dim);
3707
3708 if (!qp->upoly || !qp->div || !qp->dim)
3709 goto error;
3710
3711 isl_morph_free(morph);
3712
3713 return qp;
3714 error:
3715 isl_qpolynomial_free(qp);
3716 isl_morph_free(morph);
3717 return NULL;
3718 }
3719
3720 static int neg_entry(void **entry, void *user)
3721 {
3722 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3723
3724 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3725
3726 return *pwqp ? 0 : -1;
3727 }
3728
3729 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3730 __isl_take isl_union_pw_qpolynomial *upwqp)
3731 {
3732 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3733 if (!upwqp)
3734 return NULL;
3735
3736 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3737 &neg_entry, NULL) < 0)
3738 goto error;
3739
3740 return upwqp;
3741 error:
3742 isl_union_pw_qpolynomial_free(upwqp);
3743 return NULL;
3744 }
3745
3746 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3747 __isl_take isl_union_pw_qpolynomial *upwqp1,
3748 __isl_take isl_union_pw_qpolynomial *upwqp2)
3749 {
3750 return isl_union_pw_qpolynomial_add(upwqp1,
3751 isl_union_pw_qpolynomial_neg(upwqp2));
3752 }
3753
3754 static int mul_entry(void **entry, void *user)
3755 {
3756 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3757 uint32_t hash;
3758 struct isl_hash_table_entry *entry2;
3759 isl_pw_qpolynomial *pwpq = *entry;
3760 int empty;
3761
3762 hash = isl_dim_get_hash(pwpq->dim);
3763 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3764 hash, &has_dim, pwpq->dim, 0);
3765 if (!entry2)
3766 return 0;
3767
3768 pwpq = isl_pw_qpolynomial_copy(pwpq);
3769 pwpq = isl_pw_qpolynomial_mul(pwpq,
3770 isl_pw_qpolynomial_copy(entry2->data));
3771
3772 empty = isl_pw_qpolynomial_is_zero(pwpq);
3773 if (empty < 0) {
3774 isl_pw_qpolynomial_free(pwpq);
3775 return -1;
3776 }
3777 if (empty) {
3778 isl_pw_qpolynomial_free(pwpq);
3779 return 0;
3780 }
3781
3782 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3783
3784 return 0;
3785 }
3786
3787 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3788 __isl_take isl_union_pw_qpolynomial *upwqp1,
3789 __isl_take isl_union_pw_qpolynomial *upwqp2)
3790 {
3791 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3792 }
3793
3794 /* Reorder the columns of the given div definitions according to the
3795 * given reordering.
3796 */
3797 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3798 __isl_take isl_reordering *r)
3799 {
3800 int i, j;
3801 isl_mat *mat;
3802 int extra;
3803
3804 if (!div || !r)
3805 goto error;
3806
3807 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3808 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3809 if (!mat)
3810 goto error;
3811
3812 for (i = 0; i < div->n_row; ++i) {
3813 isl_seq_cpy(mat->row[i], div->row[i], 2);
3814 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3815 for (j = 0; j < r->len; ++j)
3816 isl_int_set(mat->row[i][2 + r->pos[j]],
3817 div->row[i][2 + j]);
3818 }
3819
3820 isl_reordering_free(r);
3821 isl_mat_free(div);
3822 return mat;
3823 error:
3824 isl_reordering_free(r);
3825 isl_mat_free(div);
3826 return NULL;
3827 }
3828
3829 /* Reorder the dimension of "qp" according to the given reordering.
3830 */
3831 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3832 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3833 {
3834 qp = isl_qpolynomial_cow(qp);
3835 if (!qp)
3836 goto error;
3837
3838 r = isl_reordering_extend(r, qp->div->n_row);
3839 if (!r)
3840 goto error;
3841
3842 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3843 if (!qp->div)
3844 goto error;
3845
3846 qp->upoly = reorder(qp->upoly, r->pos);
3847 if (!qp->upoly)
3848 goto error;
3849
3850 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3851
3852 isl_reordering_free(r);
3853 return qp;
3854 error:
3855 isl_qpolynomial_free(qp);
3856 isl_reordering_free(r);
3857 return NULL;
3858 }
3859
3860 struct isl_split_periods_data {
3861 int max_periods;
3862 isl_pw_qpolynomial *res;
3863 };
3864
3865 /* Create a slice where the integer division "div" has the fixed value "v".
3866 * In particular, if "div" refers to floor(f/m), then create a slice
3867 *
3868 * m v <= f <= m v + (m - 1)
3869 *
3870 * or
3871 *
3872 * f - m v >= 0
3873 * -f + m v + (m - 1) >= 0
3874 */
3875 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3876 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3877 {
3878 int total;
3879 isl_basic_set *bset = NULL;
3880 int k;
3881
3882 if (!dim || !qp)
3883 goto error;
3884
3885 total = isl_dim_total(dim);
3886 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3887
3888 k = isl_basic_set_alloc_inequality(bset);
3889 if (k < 0)
3890 goto error;
3891 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3892 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3893
3894 k = isl_basic_set_alloc_inequality(bset);
3895 if (k < 0)
3896 goto error;
3897 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3898 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3899 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3900 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3901
3902 isl_dim_free(dim);
3903 return isl_set_from_basic_set(bset);
3904 error:
3905 isl_basic_set_free(bset);
3906 isl_dim_free(dim);
3907 return NULL;
3908 }
3909
3910 static int split_periods(__isl_take isl_set *set,
3911 __isl_take isl_qpolynomial *qp, void *user);
3912
3913 /* Create a slice of the domain "set" such that integer division "div"
3914 * has the fixed value "v" and add the results to data->res,
3915 * replacing the integer division by "v" in "qp".
3916 */
3917 static int set_div(__isl_take isl_set *set,
3918 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3919 struct isl_split_periods_data *data)
3920 {
3921 int i;
3922 int total;
3923 isl_set *slice;
3924 struct isl_upoly *cst;
3925
3926 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3927 set = isl_set_intersect(set, slice);
3928
3929 if (!qp)
3930 goto error;
3931
3932 total = isl_dim_total(qp->dim);
3933
3934 for (i = div + 1; i < qp->div->n_row; ++i) {
3935 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
3936 continue;
3937 isl_int_addmul(qp->div->row[i][1],
3938 qp->div->row[i][2 + total + div], v);
3939 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
3940 }
3941
3942 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3943 qp = substitute_div(qp, div, cst);
3944
3945 return split_periods(set, qp, data);
3946 error:
3947 isl_set_free(set);
3948 isl_qpolynomial_free(qp);
3949 return -1;
3950 }
3951
3952 /* Split the domain "set" such that integer division "div"
3953 * has a fixed value (ranging from "min" to "max") on each slice
3954 * and add the results to data->res.
3955 */
3956 static int split_div(__isl_take isl_set *set,
3957 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
3958 struct isl_split_periods_data *data)
3959 {
3960 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
3961 isl_set *set_i = isl_set_copy(set);
3962 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
3963
3964 if (set_div(set_i, qp_i, div, min, data) < 0)
3965 goto error;
3966 }
3967 isl_set_free(set);
3968 isl_qpolynomial_free(qp);
3969 return 0;
3970 error:
3971 isl_set_free(set);
3972 isl_qpolynomial_free(qp);
3973 return -1;
3974 }
3975
3976 /* If "qp" refers to any integer division
3977 * that can only attain "max_periods" distinct values on "set"
3978 * then split the domain along those distinct values.
3979 * Add the results (or the original if no splitting occurs)
3980 * to data->res.
3981 */
3982 static int split_periods(__isl_take isl_set *set,
3983 __isl_take isl_qpolynomial *qp, void *user)
3984 {
3985 int i;
3986 isl_pw_qpolynomial *pwqp;
3987 struct isl_split_periods_data *data;
3988 isl_int min, max;
3989 int total;
3990 int r = 0;
3991
3992 data = (struct isl_split_periods_data *)user;
3993
3994 if (!set || !qp)
3995 goto error;
3996
3997 if (qp->div->n_row == 0) {
3998 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3999 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4000 return 0;
4001 }
4002
4003 isl_int_init(min);
4004 isl_int_init(max);
4005 total = isl_dim_total(qp->dim);
4006 for (i = 0; i < qp->div->n_row; ++i) {
4007 enum isl_lp_result lp_res;
4008
4009 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4010 qp->div->n_row) != -1)
4011 continue;
4012
4013 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4014 set->ctx->one, &min, NULL, NULL);
4015 if (lp_res == isl_lp_error)
4016 goto error2;
4017 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4018 continue;
4019 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4020
4021 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4022 set->ctx->one, &max, NULL, NULL);
4023 if (lp_res == isl_lp_error)
4024 goto error2;
4025 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4026 continue;
4027 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4028
4029 isl_int_sub(max, max, min);
4030 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4031 isl_int_add(max, max, min);
4032 break;
4033 }
4034 }
4035
4036 if (i < qp->div->n_row) {
4037 r = split_div(set, qp, i, min, max, data);
4038 } else {
4039 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4040 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4041 }
4042
4043 isl_int_clear(max);
4044 isl_int_clear(min);
4045
4046 return r;
4047 error2:
4048 isl_int_clear(max);
4049 isl_int_clear(min);
4050 error:
4051 isl_set_free(set);
4052 isl_qpolynomial_free(qp);
4053 return -1;
4054 }
4055
4056 /* If any quasi-polynomial in pwqp refers to any integer division
4057 * that can only attain "max_periods" distinct values on its domain
4058 * then split the domain along those distinct values.
4059 */
4060 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4061 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4062 {
4063 struct isl_split_periods_data data;
4064
4065 data.max_periods = max_periods;
4066 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4067
4068 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4069 goto error;
4070
4071 isl_pw_qpolynomial_free(pwqp);
4072
4073 return data.res;
4074 error:
4075 isl_pw_qpolynomial_free(data.res);
4076 isl_pw_qpolynomial_free(pwqp);
4077 return NULL;
4078 }
4079
4080 /* Construct a piecewise quasipolynomial that is constant on the given
4081 * domain. In particular, it is
4082 * 0 if cst == 0
4083 * 1 if cst == 1
4084 * infinity if cst == -1
4085 */
4086 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4087 __isl_take isl_basic_set *bset, int cst)
4088 {
4089 isl_dim *dim;
4090 isl_qpolynomial *qp;
4091
4092 if (!bset)
4093 return NULL;
4094
4095 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4096 dim = isl_basic_set_get_dim(bset);
4097 if (cst < 0)
4098 qp = isl_qpolynomial_infty(dim);
4099 else if (cst == 0)
4100 qp = isl_qpolynomial_zero(dim);
4101 else
4102 qp = isl_qpolynomial_one(dim);
4103 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4104 }
4105
4106 /* Factor bset, call fn on each of the factors and return the product.
4107 *
4108 * If no factors can be found, simply call fn on the input.
4109 * Otherwise, construct the factors based on the factorizer,
4110 * call fn on each factor and compute the product.
4111 */
4112 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4113 __isl_take isl_basic_set *bset,
4114 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4115 {
4116 int i, n;
4117 isl_dim *dim;
4118 isl_set *set;
4119 isl_factorizer *f;
4120 isl_qpolynomial *qp;
4121 isl_pw_qpolynomial *pwqp;
4122 unsigned nparam;
4123 unsigned nvar;
4124
4125 f = isl_basic_set_factorizer(bset);
4126 if (!f)
4127 goto error;
4128 if (f->n_group == 0) {
4129 isl_factorizer_free(f);
4130 return fn(bset);
4131 }
4132
4133 nparam = isl_basic_set_dim(bset, isl_dim_param);
4134 nvar = isl_basic_set_dim(bset, isl_dim_set);
4135
4136 dim = isl_basic_set_get_dim(bset);
4137 dim = isl_dim_domain(dim);
4138 set = isl_set_universe(isl_dim_copy(dim));
4139 qp = isl_qpolynomial_one(dim);
4140 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4141
4142 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4143
4144 for (i = 0, n = 0; i < f->n_group; ++i) {
4145 isl_basic_set *bset_i;
4146 isl_pw_qpolynomial *pwqp_i;
4147
4148 bset_i = isl_basic_set_copy(bset);
4149 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4150 nparam + n + f->len[i], nvar - n - f->len[i]);
4151 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4152 nparam, n);
4153 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4154 n + f->len[i], nvar - n - f->len[i]);
4155 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4156
4157 pwqp_i = fn(bset_i);
4158 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4159
4160 n += f->len[i];
4161 }
4162
4163 isl_basic_set_free(bset);
4164 isl_factorizer_free(f);
4165
4166 return pwqp;
4167 error:
4168 isl_basic_set_free(bset);
4169 return NULL;
4170 }
4171
4172 /* Factor bset, call fn on each of the factors and return the product.
4173 * The function is assumed to evaluate to zero on empty domains,
4174 * to one on zero-dimensional domains and to infinity on unbounded domains
4175 * and will not be called explicitly on zero-dimensional or unbounded domains.
4176 *
4177 * We first check for some special cases and remove all equalities.
4178 * Then we hand over control to compressed_multiplicative_call.
4179 */
4180 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4181 __isl_take isl_basic_set *bset,
4182 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4183 {
4184 int bounded;
4185 isl_morph *morph;
4186 isl_pw_qpolynomial *pwqp;
4187 unsigned orig_nvar, final_nvar;
4188
4189 if (!bset)
4190 return NULL;
4191
4192 if (isl_basic_set_fast_is_empty(bset))
4193 return constant_on_domain(bset, 0);
4194
4195 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4196
4197 if (orig_nvar == 0)
4198 return constant_on_domain(bset, 1);
4199
4200 bounded = isl_basic_set_is_bounded(bset);
4201 if (bounded < 0)
4202 goto error;
4203 if (!bounded)
4204 return constant_on_domain(bset, -1);
4205
4206 if (bset->n_eq == 0)
4207 return compressed_multiplicative_call(bset, fn);
4208
4209 morph = isl_basic_set_full_compression(bset);
4210 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4211
4212 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4213
4214 pwqp = compressed_multiplicative_call(bset, fn);
4215
4216 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4217 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4218 morph = isl_morph_inverse(morph);
4219
4220 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4221
4222 return pwqp;
4223 error:
4224 isl_basic_set_free(bset);
4225 return NULL;
4226 }
4227
4228 /* Drop all floors in "qp", turning each integer division [a/m] into
4229 * a rational division a/m. If "down" is set, then the integer division
4230 * is replaces by (a-(m-1))/m instead.
4231 */
4232 static __isl_give isl_qpolynomial *qp_drop_floors(
4233 __isl_take isl_qpolynomial *qp, int down)
4234 {
4235 int i;
4236 struct isl_upoly *s;
4237
4238 if (!qp)
4239 return NULL;
4240 if (qp->div->n_row == 0)
4241 return qp;
4242
4243 qp = isl_qpolynomial_cow(qp);
4244 if (!qp)
4245 return NULL;
4246
4247 for (i = qp->div->n_row - 1; i >= 0; --i) {
4248 if (down) {
4249 isl_int_sub(qp->div->row[i][1],
4250 qp->div->row[i][1], qp->div->row[i][0]);
4251 isl_int_add_ui(qp->div->row[i][1],
4252 qp->div->row[i][1], 1);
4253 }
4254 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4255 qp->div->row[i][0], qp->div->n_col - 1);
4256 qp = substitute_div(qp, i, s);
4257 if (!qp)
4258 return NULL;
4259 }
4260
4261 return qp;
4262 }
4263
4264 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4265 * a rational division a/m.
4266 */
4267 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4268 __isl_take isl_pw_qpolynomial *pwqp)
4269 {
4270 int i;
4271
4272 if (!pwqp)
4273 return NULL;
4274
4275 if (isl_pw_qpolynomial_is_zero(pwqp))
4276 return pwqp;
4277
4278 pwqp = isl_pw_qpolynomial_cow(pwqp);
4279 if (!pwqp)
4280 return NULL;
4281
4282 for (i = 0; i < pwqp->n; ++i) {
4283 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4284 if (!pwqp->p[i].qp)
4285 goto error;
4286 }
4287
4288 return pwqp;
4289 error:
4290 isl_pw_qpolynomial_free(pwqp);
4291 return NULL;
4292 }
4293
4294 /* Adjust all the integer divisions in "qp" such that they are at least
4295 * one over the given orthant (identified by "signs"). This ensures
4296 * that they will still be non-negative even after subtracting (m-1)/m.
4297 *
4298 * In particular, f is replaced by f' + v, changing f = [a/m]
4299 * to f' = [(a - m v)/m].
4300 * If the constant term k in a is smaller than m,
4301 * the constant term of v is set to floor(k/m) - 1.
4302 * For any other term, if the coefficient c and the variable x have
4303 * the same sign, then no changes are needed.
4304 * Otherwise, if the variable is positive (and c is negative),
4305 * then the coefficient of x in v is set to floor(c/m).
4306 * If the variable is negative (and c is positive),
4307 * then the coefficient of x in v is set to ceil(c/m).
4308 */
4309 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4310 int *signs)
4311 {
4312 int i, j;
4313 int total;
4314 isl_vec *v = NULL;
4315 struct isl_upoly *s;
4316
4317 qp = isl_qpolynomial_cow(qp);
4318 if (!qp)
4319 return NULL;
4320 qp->div = isl_mat_cow(qp->div);
4321 if (!qp->div)
4322 goto error;
4323
4324 total = isl_dim_total(qp->dim);
4325 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4326
4327 for (i = 0; i < qp->div->n_row; ++i) {
4328 isl_int *row = qp->div->row[i];
4329 v = isl_vec_clr(v);
4330 if (!v)
4331 goto error;
4332 if (isl_int_lt(row[1], row[0])) {
4333 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4334 isl_int_sub_ui(v->el[0], v->el[0], 1);
4335 isl_int_submul(row[1], row[0], v->el[0]);
4336 }
4337 for (j = 0; j < total; ++j) {
4338 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4339 continue;
4340 if (signs[j] < 0)
4341 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4342 else
4343 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4344 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4345 }
4346 for (j = 0; j < i; ++j) {
4347 if (isl_int_sgn(row[2 + total + j]) >= 0)
4348 continue;
4349 isl_int_fdiv_q(v->el[1 + total + j],
4350 row[2 + total + j], row[0]);
4351 isl_int_submul(row[2 + total + j],
4352 row[0], v->el[1 + total + j]);
4353 }
4354 for (j = i + 1; j < qp->div->n_row; ++j) {
4355 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4356 continue;
4357 isl_seq_combine(qp->div->row[j] + 1,
4358 qp->div->ctx->one, qp->div->row[j] + 1,
4359 qp->div->row[j][2 + total + i], v->el, v->size);
4360 }
4361 isl_int_set_si(v->el[1 + total + i], 1);
4362 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4363 qp->div->ctx->one, v->size);
4364 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4365 isl_upoly_free(s);
4366 if (!qp->upoly)
4367 goto error;
4368 }
4369
4370 isl_vec_free(v);
4371 return qp;
4372 error:
4373 isl_vec_free(v);
4374 isl_qpolynomial_free(qp);
4375 return NULL;
4376 }
4377
4378 struct isl_to_poly_data {
4379 int sign;
4380 isl_pw_qpolynomial *res;
4381 isl_qpolynomial *qp;
4382 };
4383
4384 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4385 * We first make all integer divisions positive and then split the
4386 * quasipolynomials into terms with sign data->sign (the direction
4387 * of the requested approximation) and terms with the opposite sign.
4388 * In the first set of terms, each integer division [a/m] is
4389 * overapproximated by a/m, while in the second it is underapproximated
4390 * by (a-(m-1))/m.
4391 */
4392 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4393 void *user)
4394 {
4395 struct isl_to_poly_data *data = user;
4396 isl_pw_qpolynomial *t;
4397 isl_qpolynomial *qp, *up, *down;
4398
4399 qp = isl_qpolynomial_copy(data->qp);
4400 qp = make_divs_pos(qp, signs);
4401
4402 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4403 up = qp_drop_floors(up, 0);
4404 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4405 down = qp_drop_floors(down, 1);
4406
4407 isl_qpolynomial_free(qp);
4408 qp = isl_qpolynomial_add(up, down);
4409
4410 t = isl_pw_qpolynomial_alloc(orthant, qp);
4411 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4412
4413 return 0;
4414 }
4415
4416 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4417 * the polynomial will be an overapproximation. If "sign" is negative,
4418 * it will be an underapproximation. If "sign" is zero, the approximation
4419 * will lie somewhere in between.
4420 *
4421 * In particular, is sign == 0, we simply drop the floors, turning
4422 * the integer divisions into rational divisions.
4423 * Otherwise, we split the domains into orthants, make all integer divisions
4424 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4425 * depending on the requested sign and the sign of the term in which
4426 * the integer division appears.
4427 */
4428 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4429 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4430 {
4431 int i;
4432 struct isl_to_poly_data data;
4433
4434 if (sign == 0)
4435 return pwqp_drop_floors(pwqp);
4436
4437 if (!pwqp)
4438 return NULL;
4439
4440 data.sign = sign;
4441 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4442
4443 for (i = 0; i < pwqp->n; ++i) {
4444 if (pwqp->p[i].qp->div->n_row == 0) {
4445 isl_pw_qpolynomial *t;
4446 t = isl_pw_qpolynomial_alloc(
4447 isl_set_copy(pwqp->p[i].set),
4448 isl_qpolynomial_copy(pwqp->p[i].qp));
4449 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4450 continue;
4451 }
4452 data.qp = pwqp->p[i].qp;
4453 if (isl_set_foreach_orthant(pwqp->p[i].set,
4454 &to_polynomial_on_orthant, &data) < 0)
4455 goto error;
4456 }
4457
4458 isl_pw_qpolynomial_free(pwqp);
4459
4460 return data.res;
4461 error:
4462 isl_pw_qpolynomial_free(pwqp);
4463 isl_pw_qpolynomial_free(data.res);
4464 return NULL;
4465 }
4466
4467 static int poly_entry(void **entry, void *user)
4468 {
4469 int *sign = user;
4470 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4471
4472 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4473
4474 return *pwqp ? 0 : -1;
4475 }
4476
4477 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4478 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4479 {
4480 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4481 if (!upwqp)
4482 return NULL;
4483
4484 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4485 &poly_entry, &sign) < 0)
4486 goto error;
4487
4488 return upwqp;
4489 error:
4490 isl_union_pw_qpolynomial_free(upwqp);
4491 return NULL;
4492 }
Integer set library