?  search:
summary | log | graphiclog1 | graphiclog2 | commit | commitdiff | tree | refs | edit | fork
blame | history | raw | HEAD
isl_polynomial.c: fix typo in comment
[isl.git] / isl_polynomial.c
blob889ca5856e000dda0e6ab19d45063b27f7053e4a
1 /*
2 * Copyright 2010 INRIA Saclay
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
8 * 91893 Orsay, France
9 */
10
11 #include <stdlib.h>
12 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl_factorization.h>
15 #include <isl/lp.h>
16 #include <isl/seq.h>
17 #include <isl_union_map_private.h>
18 #include <isl_polynomial_private.h>
19 #include <isl_point_private.h>
20 #include <isl_dim_private.h>
21 #include <isl_div_private.h>
22 #include <isl_mat_private.h>
23 #include <isl_range.h>
24 #include <isl_local_space_private.h>
25
26 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
27 {
28 switch (type) {
29 case isl_dim_param: return 0;
30 case isl_dim_in: return dim->nparam;
31 case isl_dim_out: return dim->nparam + dim->n_in;
32 default: return 0;
33 }
34 }
35
36 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
37 {
38 if (!up)
39 return -1;
40
41 return up->var < 0;
42 }
43
44 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
45 {
46 if (!up)
47 return NULL;
48
49 isl_assert(up->ctx, up->var < 0, return NULL);
50
51 return (struct isl_upoly_cst *)up;
52 }
53
54 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
55 {
56 if (!up)
57 return NULL;
58
59 isl_assert(up->ctx, up->var >= 0, return NULL);
60
61 return (struct isl_upoly_rec *)up;
62 }
63
64 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
65 __isl_keep struct isl_upoly *up2)
66 {
67 int i;
68 struct isl_upoly_rec *rec1, *rec2;
69
70 if (!up1 || !up2)
71 return -1;
72 if (up1 == up2)
73 return 1;
74 if (up1->var != up2->var)
75 return 0;
76 if (isl_upoly_is_cst(up1)) {
77 struct isl_upoly_cst *cst1, *cst2;
78 cst1 = isl_upoly_as_cst(up1);
79 cst2 = isl_upoly_as_cst(up2);
80 if (!cst1 || !cst2)
81 return -1;
82 return isl_int_eq(cst1->n, cst2->n) &&
83 isl_int_eq(cst1->d, cst2->d);
84 }
85
86 rec1 = isl_upoly_as_rec(up1);
87 rec2 = isl_upoly_as_rec(up2);
88 if (!rec1 || !rec2)
89 return -1;
90
91 if (rec1->n != rec2->n)
92 return 0;
93
94 for (i = 0; i < rec1->n; ++i) {
95 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
96 if (eq < 0 || !eq)
97 return eq;
98 }
99
100 return 1;
101 }
102
103 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
104 {
105 struct isl_upoly_cst *cst;
106
107 if (!up)
108 return -1;
109 if (!isl_upoly_is_cst(up))
110 return 0;
111
112 cst = isl_upoly_as_cst(up);
113 if (!cst)
114 return -1;
115
116 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
117 }
118
119 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
120 {
121 struct isl_upoly_cst *cst;
122
123 if (!up)
124 return 0;
125 if (!isl_upoly_is_cst(up))
126 return 0;
127
128 cst = isl_upoly_as_cst(up);
129 if (!cst)
130 return 0;
131
132 return isl_int_sgn(cst->n);
133 }
134
135 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
136 {
137 struct isl_upoly_cst *cst;
138
139 if (!up)
140 return -1;
141 if (!isl_upoly_is_cst(up))
142 return 0;
143
144 cst = isl_upoly_as_cst(up);
145 if (!cst)
146 return -1;
147
148 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
149 }
150
151 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
152 {
153 struct isl_upoly_cst *cst;
154
155 if (!up)
156 return -1;
157 if (!isl_upoly_is_cst(up))
158 return 0;
159
160 cst = isl_upoly_as_cst(up);
161 if (!cst)
162 return -1;
163
164 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
165 }
166
167 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
168 {
169 struct isl_upoly_cst *cst;
170
171 if (!up)
172 return -1;
173 if (!isl_upoly_is_cst(up))
174 return 0;
175
176 cst = isl_upoly_as_cst(up);
177 if (!cst)
178 return -1;
179
180 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
181 }
182
183 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
184 {
185 struct isl_upoly_cst *cst;
186
187 if (!up)
188 return -1;
189 if (!isl_upoly_is_cst(up))
190 return 0;
191
192 cst = isl_upoly_as_cst(up);
193 if (!cst)
194 return -1;
195
196 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
197 }
198
199 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
200 {
201 struct isl_upoly_cst *cst;
202
203 if (!up)
204 return -1;
205 if (!isl_upoly_is_cst(up))
206 return 0;
207
208 cst = isl_upoly_as_cst(up);
209 if (!cst)
210 return -1;
211
212 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
213 }
214
215 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
216 {
217 struct isl_upoly_cst *cst;
218
219 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
220 if (!cst)
221 return NULL;
222
223 cst->up.ref = 1;
224 cst->up.ctx = ctx;
225 isl_ctx_ref(ctx);
226 cst->up.var = -1;
227
228 isl_int_init(cst->n);
229 isl_int_init(cst->d);
230
231 return cst;
232 }
233
234 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
235 {
236 struct isl_upoly_cst *cst;
237
238 cst = isl_upoly_cst_alloc(ctx);
239 if (!cst)
240 return NULL;
241
242 isl_int_set_si(cst->n, 0);
243 isl_int_set_si(cst->d, 1);
244
245 return &cst->up;
246 }
247
248 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
249 {
250 struct isl_upoly_cst *cst;
251
252 cst = isl_upoly_cst_alloc(ctx);
253 if (!cst)
254 return NULL;
255
256 isl_int_set_si(cst->n, 1);
257 isl_int_set_si(cst->d, 1);
258
259 return &cst->up;
260 }
261
262 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
263 {
264 struct isl_upoly_cst *cst;
265
266 cst = isl_upoly_cst_alloc(ctx);
267 if (!cst)
268 return NULL;
269
270 isl_int_set_si(cst->n, 1);
271 isl_int_set_si(cst->d, 0);
272
273 return &cst->up;
274 }
275
276 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
277 {
278 struct isl_upoly_cst *cst;
279
280 cst = isl_upoly_cst_alloc(ctx);
281 if (!cst)
282 return NULL;
283
284 isl_int_set_si(cst->n, -1);
285 isl_int_set_si(cst->d, 0);
286
287 return &cst->up;
288 }
289
290 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
291 {
292 struct isl_upoly_cst *cst;
293
294 cst = isl_upoly_cst_alloc(ctx);
295 if (!cst)
296 return NULL;
297
298 isl_int_set_si(cst->n, 0);
299 isl_int_set_si(cst->d, 0);
300
301 return &cst->up;
302 }
303
304 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
305 isl_int n, isl_int d)
306 {
307 struct isl_upoly_cst *cst;
308
309 cst = isl_upoly_cst_alloc(ctx);
310 if (!cst)
311 return NULL;
312
313 isl_int_set(cst->n, n);
314 isl_int_set(cst->d, d);
315
316 return &cst->up;
317 }
318
319 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
320 int var, int size)
321 {
322 struct isl_upoly_rec *rec;
323
324 isl_assert(ctx, var >= 0, return NULL);
325 isl_assert(ctx, size >= 0, return NULL);
326 rec = isl_calloc(ctx, struct isl_upoly_rec,
327 sizeof(struct isl_upoly_rec) +
328 (size - 1) * sizeof(struct isl_upoly *));
329 if (!rec)
330 return NULL;
331
332 rec->up.ref = 1;
333 rec->up.ctx = ctx;
334 isl_ctx_ref(ctx);
335 rec->up.var = var;
336
337 rec->n = 0;
338 rec->size = size;
339
340 return rec;
341 }
342
343 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
344 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
345 {
346 qp = isl_qpolynomial_cow(qp);
347 if (!qp || !dim)
348 goto error;
349
350 isl_dim_free(qp->dim);
351 qp->dim = dim;
352
353 return qp;
354 error:
355 isl_qpolynomial_free(qp);
356 isl_dim_free(dim);
357 return NULL;
358 }
359
360 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
361 {
362 return qp ? qp->dim->ctx : NULL;
363 }
364
365 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
366 {
367 return qp ? isl_dim_copy(qp->dim) : NULL;
368 }
369
370 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
371 enum isl_dim_type type)
372 {
373 return qp ? isl_dim_size(qp->dim, type) : 0;
374 }
375
376 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
377 {
378 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
379 }
380
381 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
382 {
383 return qp ? isl_upoly_is_one(qp->upoly) : -1;
384 }
385
386 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
387 {
388 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
389 }
390
391 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
392 {
393 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
394 }
395
396 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
397 {
398 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
399 }
400
401 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
402 {
403 return qp ? isl_upoly_sgn(qp->upoly) : 0;
404 }
405
406 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
407 {
408 isl_int_clear(cst->n);
409 isl_int_clear(cst->d);
410 }
411
412 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
413 {
414 int i;
415
416 for (i = 0; i < rec->n; ++i)
417 isl_upoly_free(rec->p[i]);
418 }
419
420 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
421 {
422 if (!up)
423 return NULL;
424
425 up->ref++;
426 return up;
427 }
428
429 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
430 {
431 struct isl_upoly_cst *cst;
432 struct isl_upoly_cst *dup;
433
434 cst = isl_upoly_as_cst(up);
435 if (!cst)
436 return NULL;
437
438 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
439 if (!dup)
440 return NULL;
441 isl_int_set(dup->n, cst->n);
442 isl_int_set(dup->d, cst->d);
443
444 return &dup->up;
445 }
446
447 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
448 {
449 int i;
450 struct isl_upoly_rec *rec;
451 struct isl_upoly_rec *dup;
452
453 rec = isl_upoly_as_rec(up);
454 if (!rec)
455 return NULL;
456
457 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
458 if (!dup)
459 return NULL;
460
461 for (i = 0; i < rec->n; ++i) {
462 dup->p[i] = isl_upoly_copy(rec->p[i]);
463 if (!dup->p[i])
464 goto error;
465 dup->n++;
466 }
467
468 return &dup->up;
469 error:
470 isl_upoly_free(&dup->up);
471 return NULL;
472 }
473
474 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
475 {
476 struct isl_upoly *dup;
477
478 if (!up)
479 return NULL;
480
481 if (isl_upoly_is_cst(up))
482 return isl_upoly_dup_cst(up);
483 else
484 return isl_upoly_dup_rec(up);
485 }
486
487 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
488 {
489 if (!up)
490 return NULL;
491
492 if (up->ref == 1)
493 return up;
494 up->ref--;
495 return isl_upoly_dup(up);
496 }
497
498 void isl_upoly_free(__isl_take struct isl_upoly *up)
499 {
500 if (!up)
501 return;
502
503 if (--up->ref > 0)
504 return;
505
506 if (up->var < 0)
507 upoly_free_cst((struct isl_upoly_cst *)up);
508 else
509 upoly_free_rec((struct isl_upoly_rec *)up);
510
511 isl_ctx_deref(up->ctx);
512 free(up);
513 }
514
515 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
516 {
517 isl_int gcd;
518
519 isl_int_init(gcd);
520 isl_int_gcd(gcd, cst->n, cst->d);
521 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
522 isl_int_divexact(cst->n, cst->n, gcd);
523 isl_int_divexact(cst->d, cst->d, gcd);
524 }
525 isl_int_clear(gcd);
526 }
527
528 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
529 __isl_take struct isl_upoly *up2)
530 {
531 struct isl_upoly_cst *cst1;
532 struct isl_upoly_cst *cst2;
533
534 up1 = isl_upoly_cow(up1);
535 if (!up1 || !up2)
536 goto error;
537
538 cst1 = isl_upoly_as_cst(up1);
539 cst2 = isl_upoly_as_cst(up2);
540
541 if (isl_int_eq(cst1->d, cst2->d))
542 isl_int_add(cst1->n, cst1->n, cst2->n);
543 else {
544 isl_int_mul(cst1->n, cst1->n, cst2->d);
545 isl_int_addmul(cst1->n, cst2->n, cst1->d);
546 isl_int_mul(cst1->d, cst1->d, cst2->d);
547 }
548
549 isl_upoly_cst_reduce(cst1);
550
551 isl_upoly_free(up2);
552 return up1;
553 error:
554 isl_upoly_free(up1);
555 isl_upoly_free(up2);
556 return NULL;
557 }
558
559 static __isl_give struct isl_upoly *replace_by_zero(
560 __isl_take struct isl_upoly *up)
561 {
562 struct isl_ctx *ctx;
563
564 if (!up)
565 return NULL;
566 ctx = up->ctx;
567 isl_upoly_free(up);
568 return isl_upoly_zero(ctx);
569 }
570
571 static __isl_give struct isl_upoly *replace_by_constant_term(
572 __isl_take struct isl_upoly *up)
573 {
574 struct isl_upoly_rec *rec;
575 struct isl_upoly *cst;
576
577 if (!up)
578 return NULL;
579
580 rec = isl_upoly_as_rec(up);
581 if (!rec)
582 goto error;
583 cst = isl_upoly_copy(rec->p[0]);
584 isl_upoly_free(up);
585 return cst;
586 error:
587 isl_upoly_free(up);
588 return NULL;
589 }
590
591 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
592 __isl_take struct isl_upoly *up2)
593 {
594 int i;
595 struct isl_upoly_rec *rec1, *rec2;
596
597 if (!up1 || !up2)
598 goto error;
599
600 if (isl_upoly_is_nan(up1)) {
601 isl_upoly_free(up2);
602 return up1;
603 }
604
605 if (isl_upoly_is_nan(up2)) {
606 isl_upoly_free(up1);
607 return up2;
608 }
609
610 if (isl_upoly_is_zero(up1)) {
611 isl_upoly_free(up1);
612 return up2;
613 }
614
615 if (isl_upoly_is_zero(up2)) {
616 isl_upoly_free(up2);
617 return up1;
618 }
619
620 if (up1->var < up2->var)
621 return isl_upoly_sum(up2, up1);
622
623 if (up2->var < up1->var) {
624 struct isl_upoly_rec *rec;
625 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
626 isl_upoly_free(up1);
627 return up2;
628 }
629 up1 = isl_upoly_cow(up1);
630 rec = isl_upoly_as_rec(up1);
631 if (!rec)
632 goto error;
633 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
634 if (rec->n == 1)
635 up1 = replace_by_constant_term(up1);
636 return up1;
637 }
638
639 if (isl_upoly_is_cst(up1))
640 return isl_upoly_sum_cst(up1, up2);
641
642 rec1 = isl_upoly_as_rec(up1);
643 rec2 = isl_upoly_as_rec(up2);
644 if (!rec1 || !rec2)
645 goto error;
646
647 if (rec1->n < rec2->n)
648 return isl_upoly_sum(up2, up1);
649
650 up1 = isl_upoly_cow(up1);
651 rec1 = isl_upoly_as_rec(up1);
652 if (!rec1)
653 goto error;
654
655 for (i = rec2->n - 1; i >= 0; --i) {
656 rec1->p[i] = isl_upoly_sum(rec1->p[i],
657 isl_upoly_copy(rec2->p[i]));
658 if (!rec1->p[i])
659 goto error;
660 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
661 isl_upoly_free(rec1->p[i]);
662 rec1->n--;
663 }
664 }
665
666 if (rec1->n == 0)
667 up1 = replace_by_zero(up1);
668 else if (rec1->n == 1)
669 up1 = replace_by_constant_term(up1);
670
671 isl_upoly_free(up2);
672
673 return up1;
674 error:
675 isl_upoly_free(up1);
676 isl_upoly_free(up2);
677 return NULL;
678 }
679
680 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
681 __isl_take struct isl_upoly *up, isl_int v)
682 {
683 struct isl_upoly_cst *cst;
684
685 up = isl_upoly_cow(up);
686 if (!up)
687 return NULL;
688
689 cst = isl_upoly_as_cst(up);
690
691 isl_int_addmul(cst->n, cst->d, v);
692
693 return up;
694 }
695
696 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
697 __isl_take struct isl_upoly *up, isl_int v)
698 {
699 struct isl_upoly_rec *rec;
700
701 if (!up)
702 return NULL;
703
704 if (isl_upoly_is_cst(up))
705 return isl_upoly_cst_add_isl_int(up, v);
706
707 up = isl_upoly_cow(up);
708 rec = isl_upoly_as_rec(up);
709 if (!rec)
710 goto error;
711
712 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
713 if (!rec->p[0])
714 goto error;
715
716 return up;
717 error:
718 isl_upoly_free(up);
719 return NULL;
720 }
721
722 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
723 __isl_take struct isl_upoly *up, isl_int v)
724 {
725 struct isl_upoly_cst *cst;
726
727 if (isl_upoly_is_zero(up))
728 return up;
729
730 up = isl_upoly_cow(up);
731 if (!up)
732 return NULL;
733
734 cst = isl_upoly_as_cst(up);
735
736 isl_int_mul(cst->n, cst->n, v);
737
738 return up;
739 }
740
741 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
742 __isl_take struct isl_upoly *up, isl_int v)
743 {
744 int i;
745 struct isl_upoly_rec *rec;
746
747 if (!up)
748 return NULL;
749
750 if (isl_upoly_is_cst(up))
751 return isl_upoly_cst_mul_isl_int(up, v);
752
753 up = isl_upoly_cow(up);
754 rec = isl_upoly_as_rec(up);
755 if (!rec)
756 goto error;
757
758 for (i = 0; i < rec->n; ++i) {
759 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
760 if (!rec->p[i])
761 goto error;
762 }
763
764 return up;
765 error:
766 isl_upoly_free(up);
767 return NULL;
768 }
769
770 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
771 __isl_take struct isl_upoly *up2)
772 {
773 struct isl_upoly_cst *cst1;
774 struct isl_upoly_cst *cst2;
775
776 up1 = isl_upoly_cow(up1);
777 if (!up1 || !up2)
778 goto error;
779
780 cst1 = isl_upoly_as_cst(up1);
781 cst2 = isl_upoly_as_cst(up2);
782
783 isl_int_mul(cst1->n, cst1->n, cst2->n);
784 isl_int_mul(cst1->d, cst1->d, cst2->d);
785
786 isl_upoly_cst_reduce(cst1);
787
788 isl_upoly_free(up2);
789 return up1;
790 error:
791 isl_upoly_free(up1);
792 isl_upoly_free(up2);
793 return NULL;
794 }
795
796 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
797 __isl_take struct isl_upoly *up2)
798 {
799 struct isl_upoly_rec *rec1;
800 struct isl_upoly_rec *rec2;
801 struct isl_upoly_rec *res;
802 int i, j;
803 int size;
804
805 rec1 = isl_upoly_as_rec(up1);
806 rec2 = isl_upoly_as_rec(up2);
807 if (!rec1 || !rec2)
808 goto error;
809 size = rec1->n + rec2->n - 1;
810 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
811 if (!res)
812 goto error;
813
814 for (i = 0; i < rec1->n; ++i) {
815 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
816 isl_upoly_copy(rec1->p[i]));
817 if (!res->p[i])
818 goto error;
819 res->n++;
820 }
821 for (; i < size; ++i) {
822 res->p[i] = isl_upoly_zero(up1->ctx);
823 if (!res->p[i])
824 goto error;
825 res->n++;
826 }
827 for (i = 0; i < rec1->n; ++i) {
828 for (j = 1; j < rec2->n; ++j) {
829 struct isl_upoly *up;
830 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
831 isl_upoly_copy(rec1->p[i]));
832 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
833 if (!res->p[i + j])
834 goto error;
835 }
836 }
837
838 isl_upoly_free(up1);
839 isl_upoly_free(up2);
840
841 return &res->up;
842 error:
843 isl_upoly_free(up1);
844 isl_upoly_free(up2);
845 isl_upoly_free(&res->up);
846 return NULL;
847 }
848
849 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
850 __isl_take struct isl_upoly *up2)
851 {
852 if (!up1 || !up2)
853 goto error;
854
855 if (isl_upoly_is_nan(up1)) {
856 isl_upoly_free(up2);
857 return up1;
858 }
859
860 if (isl_upoly_is_nan(up2)) {
861 isl_upoly_free(up1);
862 return up2;
863 }
864
865 if (isl_upoly_is_zero(up1)) {
866 isl_upoly_free(up2);
867 return up1;
868 }
869
870 if (isl_upoly_is_zero(up2)) {
871 isl_upoly_free(up1);
872 return up2;
873 }
874
875 if (isl_upoly_is_one(up1)) {
876 isl_upoly_free(up1);
877 return up2;
878 }
879
880 if (isl_upoly_is_one(up2)) {
881 isl_upoly_free(up2);
882 return up1;
883 }
884
885 if (up1->var < up2->var)
886 return isl_upoly_mul(up2, up1);
887
888 if (up2->var < up1->var) {
889 int i;
890 struct isl_upoly_rec *rec;
891 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
892 isl_ctx *ctx = up1->ctx;
893 isl_upoly_free(up1);
894 isl_upoly_free(up2);
895 return isl_upoly_nan(ctx);
896 }
897 up1 = isl_upoly_cow(up1);
898 rec = isl_upoly_as_rec(up1);
899 if (!rec)
900 goto error;
901
902 for (i = 0; i < rec->n; ++i) {
903 rec->p[i] = isl_upoly_mul(rec->p[i],
904 isl_upoly_copy(up2));
905 if (!rec->p[i])
906 goto error;
907 }
908 isl_upoly_free(up2);
909 return up1;
910 }
911
912 if (isl_upoly_is_cst(up1))
913 return isl_upoly_mul_cst(up1, up2);
914
915 return isl_upoly_mul_rec(up1, up2);
916 error:
917 isl_upoly_free(up1);
918 isl_upoly_free(up2);
919 return NULL;
920 }
921
922 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
923 unsigned power)
924 {
925 struct isl_upoly *res;
926
927 if (!up)
928 return NULL;
929 if (power == 1)
930 return up;
931
932 if (power % 2)
933 res = isl_upoly_copy(up);
934 else
935 res = isl_upoly_one(up->ctx);
936
937 while (power >>= 1) {
938 up = isl_upoly_mul(up, isl_upoly_copy(up));
939 if (power % 2)
940 res = isl_upoly_mul(res, isl_upoly_copy(up));
941 }
942
943 isl_upoly_free(up);
944 return res;
945 }
946
947 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
948 unsigned n_div, __isl_take struct isl_upoly *up)
949 {
950 struct isl_qpolynomial *qp = NULL;
951 unsigned total;
952
953 if (!dim || !up)
954 goto error;
955
956 total = isl_dim_total(dim);
957
958 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
959 if (!qp)
960 goto error;
961
962 qp->ref = 1;
963 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
964 if (!qp->div)
965 goto error;
966
967 qp->dim = dim;
968 qp->upoly = up;
969
970 return qp;
971 error:
972 isl_dim_free(dim);
973 isl_upoly_free(up);
974 isl_qpolynomial_free(qp);
975 return NULL;
976 }
977
978 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
979 {
980 if (!qp)
981 return NULL;
982
983 qp->ref++;
984 return qp;
985 }
986
987 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
988 {
989 struct isl_qpolynomial *dup;
990
991 if (!qp)
992 return NULL;
993
994 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
995 isl_upoly_copy(qp->upoly));
996 if (!dup)
997 return NULL;
998 isl_mat_free(dup->div);
999 dup->div = isl_mat_copy(qp->div);
1000 if (!dup->div)
1001 goto error;
1002
1003 return dup;
1004 error:
1005 isl_qpolynomial_free(dup);
1006 return NULL;
1007 }
1008
1009 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1010 {
1011 if (!qp)
1012 return NULL;
1013
1014 if (qp->ref == 1)
1015 return qp;
1016 qp->ref--;
1017 return isl_qpolynomial_dup(qp);
1018 }
1019
1020 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1021 {
1022 if (!qp)
1023 return;
1024
1025 if (--qp->ref > 0)
1026 return;
1027
1028 isl_dim_free(qp->dim);
1029 isl_mat_free(qp->div);
1030 isl_upoly_free(qp->upoly);
1031
1032 free(qp);
1033 }
1034
1035 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1036 {
1037 int i;
1038 struct isl_upoly *up;
1039 struct isl_upoly_rec *rec;
1040 struct isl_upoly_cst *cst;
1041
1042 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1043 if (!rec)
1044 return NULL;
1045 for (i = 0; i < 1 + power; ++i) {
1046 rec->p[i] = isl_upoly_zero(ctx);
1047 if (!rec->p[i])
1048 goto error;
1049 rec->n++;
1050 }
1051 cst = isl_upoly_as_cst(rec->p[power]);
1052 isl_int_set_si(cst->n, 1);
1053
1054 return &rec->up;
1055 error:
1056 isl_upoly_free(&rec->up);
1057 return NULL;
1058 }
1059
1060 /* r array maps original positions to new positions.
1061 */
1062 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1063 int *r)
1064 {
1065 int i;
1066 struct isl_upoly_rec *rec;
1067 struct isl_upoly *base;
1068 struct isl_upoly *res;
1069
1070 if (isl_upoly_is_cst(up))
1071 return up;
1072
1073 rec = isl_upoly_as_rec(up);
1074 if (!rec)
1075 goto error;
1076
1077 isl_assert(up->ctx, rec->n >= 1, goto error);
1078
1079 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1080 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1081
1082 for (i = rec->n - 2; i >= 0; --i) {
1083 res = isl_upoly_mul(res, isl_upoly_copy(base));
1084 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1085 }
1086
1087 isl_upoly_free(base);
1088 isl_upoly_free(up);
1089
1090 return res;
1091 error:
1092 isl_upoly_free(up);
1093 return NULL;
1094 }
1095
1096 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1097 {
1098 int n_row, n_col;
1099 int equal;
1100
1101 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1102 div1->n_col >= div2->n_col, return -1);
1103
1104 if (div1->n_row == div2->n_row)
1105 return isl_mat_is_equal(div1, div2);
1106
1107 n_row = div1->n_row;
1108 n_col = div1->n_col;
1109 div1->n_row = div2->n_row;
1110 div1->n_col = div2->n_col;
1111
1112 equal = isl_mat_is_equal(div1, div2);
1113
1114 div1->n_row = n_row;
1115 div1->n_col = n_col;
1116
1117 return equal;
1118 }
1119
1120 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1121 {
1122 int li, lj;
1123
1124 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1125 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1126
1127 if (li != lj)
1128 return li - lj;
1129
1130 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1131 }
1132
1133 struct isl_div_sort_info {
1134 isl_mat *div;
1135 int row;
1136 };
1137
1138 static int div_sort_cmp(const void *p1, const void *p2)
1139 {
1140 const struct isl_div_sort_info *i1, *i2;
1141 i1 = (const struct isl_div_sort_info *) p1;
1142 i2 = (const struct isl_div_sort_info *) p2;
1143
1144 return cmp_row(i1->div, i1->row, i2->row);
1145 }
1146
1147 /* Sort divs and remove duplicates.
1148 */
1149 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1150 {
1151 int i;
1152 int skip;
1153 int len;
1154 struct isl_div_sort_info *array = NULL;
1155 int *pos = NULL, *at = NULL;
1156 int *reordering = NULL;
1157 unsigned div_pos;
1158
1159 if (!qp)
1160 return NULL;
1161 if (qp->div->n_row <= 1)
1162 return qp;
1163
1164 div_pos = isl_dim_total(qp->dim);
1165
1166 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1167 qp->div->n_row);
1168 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1169 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1170 len = qp->div->n_col - 2;
1171 reordering = isl_alloc_array(qp->div->ctx, int, len);
1172 if (!array || !pos || !at || !reordering)
1173 goto error;
1174
1175 for (i = 0; i < qp->div->n_row; ++i) {
1176 array[i].div = qp->div;
1177 array[i].row = i;
1178 pos[i] = i;
1179 at[i] = i;
1180 }
1181
1182 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1183 div_sort_cmp);
1184
1185 for (i = 0; i < div_pos; ++i)
1186 reordering[i] = i;
1187
1188 for (i = 0; i < qp->div->n_row; ++i) {
1189 if (pos[array[i].row] == i)
1190 continue;
1191 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1192 pos[at[i]] = pos[array[i].row];
1193 at[pos[array[i].row]] = at[i];
1194 at[i] = array[i].row;
1195 pos[array[i].row] = i;
1196 }
1197
1198 skip = 0;
1199 for (i = 0; i < len - div_pos; ++i) {
1200 if (i > 0 &&
1201 isl_seq_eq(qp->div->row[i - skip - 1],
1202 qp->div->row[i - skip], qp->div->n_col)) {
1203 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1204 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1205 2 + div_pos + i - skip);
1206 qp->div = isl_mat_drop_cols(qp->div,
1207 2 + div_pos + i - skip, 1);
1208 skip++;
1209 }
1210 reordering[div_pos + array[i].row] = div_pos + i - skip;
1211 }
1212
1213 qp->upoly = reorder(qp->upoly, reordering);
1214
1215 if (!qp->upoly || !qp->div)
1216 goto error;
1217
1218 free(at);
1219 free(pos);
1220 free(array);
1221 free(reordering);
1222
1223 return qp;
1224 error:
1225 free(at);
1226 free(pos);
1227 free(array);
1228 free(reordering);
1229 isl_qpolynomial_free(qp);
1230 return NULL;
1231 }
1232
1233 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1234 int *exp, int first)
1235 {
1236 int i;
1237 struct isl_upoly_rec *rec;
1238
1239 if (isl_upoly_is_cst(up))
1240 return up;
1241
1242 if (up->var < first)
1243 return up;
1244
1245 if (exp[up->var - first] == up->var - first)
1246 return up;
1247
1248 up = isl_upoly_cow(up);
1249 if (!up)
1250 goto error;
1251
1252 up->var = exp[up->var - first] + first;
1253
1254 rec = isl_upoly_as_rec(up);
1255 if (!rec)
1256 goto error;
1257
1258 for (i = 0; i < rec->n; ++i) {
1259 rec->p[i] = expand(rec->p[i], exp, first);
1260 if (!rec->p[i])
1261 goto error;
1262 }
1263
1264 return up;
1265 error:
1266 isl_upoly_free(up);
1267 return NULL;
1268 }
1269
1270 static __isl_give isl_qpolynomial *with_merged_divs(
1271 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1272 __isl_take isl_qpolynomial *qp2),
1273 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1274 {
1275 int *exp1 = NULL;
1276 int *exp2 = NULL;
1277 isl_mat *div = NULL;
1278
1279 qp1 = isl_qpolynomial_cow(qp1);
1280 qp2 = isl_qpolynomial_cow(qp2);
1281
1282 if (!qp1 || !qp2)
1283 goto error;
1284
1285 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1286 qp1->div->n_col >= qp2->div->n_col, goto error);
1287
1288 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1289 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1290 if (!exp1 || !exp2)
1291 goto error;
1292
1293 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1294 if (!div)
1295 goto error;
1296
1297 isl_mat_free(qp1->div);
1298 qp1->div = isl_mat_copy(div);
1299 isl_mat_free(qp2->div);
1300 qp2->div = isl_mat_copy(div);
1301
1302 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1303 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1304
1305 if (!qp1->upoly || !qp2->upoly)
1306 goto error;
1307
1308 isl_mat_free(div);
1309 free(exp1);
1310 free(exp2);
1311
1312 return fn(qp1, qp2);
1313 error:
1314 isl_mat_free(div);
1315 free(exp1);
1316 free(exp2);
1317 isl_qpolynomial_free(qp1);
1318 isl_qpolynomial_free(qp2);
1319 return NULL;
1320 }
1321
1322 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1323 __isl_take isl_qpolynomial *qp2)
1324 {
1325 qp1 = isl_qpolynomial_cow(qp1);
1326
1327 if (!qp1 || !qp2)
1328 goto error;
1329
1330 if (qp1->div->n_row < qp2->div->n_row)
1331 return isl_qpolynomial_add(qp2, qp1);
1332
1333 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1334 if (!compatible_divs(qp1->div, qp2->div))
1335 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1336
1337 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1338 if (!qp1->upoly)
1339 goto error;
1340
1341 isl_qpolynomial_free(qp2);
1342
1343 return qp1;
1344 error:
1345 isl_qpolynomial_free(qp1);
1346 isl_qpolynomial_free(qp2);
1347 return NULL;
1348 }
1349
1350 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1351 __isl_keep isl_set *dom,
1352 __isl_take isl_qpolynomial *qp1,
1353 __isl_take isl_qpolynomial *qp2)
1354 {
1355 qp1 = isl_qpolynomial_add(qp1, qp2);
1356 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1357 return qp1;
1358 }
1359
1360 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1361 __isl_take isl_qpolynomial *qp2)
1362 {
1363 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1364 }
1365
1366 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1367 __isl_take isl_qpolynomial *qp, isl_int v)
1368 {
1369 if (isl_int_is_zero(v))
1370 return qp;
1371
1372 qp = isl_qpolynomial_cow(qp);
1373 if (!qp)
1374 return NULL;
1375
1376 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1377 if (!qp->upoly)
1378 goto error;
1379
1380 return qp;
1381 error:
1382 isl_qpolynomial_free(qp);
1383 return NULL;
1384
1385 }
1386
1387 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1388 {
1389 if (!qp)
1390 return NULL;
1391
1392 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1393 }
1394
1395 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1396 __isl_take isl_qpolynomial *qp, isl_int v)
1397 {
1398 if (isl_int_is_one(v))
1399 return qp;
1400
1401 if (qp && isl_int_is_zero(v)) {
1402 isl_qpolynomial *zero;
1403 zero = isl_qpolynomial_zero(isl_dim_copy(qp->dim));
1404 isl_qpolynomial_free(qp);
1405 return zero;
1406 }
1407
1408 qp = isl_qpolynomial_cow(qp);
1409 if (!qp)
1410 return NULL;
1411
1412 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1413 if (!qp->upoly)
1414 goto error;
1415
1416 return qp;
1417 error:
1418 isl_qpolynomial_free(qp);
1419 return NULL;
1420 }
1421
1422 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1423 __isl_take isl_qpolynomial *qp2)
1424 {
1425 qp1 = isl_qpolynomial_cow(qp1);
1426
1427 if (!qp1 || !qp2)
1428 goto error;
1429
1430 if (qp1->div->n_row < qp2->div->n_row)
1431 return isl_qpolynomial_mul(qp2, qp1);
1432
1433 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1434 if (!compatible_divs(qp1->div, qp2->div))
1435 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1436
1437 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1438 if (!qp1->upoly)
1439 goto error;
1440
1441 isl_qpolynomial_free(qp2);
1442
1443 return qp1;
1444 error:
1445 isl_qpolynomial_free(qp1);
1446 isl_qpolynomial_free(qp2);
1447 return NULL;
1448 }
1449
1450 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1451 unsigned power)
1452 {
1453 qp = isl_qpolynomial_cow(qp);
1454
1455 if (!qp)
1456 return NULL;
1457
1458 qp->upoly = isl_upoly_pow(qp->upoly, power);
1459 if (!qp->upoly)
1460 goto error;
1461
1462 return qp;
1463 error:
1464 isl_qpolynomial_free(qp);
1465 return NULL;
1466 }
1467
1468 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1469 {
1470 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1471 }
1472
1473 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1474 {
1475 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1476 }
1477
1478 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1479 {
1480 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1481 }
1482
1483 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1484 {
1485 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1486 }
1487
1488 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1489 {
1490 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1491 }
1492
1493 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1494 isl_int v)
1495 {
1496 struct isl_qpolynomial *qp;
1497 struct isl_upoly_cst *cst;
1498
1499 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1500 if (!qp)
1501 return NULL;
1502
1503 cst = isl_upoly_as_cst(qp->upoly);
1504 isl_int_set(cst->n, v);
1505
1506 return qp;
1507 }
1508
1509 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1510 isl_int *n, isl_int *d)
1511 {
1512 struct isl_upoly_cst *cst;
1513
1514 if (!qp)
1515 return -1;
1516
1517 if (!isl_upoly_is_cst(qp->upoly))
1518 return 0;
1519
1520 cst = isl_upoly_as_cst(qp->upoly);
1521 if (!cst)
1522 return -1;
1523
1524 if (n)
1525 isl_int_set(*n, cst->n);
1526 if (d)
1527 isl_int_set(*d, cst->d);
1528
1529 return 1;
1530 }
1531
1532 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1533 {
1534 int is_cst;
1535 struct isl_upoly_rec *rec;
1536
1537 if (!up)
1538 return -1;
1539
1540 if (up->var < 0)
1541 return 1;
1542
1543 rec = isl_upoly_as_rec(up);
1544 if (!rec)
1545 return -1;
1546
1547 if (rec->n > 2)
1548 return 0;
1549
1550 isl_assert(up->ctx, rec->n > 1, return -1);
1551
1552 is_cst = isl_upoly_is_cst(rec->p[1]);
1553 if (is_cst < 0)
1554 return -1;
1555 if (!is_cst)
1556 return 0;
1557
1558 return isl_upoly_is_affine(rec->p[0]);
1559 }
1560
1561 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1562 {
1563 if (!qp)
1564 return -1;
1565
1566 if (qp->div->n_row > 0)
1567 return 0;
1568
1569 return isl_upoly_is_affine(qp->upoly);
1570 }
1571
1572 static void update_coeff(__isl_keep isl_vec *aff,
1573 __isl_keep struct isl_upoly_cst *cst, int pos)
1574 {
1575 isl_int gcd;
1576 isl_int f;
1577
1578 if (isl_int_is_zero(cst->n))
1579 return;
1580
1581 isl_int_init(gcd);
1582 isl_int_init(f);
1583 isl_int_gcd(gcd, cst->d, aff->el[0]);
1584 isl_int_divexact(f, cst->d, gcd);
1585 isl_int_divexact(gcd, aff->el[0], gcd);
1586 isl_seq_scale(aff->el, aff->el, f, aff->size);
1587 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1588 isl_int_clear(gcd);
1589 isl_int_clear(f);
1590 }
1591
1592 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1593 __isl_keep isl_vec *aff)
1594 {
1595 struct isl_upoly_cst *cst;
1596 struct isl_upoly_rec *rec;
1597
1598 if (!up || !aff)
1599 return -1;
1600
1601 if (up->var < 0) {
1602 struct isl_upoly_cst *cst;
1603
1604 cst = isl_upoly_as_cst(up);
1605 if (!cst)
1606 return -1;
1607 update_coeff(aff, cst, 0);
1608 return 0;
1609 }
1610
1611 rec = isl_upoly_as_rec(up);
1612 if (!rec)
1613 return -1;
1614 isl_assert(up->ctx, rec->n == 2, return -1);
1615
1616 cst = isl_upoly_as_cst(rec->p[1]);
1617 if (!cst)
1618 return -1;
1619 update_coeff(aff, cst, 1 + up->var);
1620
1621 return isl_upoly_update_affine(rec->p[0], aff);
1622 }
1623
1624 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1625 __isl_keep isl_qpolynomial *qp)
1626 {
1627 isl_vec *aff;
1628 unsigned d;
1629
1630 if (!qp)
1631 return NULL;
1632
1633 d = isl_dim_total(qp->dim);
1634 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1635 if (!aff)
1636 return NULL;
1637
1638 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1639 isl_int_set_si(aff->el[0], 1);
1640
1641 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1642 goto error;
1643
1644 return aff;
1645 error:
1646 isl_vec_free(aff);
1647 return NULL;
1648 }
1649
1650 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1651 __isl_keep isl_qpolynomial *qp2)
1652 {
1653 if (!qp1 || !qp2)
1654 return -1;
1655
1656 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1657 }
1658
1659 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1660 {
1661 int i;
1662 struct isl_upoly_rec *rec;
1663
1664 if (isl_upoly_is_cst(up)) {
1665 struct isl_upoly_cst *cst;
1666 cst = isl_upoly_as_cst(up);
1667 if (!cst)
1668 return;
1669 isl_int_lcm(*d, *d, cst->d);
1670 return;
1671 }
1672
1673 rec = isl_upoly_as_rec(up);
1674 if (!rec)
1675 return;
1676
1677 for (i = 0; i < rec->n; ++i)
1678 upoly_update_den(rec->p[i], d);
1679 }
1680
1681 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1682 {
1683 isl_int_set_si(*d, 1);
1684 if (!qp)
1685 return;
1686 upoly_update_den(qp->upoly, d);
1687 }
1688
1689 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1690 int pos, int power)
1691 {
1692 struct isl_ctx *ctx;
1693
1694 if (!dim)
1695 return NULL;
1696
1697 ctx = dim->ctx;
1698
1699 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1700 }
1701
1702 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1703 enum isl_dim_type type, unsigned pos)
1704 {
1705 if (!dim)
1706 return NULL;
1707
1708 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1709 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1710
1711 if (type == isl_dim_set)
1712 pos += isl_dim_size(dim, isl_dim_param);
1713
1714 return isl_qpolynomial_var_pow(dim, pos, 1);
1715 error:
1716 isl_dim_free(dim);
1717 return NULL;
1718 }
1719
1720 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1721 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1722 {
1723 int i;
1724 struct isl_upoly_rec *rec;
1725 struct isl_upoly *base, *res;
1726
1727 if (!up)
1728 return NULL;
1729
1730 if (isl_upoly_is_cst(up))
1731 return up;
1732
1733 if (up->var < first)
1734 return up;
1735
1736 rec = isl_upoly_as_rec(up);
1737 if (!rec)
1738 goto error;
1739
1740 isl_assert(up->ctx, rec->n >= 1, goto error);
1741
1742 if (up->var >= first + n)
1743 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1744 else
1745 base = isl_upoly_copy(subs[up->var - first]);
1746
1747 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1748 for (i = rec->n - 2; i >= 0; --i) {
1749 struct isl_upoly *t;
1750 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1751 res = isl_upoly_mul(res, isl_upoly_copy(base));
1752 res = isl_upoly_sum(res, t);
1753 }
1754
1755 isl_upoly_free(base);
1756 isl_upoly_free(up);
1757
1758 return res;
1759 error:
1760 isl_upoly_free(up);
1761 return NULL;
1762 }
1763
1764 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1765 isl_int denom, unsigned len)
1766 {
1767 int i;
1768 struct isl_upoly *up;
1769
1770 isl_assert(ctx, len >= 1, return NULL);
1771
1772 up = isl_upoly_rat_cst(ctx, f[0], denom);
1773 for (i = 0; i < len - 1; ++i) {
1774 struct isl_upoly *t;
1775 struct isl_upoly *c;
1776
1777 if (isl_int_is_zero(f[1 + i]))
1778 continue;
1779
1780 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1781 t = isl_upoly_var_pow(ctx, i, 1);
1782 t = isl_upoly_mul(c, t);
1783 up = isl_upoly_sum(up, t);
1784 }
1785
1786 return up;
1787 }
1788
1789 /* Remove common factor of non-constant terms and denominator.
1790 */
1791 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1792 {
1793 isl_ctx *ctx = qp->div->ctx;
1794 unsigned total = qp->div->n_col - 2;
1795
1796 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1797 isl_int_gcd(ctx->normalize_gcd,
1798 ctx->normalize_gcd, qp->div->row[div][0]);
1799 if (isl_int_is_one(ctx->normalize_gcd))
1800 return;
1801
1802 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1803 ctx->normalize_gcd, total);
1804 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1805 ctx->normalize_gcd);
1806 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1807 ctx->normalize_gcd);
1808 }
1809
1810 /* Replace the integer division identified by "div" by the polynomial "s".
1811 * The integer division is assumed not to appear in the definition
1812 * of any other integer divisions.
1813 */
1814 static __isl_give isl_qpolynomial *substitute_div(
1815 __isl_take isl_qpolynomial *qp,
1816 int div, __isl_take struct isl_upoly *s)
1817 {
1818 int i;
1819 int total;
1820 int *reordering;
1821
1822 if (!qp || !s)
1823 goto error;
1824
1825 qp = isl_qpolynomial_cow(qp);
1826 if (!qp)
1827 goto error;
1828
1829 total = isl_dim_total(qp->dim);
1830 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1831 if (!qp->upoly)
1832 goto error;
1833
1834 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1835 if (!reordering)
1836 goto error;
1837 for (i = 0; i < total + div; ++i)
1838 reordering[i] = i;
1839 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1840 reordering[i] = i - 1;
1841 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1842 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1843 qp->upoly = reorder(qp->upoly, reordering);
1844 free(reordering);
1845
1846 if (!qp->upoly || !qp->div)
1847 goto error;
1848
1849 isl_upoly_free(s);
1850 return qp;
1851 error:
1852 isl_qpolynomial_free(qp);
1853 isl_upoly_free(s);
1854 return NULL;
1855 }
1856
1857 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1858 * divisions because d is equal to 1 by their definition, i.e., e.
1859 */
1860 static __isl_give isl_qpolynomial *substitute_non_divs(
1861 __isl_take isl_qpolynomial *qp)
1862 {
1863 int i, j;
1864 int total;
1865 struct isl_upoly *s;
1866
1867 if (!qp)
1868 return NULL;
1869
1870 total = isl_dim_total(qp->dim);
1871 for (i = 0; qp && i < qp->div->n_row; ++i) {
1872 if (!isl_int_is_one(qp->div->row[i][0]))
1873 continue;
1874 for (j = i + 1; j < qp->div->n_row; ++j) {
1875 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1876 continue;
1877 isl_seq_combine(qp->div->row[j] + 1,
1878 qp->div->ctx->one, qp->div->row[j] + 1,
1879 qp->div->row[j][2 + total + i],
1880 qp->div->row[i] + 1, 1 + total + i);
1881 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1882 normalize_div(qp, j);
1883 }
1884 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1885 qp->div->row[i][0], qp->div->n_col - 1);
1886 qp = substitute_div(qp, i, s);
1887 --i;
1888 }
1889
1890 return qp;
1891 }
1892
1893 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1894 * with d the denominator. When replacing the coefficient e of x by
1895 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1896 * inside the division, so we need to add floor(e/d) * x outside.
1897 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1898 * to adjust the coefficient of x in each later div that depends on the
1899 * current div "div" and also in the affine expression "aff"
1900 * (if it too depends on "div").
1901 */
1902 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1903 __isl_keep isl_vec *aff)
1904 {
1905 int i, j;
1906 isl_int v;
1907 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1908
1909 isl_int_init(v);
1910 for (i = 0; i < 1 + total + div; ++i) {
1911 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1912 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1913 continue;
1914 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1915 isl_int_fdiv_r(qp->div->row[div][1 + i],
1916 qp->div->row[div][1 + i], qp->div->row[div][0]);
1917 if (!isl_int_is_zero(aff->el[1 + total + div]))
1918 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1919 for (j = div + 1; j < qp->div->n_row; ++j) {
1920 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1921 continue;
1922 isl_int_addmul(qp->div->row[j][1 + i],
1923 v, qp->div->row[j][2 + total + div]);
1924 }
1925 }
1926 isl_int_clear(v);
1927 }
1928
1929 /* Check if the last non-zero coefficient is bigger that half of the
1930 * denominator. If so, we will invert the div to further reduce the number
1931 * of distinct divs that may appear.
1932 * If the last non-zero coefficient is exactly half the denominator,
1933 * then we continue looking for earlier coefficients that are bigger
1934 * than half the denominator.
1935 */
1936 static int needs_invert(__isl_keep isl_mat *div, int row)
1937 {
1938 int i;
1939 int cmp;
1940
1941 for (i = div->n_col - 1; i >= 1; --i) {
1942 if (isl_int_is_zero(div->row[row][i]))
1943 continue;
1944 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1945 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1946 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1947 if (cmp)
1948 return cmp > 0;
1949 if (i == 1)
1950 return 1;
1951 }
1952
1953 return 0;
1954 }
1955
1956 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1957 * We only invert the coefficients of e (and the coefficient of q in
1958 * later divs and in "aff"). After calling this function, the
1959 * coefficients of e should be reduced again.
1960 */
1961 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1962 __isl_keep isl_vec *aff)
1963 {
1964 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1965
1966 isl_seq_neg(qp->div->row[div] + 1,
1967 qp->div->row[div] + 1, qp->div->n_col - 1);
1968 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
1969 isl_int_add(qp->div->row[div][1],
1970 qp->div->row[div][1], qp->div->row[div][0]);
1971 if (!isl_int_is_zero(aff->el[1 + total + div]))
1972 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
1973 isl_mat_col_mul(qp->div, 2 + total + div,
1974 qp->div->ctx->negone, 2 + total + div);
1975 }
1976
1977 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
1978 * in the interval [0, d-1], with d the denominator and such that the
1979 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
1980 *
1981 * After the reduction, some divs may have become redundant or identical,
1982 * so we call substitute_non_divs and sort_divs. If these functions
1983 * eliminate divs or merge two or more divs into one, the coefficients
1984 * of the enclosing divs may have to be reduced again, so we call
1985 * ourselves recursively if the number of divs decreases.
1986 */
1987 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
1988 {
1989 int i, j;
1990 isl_vec *aff = NULL;
1991 struct isl_upoly *s;
1992 unsigned n_div;
1993
1994 if (!qp)
1995 return NULL;
1996
1997 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
1998 aff = isl_vec_clr(aff);
1999 if (!aff)
2000 goto error;
2001
2002 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2003
2004 for (i = 0; i < qp->div->n_row; ++i) {
2005 normalize_div(qp, i);
2006 reduce_div(qp, i, aff);
2007 if (needs_invert(qp->div, i)) {
2008 invert_div(qp, i, aff);
2009 reduce_div(qp, i, aff);
2010 }
2011 }
2012
2013 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2014 qp->div->ctx->one, aff->size);
2015 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2016 isl_upoly_free(s);
2017 if (!qp->upoly)
2018 goto error;
2019
2020 isl_vec_free(aff);
2021
2022 n_div = qp->div->n_row;
2023 qp = substitute_non_divs(qp);
2024 qp = sort_divs(qp);
2025 if (qp && qp->div->n_row < n_div)
2026 return reduce_divs(qp);
2027
2028 return qp;
2029 error:
2030 isl_qpolynomial_free(qp);
2031 isl_vec_free(aff);
2032 return NULL;
2033 }
2034
2035 /* Assumes each div only depends on earlier divs.
2036 */
2037 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2038 int power)
2039 {
2040 struct isl_qpolynomial *qp = NULL;
2041 struct isl_upoly_rec *rec;
2042 struct isl_upoly_cst *cst;
2043 int i, d;
2044 int pos;
2045
2046 if (!div)
2047 return NULL;
2048
2049 d = div->line - div->bmap->div;
2050
2051 pos = isl_dim_total(div->bmap->dim) + d;
2052 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2053 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2054 div->bmap->n_div, &rec->up);
2055 if (!qp)
2056 goto error;
2057
2058 for (i = 0; i < div->bmap->n_div; ++i)
2059 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2060
2061 for (i = 0; i < 1 + power; ++i) {
2062 rec->p[i] = isl_upoly_zero(div->ctx);
2063 if (!rec->p[i])
2064 goto error;
2065 rec->n++;
2066 }
2067 cst = isl_upoly_as_cst(rec->p[power]);
2068 isl_int_set_si(cst->n, 1);
2069
2070 isl_div_free(div);
2071
2072 qp = reduce_divs(qp);
2073
2074 return qp;
2075 error:
2076 isl_qpolynomial_free(qp);
2077 isl_div_free(div);
2078 return NULL;
2079 }
2080
2081 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2082 {
2083 return isl_qpolynomial_div_pow(div, 1);
2084 }
2085
2086 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2087 const isl_int n, const isl_int d)
2088 {
2089 struct isl_qpolynomial *qp;
2090 struct isl_upoly_cst *cst;
2091
2092 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2093 if (!qp)
2094 return NULL;
2095
2096 cst = isl_upoly_as_cst(qp->upoly);
2097 isl_int_set(cst->n, n);
2098 isl_int_set(cst->d, d);
2099
2100 return qp;
2101 }
2102
2103 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2104 {
2105 struct isl_upoly_rec *rec;
2106 int i;
2107
2108 if (!up)
2109 return -1;
2110
2111 if (isl_upoly_is_cst(up))
2112 return 0;
2113
2114 if (up->var < d)
2115 active[up->var] = 1;
2116
2117 rec = isl_upoly_as_rec(up);
2118 for (i = 0; i < rec->n; ++i)
2119 if (up_set_active(rec->p[i], active, d) < 0)
2120 return -1;
2121
2122 return 0;
2123 }
2124
2125 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2126 {
2127 int i, j;
2128 int d = isl_dim_total(qp->dim);
2129
2130 if (!qp || !active)
2131 return -1;
2132
2133 for (i = 0; i < d; ++i)
2134 for (j = 0; j < qp->div->n_row; ++j) {
2135 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2136 continue;
2137 active[i] = 1;
2138 break;
2139 }
2140
2141 return up_set_active(qp->upoly, active, d);
2142 }
2143
2144 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2145 enum isl_dim_type type, unsigned first, unsigned n)
2146 {
2147 int i;
2148 int *active = NULL;
2149 int involves = 0;
2150
2151 if (!qp)
2152 return -1;
2153 if (n == 0)
2154 return 0;
2155
2156 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2157 return -1);
2158 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2159 type == isl_dim_set, return -1);
2160
2161 active = isl_calloc_array(set->ctx, int, isl_dim_total(qp->dim));
2162 if (set_active(qp, active) < 0)
2163 goto error;
2164
2165 if (type == isl_dim_set)
2166 first += isl_dim_size(qp->dim, isl_dim_param);
2167 for (i = 0; i < n; ++i)
2168 if (active[first + i]) {
2169 involves = 1;
2170 break;
2171 }
2172
2173 free(active);
2174
2175 return involves;
2176 error:
2177 free(active);
2178 return -1;
2179 }
2180
2181 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2182 unsigned first, unsigned n)
2183 {
2184 int i;
2185 struct isl_upoly_rec *rec;
2186
2187 if (!up)
2188 return NULL;
2189 if (n == 0 || up->var < 0 || up->var < first)
2190 return up;
2191 if (up->var < first + n) {
2192 up = replace_by_constant_term(up);
2193 return isl_upoly_drop(up, first, n);
2194 }
2195 up = isl_upoly_cow(up);
2196 if (!up)
2197 return NULL;
2198 up->var -= n;
2199 rec = isl_upoly_as_rec(up);
2200 if (!rec)
2201 goto error;
2202
2203 for (i = 0; i < rec->n; ++i) {
2204 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2205 if (!rec->p[i])
2206 goto error;
2207 }
2208
2209 return up;
2210 error:
2211 isl_upoly_free(up);
2212 return NULL;
2213 }
2214
2215 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2216 __isl_take isl_qpolynomial *qp,
2217 enum isl_dim_type type, unsigned pos, const char *s)
2218 {
2219 qp = isl_qpolynomial_cow(qp);
2220 if (!qp)
2221 return NULL;
2222 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2223 if (!qp->dim)
2224 goto error;
2225 return qp;
2226 error:
2227 isl_qpolynomial_free(qp);
2228 return NULL;
2229 }
2230
2231 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2232 __isl_take isl_qpolynomial *qp,
2233 enum isl_dim_type type, unsigned first, unsigned n)
2234 {
2235 if (!qp)
2236 return NULL;
2237 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
2238 return qp;
2239
2240 qp = isl_qpolynomial_cow(qp);
2241 if (!qp)
2242 return NULL;
2243
2244 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2245 goto error);
2246 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2247 type == isl_dim_set, goto error);
2248
2249 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2250 if (!qp->dim)
2251 goto error;
2252
2253 if (type == isl_dim_set)
2254 first += isl_dim_size(qp->dim, isl_dim_param);
2255
2256 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2257 if (!qp->div)
2258 goto error;
2259
2260 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2261 if (!qp->upoly)
2262 goto error;
2263
2264 return qp;
2265 error:
2266 isl_qpolynomial_free(qp);
2267 return NULL;
2268 }
2269
2270 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2271 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2272 {
2273 int i, j, k;
2274 isl_int denom;
2275 unsigned total;
2276 unsigned n_div;
2277 struct isl_upoly *up;
2278
2279 if (!eq)
2280 goto error;
2281 if (eq->n_eq == 0) {
2282 isl_basic_set_free(eq);
2283 return qp;
2284 }
2285
2286 qp = isl_qpolynomial_cow(qp);
2287 if (!qp)
2288 goto error;
2289 qp->div = isl_mat_cow(qp->div);
2290 if (!qp->div)
2291 goto error;
2292
2293 total = 1 + isl_dim_total(eq->dim);
2294 n_div = eq->n_div;
2295 isl_int_init(denom);
2296 for (i = 0; i < eq->n_eq; ++i) {
2297 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2298 if (j < 0 || j == 0 || j >= total)
2299 continue;
2300
2301 for (k = 0; k < qp->div->n_row; ++k) {
2302 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2303 continue;
2304 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2305 &qp->div->row[k][0]);
2306 normalize_div(qp, k);
2307 }
2308
2309 if (isl_int_is_pos(eq->eq[i][j]))
2310 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2311 isl_int_abs(denom, eq->eq[i][j]);
2312 isl_int_set_si(eq->eq[i][j], 0);
2313
2314 up = isl_upoly_from_affine(qp->dim->ctx,
2315 eq->eq[i], denom, total);
2316 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2317 isl_upoly_free(up);
2318 }
2319 isl_int_clear(denom);
2320
2321 if (!qp->upoly)
2322 goto error;
2323
2324 isl_basic_set_free(eq);
2325
2326 qp = substitute_non_divs(qp);
2327 qp = sort_divs(qp);
2328
2329 return qp;
2330 error:
2331 isl_basic_set_free(eq);
2332 isl_qpolynomial_free(qp);
2333 return NULL;
2334 }
2335
2336 static __isl_give isl_basic_set *add_div_constraints(
2337 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2338 {
2339 int i;
2340 unsigned total;
2341
2342 if (!bset || !div)
2343 goto error;
2344
2345 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2346 if (!bset)
2347 goto error;
2348 total = isl_basic_set_total_dim(bset);
2349 for (i = 0; i < div->n_row; ++i)
2350 if (isl_basic_set_add_div_constraints_var(bset,
2351 total - div->n_row + i, div->row[i]) < 0)
2352 goto error;
2353
2354 isl_mat_free(div);
2355 return bset;
2356 error:
2357 isl_mat_free(div);
2358 isl_basic_set_free(bset);
2359 return NULL;
2360 }
2361
2362 /* Look for equalities among the variables shared by context and qp
2363 * and the integer divisions of qp, if any.
2364 * The equalities are then used to eliminate variables and/or integer
2365 * divisions from qp.
2366 */
2367 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2368 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2369 {
2370 isl_basic_set *aff;
2371
2372 if (!qp)
2373 goto error;
2374 if (qp->div->n_row > 0) {
2375 isl_basic_set *bset;
2376 context = isl_set_add_dims(context, isl_dim_set,
2377 qp->div->n_row);
2378 bset = isl_basic_set_universe(isl_set_get_dim(context));
2379 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2380 context = isl_set_intersect(context,
2381 isl_set_from_basic_set(bset));
2382 }
2383
2384 aff = isl_set_affine_hull(context);
2385 return isl_qpolynomial_substitute_equalities(qp, aff);
2386 error:
2387 isl_qpolynomial_free(qp);
2388 isl_set_free(context);
2389 return NULL;
2390 }
2391
2392 #undef PW
2393 #define PW isl_pw_qpolynomial
2394 #undef EL
2395 #define EL isl_qpolynomial
2396 #undef IS_ZERO
2397 #define IS_ZERO is_zero
2398 #undef FIELD
2399 #define FIELD qp
2400
2401 #include <isl_pw_templ.c>
2402
2403 #undef UNION
2404 #define UNION isl_union_pw_qpolynomial
2405 #undef PART
2406 #define PART isl_pw_qpolynomial
2407 #undef PARTS
2408 #define PARTS pw_qpolynomial
2409
2410 #include <isl_union_templ.c>
2411
2412 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2413 {
2414 if (!pwqp)
2415 return -1;
2416
2417 if (pwqp->n != -1)
2418 return 0;
2419
2420 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2421 return 0;
2422
2423 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2424 }
2425
2426 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2427 __isl_take isl_pw_qpolynomial *pwqp1,
2428 __isl_take isl_pw_qpolynomial *pwqp2)
2429 {
2430 int i, j, n;
2431 struct isl_pw_qpolynomial *res;
2432 isl_set *set;
2433
2434 if (!pwqp1 || !pwqp2)
2435 goto error;
2436
2437 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2438 goto error);
2439
2440 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2441 isl_pw_qpolynomial_free(pwqp2);
2442 return pwqp1;
2443 }
2444
2445 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2446 isl_pw_qpolynomial_free(pwqp1);
2447 return pwqp2;
2448 }
2449
2450 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2451 isl_pw_qpolynomial_free(pwqp1);
2452 return pwqp2;
2453 }
2454
2455 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2456 isl_pw_qpolynomial_free(pwqp2);
2457 return pwqp1;
2458 }
2459
2460 n = pwqp1->n * pwqp2->n;
2461 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2462
2463 for (i = 0; i < pwqp1->n; ++i) {
2464 for (j = 0; j < pwqp2->n; ++j) {
2465 struct isl_set *common;
2466 struct isl_qpolynomial *prod;
2467 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2468 isl_set_copy(pwqp2->p[j].set));
2469 if (isl_set_plain_is_empty(common)) {
2470 isl_set_free(common);
2471 continue;
2472 }
2473
2474 prod = isl_qpolynomial_mul(
2475 isl_qpolynomial_copy(pwqp1->p[i].qp),
2476 isl_qpolynomial_copy(pwqp2->p[j].qp));
2477
2478 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2479 }
2480 }
2481
2482 isl_pw_qpolynomial_free(pwqp1);
2483 isl_pw_qpolynomial_free(pwqp2);
2484
2485 return res;
2486 error:
2487 isl_pw_qpolynomial_free(pwqp1);
2488 isl_pw_qpolynomial_free(pwqp2);
2489 return NULL;
2490 }
2491
2492 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2493 __isl_take isl_pw_qpolynomial *pwqp)
2494 {
2495 int i;
2496
2497 if (!pwqp)
2498 return NULL;
2499
2500 if (isl_pw_qpolynomial_is_zero(pwqp))
2501 return pwqp;
2502
2503 pwqp = isl_pw_qpolynomial_cow(pwqp);
2504 if (!pwqp)
2505 return NULL;
2506
2507 for (i = 0; i < pwqp->n; ++i) {
2508 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2509 if (!pwqp->p[i].qp)
2510 goto error;
2511 }
2512
2513 return pwqp;
2514 error:
2515 isl_pw_qpolynomial_free(pwqp);
2516 return NULL;
2517 }
2518
2519 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2520 __isl_take isl_pw_qpolynomial *pwqp1,
2521 __isl_take isl_pw_qpolynomial *pwqp2)
2522 {
2523 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2524 }
2525
2526 __isl_give struct isl_upoly *isl_upoly_eval(
2527 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2528 {
2529 int i;
2530 struct isl_upoly_rec *rec;
2531 struct isl_upoly *res;
2532 struct isl_upoly *base;
2533
2534 if (isl_upoly_is_cst(up)) {
2535 isl_vec_free(vec);
2536 return up;
2537 }
2538
2539 rec = isl_upoly_as_rec(up);
2540 if (!rec)
2541 goto error;
2542
2543 isl_assert(up->ctx, rec->n >= 1, goto error);
2544
2545 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2546
2547 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2548 isl_vec_copy(vec));
2549
2550 for (i = rec->n - 2; i >= 0; --i) {
2551 res = isl_upoly_mul(res, isl_upoly_copy(base));
2552 res = isl_upoly_sum(res,
2553 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2554 isl_vec_copy(vec)));
2555 }
2556
2557 isl_upoly_free(base);
2558 isl_upoly_free(up);
2559 isl_vec_free(vec);
2560 return res;
2561 error:
2562 isl_upoly_free(up);
2563 isl_vec_free(vec);
2564 return NULL;
2565 }
2566
2567 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2568 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2569 {
2570 isl_vec *ext;
2571 struct isl_upoly *up;
2572 isl_dim *dim;
2573
2574 if (!qp || !pnt)
2575 goto error;
2576 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2577
2578 if (qp->div->n_row == 0)
2579 ext = isl_vec_copy(pnt->vec);
2580 else {
2581 int i;
2582 unsigned dim = isl_dim_total(qp->dim);
2583 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2584 if (!ext)
2585 goto error;
2586
2587 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2588 for (i = 0; i < qp->div->n_row; ++i) {
2589 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2590 1 + dim + i, &ext->el[1+dim+i]);
2591 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2592 qp->div->row[i][0]);
2593 }
2594 }
2595
2596 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2597 if (!up)
2598 goto error;
2599
2600 dim = isl_dim_copy(qp->dim);
2601 isl_qpolynomial_free(qp);
2602 isl_point_free(pnt);
2603
2604 return isl_qpolynomial_alloc(dim, 0, up);
2605 error:
2606 isl_qpolynomial_free(qp);
2607 isl_point_free(pnt);
2608 return NULL;
2609 }
2610
2611 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2612 __isl_keep struct isl_upoly_cst *cst2)
2613 {
2614 int cmp;
2615 isl_int t;
2616 isl_int_init(t);
2617 isl_int_mul(t, cst1->n, cst2->d);
2618 isl_int_submul(t, cst2->n, cst1->d);
2619 cmp = isl_int_sgn(t);
2620 isl_int_clear(t);
2621 return cmp;
2622 }
2623
2624 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2625 __isl_keep isl_qpolynomial *qp2)
2626 {
2627 struct isl_upoly_cst *cst1, *cst2;
2628
2629 if (!qp1 || !qp2)
2630 return -1;
2631 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2632 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2633 if (isl_qpolynomial_is_nan(qp1))
2634 return -1;
2635 if (isl_qpolynomial_is_nan(qp2))
2636 return -1;
2637 cst1 = isl_upoly_as_cst(qp1->upoly);
2638 cst2 = isl_upoly_as_cst(qp2->upoly);
2639
2640 return isl_upoly_cmp(cst1, cst2) <= 0;
2641 }
2642
2643 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2644 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2645 {
2646 struct isl_upoly_cst *cst1, *cst2;
2647 int cmp;
2648
2649 if (!qp1 || !qp2)
2650 goto error;
2651 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2652 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2653 cst1 = isl_upoly_as_cst(qp1->upoly);
2654 cst2 = isl_upoly_as_cst(qp2->upoly);
2655 cmp = isl_upoly_cmp(cst1, cst2);
2656
2657 if (cmp <= 0) {
2658 isl_qpolynomial_free(qp2);
2659 } else {
2660 isl_qpolynomial_free(qp1);
2661 qp1 = qp2;
2662 }
2663 return qp1;
2664 error:
2665 isl_qpolynomial_free(qp1);
2666 isl_qpolynomial_free(qp2);
2667 return NULL;
2668 }
2669
2670 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2671 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2672 {
2673 struct isl_upoly_cst *cst1, *cst2;
2674 int cmp;
2675
2676 if (!qp1 || !qp2)
2677 goto error;
2678 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2679 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2680 cst1 = isl_upoly_as_cst(qp1->upoly);
2681 cst2 = isl_upoly_as_cst(qp2->upoly);
2682 cmp = isl_upoly_cmp(cst1, cst2);
2683
2684 if (cmp >= 0) {
2685 isl_qpolynomial_free(qp2);
2686 } else {
2687 isl_qpolynomial_free(qp1);
2688 qp1 = qp2;
2689 }
2690 return qp1;
2691 error:
2692 isl_qpolynomial_free(qp1);
2693 isl_qpolynomial_free(qp2);
2694 return NULL;
2695 }
2696
2697 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2698 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2699 unsigned first, unsigned n)
2700 {
2701 unsigned total;
2702 unsigned g_pos;
2703 int *exp;
2704
2705 if (n == 0)
2706 return qp;
2707
2708 qp = isl_qpolynomial_cow(qp);
2709 if (!qp)
2710 return NULL;
2711
2712 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2713 goto error);
2714
2715 g_pos = pos(qp->dim, type) + first;
2716
2717 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2718 if (!qp->div)
2719 goto error;
2720
2721 total = qp->div->n_col - 2;
2722 if (total > g_pos) {
2723 int i;
2724 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2725 if (!exp)
2726 goto error;
2727 for (i = 0; i < total - g_pos; ++i)
2728 exp[i] = i + n;
2729 qp->upoly = expand(qp->upoly, exp, g_pos);
2730 free(exp);
2731 if (!qp->upoly)
2732 goto error;
2733 }
2734
2735 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2736 if (!qp->dim)
2737 goto error;
2738
2739 return qp;
2740 error:
2741 isl_qpolynomial_free(qp);
2742 return NULL;
2743 }
2744
2745 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2746 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2747 {
2748 unsigned pos;
2749
2750 pos = isl_qpolynomial_dim(qp, type);
2751
2752 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2753 }
2754
2755 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2756 __isl_take isl_pw_qpolynomial *pwqp,
2757 enum isl_dim_type type, unsigned n)
2758 {
2759 unsigned pos;
2760
2761 pos = isl_pw_qpolynomial_dim(pwqp, type);
2762
2763 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2764 }
2765
2766 static int *reordering_move(isl_ctx *ctx,
2767 unsigned len, unsigned dst, unsigned src, unsigned n)
2768 {
2769 int i;
2770 int *reordering;
2771
2772 reordering = isl_alloc_array(ctx, int, len);
2773 if (!reordering)
2774 return NULL;
2775
2776 if (dst <= src) {
2777 for (i = 0; i < dst; ++i)
2778 reordering[i] = i;
2779 for (i = 0; i < n; ++i)
2780 reordering[src + i] = dst + i;
2781 for (i = 0; i < src - dst; ++i)
2782 reordering[dst + i] = dst + n + i;
2783 for (i = 0; i < len - src - n; ++i)
2784 reordering[src + n + i] = src + n + i;
2785 } else {
2786 for (i = 0; i < src; ++i)
2787 reordering[i] = i;
2788 for (i = 0; i < n; ++i)
2789 reordering[src + i] = dst + i;
2790 for (i = 0; i < dst - src; ++i)
2791 reordering[src + n + i] = src + i;
2792 for (i = 0; i < len - dst - n; ++i)
2793 reordering[dst + n + i] = dst + n + i;
2794 }
2795
2796 return reordering;
2797 }
2798
2799 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2800 __isl_take isl_qpolynomial *qp,
2801 enum isl_dim_type dst_type, unsigned dst_pos,
2802 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2803 {
2804 unsigned g_dst_pos;
2805 unsigned g_src_pos;
2806 int *reordering;
2807
2808 qp = isl_qpolynomial_cow(qp);
2809 if (!qp)
2810 return NULL;
2811
2812 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2813 goto error);
2814
2815 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2816 g_src_pos = pos(qp->dim, src_type) + src_pos;
2817 if (dst_type > src_type)
2818 g_dst_pos -= n;
2819
2820 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2821 if (!qp->div)
2822 goto error;
2823 qp = sort_divs(qp);
2824 if (!qp)
2825 goto error;
2826
2827 reordering = reordering_move(qp->dim->ctx,
2828 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2829 if (!reordering)
2830 goto error;
2831
2832 qp->upoly = reorder(qp->upoly, reordering);
2833 free(reordering);
2834 if (!qp->upoly)
2835 goto error;
2836
2837 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2838 if (!qp->dim)
2839 goto error;
2840
2841 return qp;
2842 error:
2843 isl_qpolynomial_free(qp);
2844 return NULL;
2845 }
2846
2847 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2848 isl_int *f, isl_int denom)
2849 {
2850 struct isl_upoly *up;
2851
2852 if (!dim)
2853 return NULL;
2854
2855 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2856
2857 return isl_qpolynomial_alloc(dim, 0, up);
2858 }
2859
2860 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2861 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2862 {
2863 isl_int denom;
2864 isl_dim *dim;
2865 struct isl_upoly *up;
2866 isl_qpolynomial *qp;
2867 int sgn;
2868
2869 if (!c)
2870 return NULL;
2871
2872 isl_int_init(denom);
2873
2874 isl_constraint_get_coefficient(c, type, pos, &denom);
2875 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
2876 sgn = isl_int_sgn(denom);
2877 isl_int_abs(denom, denom);
2878 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
2879 1 + isl_constraint_dim(c, isl_dim_all));
2880 if (sgn < 0)
2881 isl_int_neg(denom, denom);
2882 isl_constraint_set_coefficient(c, type, pos, denom);
2883
2884 dim = isl_dim_copy(c->bmap->dim);
2885
2886 isl_int_clear(denom);
2887 isl_constraint_free(c);
2888
2889 qp = isl_qpolynomial_alloc(dim, 0, up);
2890 if (sgn > 0)
2891 qp = isl_qpolynomial_neg(qp);
2892 return qp;
2893 }
2894
2895 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2896 * in "qp" by subs[i].
2897 */
2898 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2899 __isl_take isl_qpolynomial *qp,
2900 enum isl_dim_type type, unsigned first, unsigned n,
2901 __isl_keep isl_qpolynomial **subs)
2902 {
2903 int i;
2904 struct isl_upoly **ups;
2905
2906 if (n == 0)
2907 return qp;
2908
2909 qp = isl_qpolynomial_cow(qp);
2910 if (!qp)
2911 return NULL;
2912 for (i = 0; i < n; ++i)
2913 if (!subs[i])
2914 goto error;
2915
2916 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2917 goto error);
2918
2919 for (i = 0; i < n; ++i)
2920 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
2921 goto error);
2922
2923 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
2924 for (i = 0; i < n; ++i)
2925 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
2926
2927 first += pos(qp->dim, type);
2928
2929 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
2930 if (!ups)
2931 goto error;
2932 for (i = 0; i < n; ++i)
2933 ups[i] = subs[i]->upoly;
2934
2935 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
2936
2937 free(ups);
2938
2939 if (!qp->upoly)
2940 goto error;
2941
2942 return qp;
2943 error:
2944 isl_qpolynomial_free(qp);
2945 return NULL;
2946 }
2947
2948 /* Extend "bset" with extra set dimensions for each integer division
2949 * in "qp" and then call "fn" with the extended bset and the polynomial
2950 * that results from replacing each of the integer divisions by the
2951 * corresponding extra set dimension.
2952 */
2953 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
2954 __isl_keep isl_basic_set *bset,
2955 int (*fn)(__isl_take isl_basic_set *bset,
2956 __isl_take isl_qpolynomial *poly, void *user), void *user)
2957 {
2958 isl_dim *dim;
2959 isl_mat *div;
2960 isl_qpolynomial *poly;
2961
2962 if (!qp || !bset)
2963 goto error;
2964 if (qp->div->n_row == 0)
2965 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
2966 user);
2967
2968 div = isl_mat_copy(qp->div);
2969 dim = isl_dim_copy(qp->dim);
2970 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
2971 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
2972 bset = isl_basic_set_copy(bset);
2973 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
2974 bset = add_div_constraints(bset, div);
2975
2976 return fn(bset, poly, user);
2977 error:
2978 return -1;
2979 }
2980
2981 /* Return total degree in variables first (inclusive) up to last (exclusive).
2982 */
2983 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
2984 {
2985 int deg = -1;
2986 int i;
2987 struct isl_upoly_rec *rec;
2988
2989 if (!up)
2990 return -2;
2991 if (isl_upoly_is_zero(up))
2992 return -1;
2993 if (isl_upoly_is_cst(up) || up->var < first)
2994 return 0;
2995
2996 rec = isl_upoly_as_rec(up);
2997 if (!rec)
2998 return -2;
2999
3000 for (i = 0; i < rec->n; ++i) {
3001 int d;
3002
3003 if (isl_upoly_is_zero(rec->p[i]))
3004 continue;
3005 d = isl_upoly_degree(rec->p[i], first, last);
3006 if (up->var < last)
3007 d += i;
3008 if (d > deg)
3009 deg = d;
3010 }
3011
3012 return deg;
3013 }
3014
3015 /* Return total degree in set variables.
3016 */
3017 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3018 {
3019 unsigned ovar;
3020 unsigned nvar;
3021
3022 if (!poly)
3023 return -2;
3024
3025 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3026 nvar = isl_dim_size(poly->dim, isl_dim_set);
3027 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3028 }
3029
3030 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3031 unsigned pos, int deg)
3032 {
3033 int i;
3034 struct isl_upoly_rec *rec;
3035
3036 if (!up)
3037 return NULL;
3038
3039 if (isl_upoly_is_cst(up) || up->var < pos) {
3040 if (deg == 0)
3041 return isl_upoly_copy(up);
3042 else
3043 return isl_upoly_zero(up->ctx);
3044 }
3045
3046 rec = isl_upoly_as_rec(up);
3047 if (!rec)
3048 return NULL;
3049
3050 if (up->var == pos) {
3051 if (deg < rec->n)
3052 return isl_upoly_copy(rec->p[deg]);
3053 else
3054 return isl_upoly_zero(up->ctx);
3055 }
3056
3057 up = isl_upoly_copy(up);
3058 up = isl_upoly_cow(up);
3059 rec = isl_upoly_as_rec(up);
3060 if (!rec)
3061 goto error;
3062
3063 for (i = 0; i < rec->n; ++i) {
3064 struct isl_upoly *t;
3065 t = isl_upoly_coeff(rec->p[i], pos, deg);
3066 if (!t)
3067 goto error;
3068 isl_upoly_free(rec->p[i]);
3069 rec->p[i] = t;
3070 }
3071
3072 return up;
3073 error:
3074 isl_upoly_free(up);
3075 return NULL;
3076 }
3077
3078 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3079 */
3080 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3081 __isl_keep isl_qpolynomial *qp,
3082 enum isl_dim_type type, unsigned t_pos, int deg)
3083 {
3084 unsigned g_pos;
3085 struct isl_upoly *up;
3086 isl_qpolynomial *c;
3087
3088 if (!qp)
3089 return NULL;
3090
3091 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3092 return NULL);
3093
3094 g_pos = pos(qp->dim, type) + t_pos;
3095 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3096
3097 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3098 if (!c)
3099 return NULL;
3100 isl_mat_free(c->div);
3101 c->div = isl_mat_copy(qp->div);
3102 if (!c->div)
3103 goto error;
3104 return c;
3105 error:
3106 isl_qpolynomial_free(c);
3107 return NULL;
3108 }
3109
3110 /* Homogenize the polynomial in the variables first (inclusive) up to
3111 * last (exclusive) by inserting powers of variable first.
3112 * Variable first is assumed not to appear in the input.
3113 */
3114 __isl_give struct isl_upoly *isl_upoly_homogenize(
3115 __isl_take struct isl_upoly *up, int deg, int target,
3116 int first, int last)
3117 {
3118 int i;
3119 struct isl_upoly_rec *rec;
3120
3121 if (!up)
3122 return NULL;
3123 if (isl_upoly_is_zero(up))
3124 return up;
3125 if (deg == target)
3126 return up;
3127 if (isl_upoly_is_cst(up) || up->var < first) {
3128 struct isl_upoly *hom;
3129
3130 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3131 if (!hom)
3132 goto error;
3133 rec = isl_upoly_as_rec(hom);
3134 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3135
3136 return hom;
3137 }
3138
3139 up = isl_upoly_cow(up);
3140 rec = isl_upoly_as_rec(up);
3141 if (!rec)
3142 goto error;
3143
3144 for (i = 0; i < rec->n; ++i) {
3145 if (isl_upoly_is_zero(rec->p[i]))
3146 continue;
3147 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3148 up->var < last ? deg + i : i, target,
3149 first, last);
3150 if (!rec->p[i])
3151 goto error;
3152 }
3153
3154 return up;
3155 error:
3156 isl_upoly_free(up);
3157 return NULL;
3158 }
3159
3160 /* Homogenize the polynomial in the set variables by introducing
3161 * powers of an extra set variable at position 0.
3162 */
3163 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3164 __isl_take isl_qpolynomial *poly)
3165 {
3166 unsigned ovar;
3167 unsigned nvar;
3168 int deg = isl_qpolynomial_degree(poly);
3169
3170 if (deg < -1)
3171 goto error;
3172
3173 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3174 poly = isl_qpolynomial_cow(poly);
3175 if (!poly)
3176 goto error;
3177
3178 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3179 nvar = isl_dim_size(poly->dim, isl_dim_set);
3180 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3181 ovar, ovar + nvar);
3182 if (!poly->upoly)
3183 goto error;
3184
3185 return poly;
3186 error:
3187 isl_qpolynomial_free(poly);
3188 return NULL;
3189 }
3190
3191 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3192 __isl_take isl_mat *div)
3193 {
3194 isl_term *term;
3195 int n;
3196
3197 if (!dim || !div)
3198 goto error;
3199
3200 n = isl_dim_total(dim) + div->n_row;
3201
3202 term = isl_calloc(dim->ctx, struct isl_term,
3203 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3204 if (!term)
3205 goto error;
3206
3207 term->ref = 1;
3208 term->dim = dim;
3209 term->div = div;
3210 isl_int_init(term->n);
3211 isl_int_init(term->d);
3212
3213 return term;
3214 error:
3215 isl_dim_free(dim);
3216 isl_mat_free(div);
3217 return NULL;
3218 }
3219
3220 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3221 {
3222 if (!term)
3223 return NULL;
3224
3225 term->ref++;
3226 return term;
3227 }
3228
3229 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3230 {
3231 int i;
3232 isl_term *dup;
3233 unsigned total;
3234
3235 if (term)
3236 return NULL;
3237
3238 total = isl_dim_total(term->dim) + term->div->n_row;
3239
3240 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3241 if (!dup)
3242 return NULL;
3243
3244 isl_int_set(dup->n, term->n);
3245 isl_int_set(dup->d, term->d);
3246
3247 for (i = 0; i < total; ++i)
3248 dup->pow[i] = term->pow[i];
3249
3250 return dup;
3251 }
3252
3253 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3254 {
3255 if (!term)
3256 return NULL;
3257
3258 if (term->ref == 1)
3259 return term;
3260 term->ref--;
3261 return isl_term_dup(term);
3262 }
3263
3264 void isl_term_free(__isl_take isl_term *term)
3265 {
3266 if (!term)
3267 return;
3268
3269 if (--term->ref > 0)
3270 return;
3271
3272 isl_dim_free(term->dim);
3273 isl_mat_free(term->div);
3274 isl_int_clear(term->n);
3275 isl_int_clear(term->d);
3276 free(term);
3277 }
3278
3279 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3280 {
3281 if (!term)
3282 return 0;
3283
3284 switch (type) {
3285 case isl_dim_param:
3286 case isl_dim_in:
3287 case isl_dim_out: return isl_dim_size(term->dim, type);
3288 case isl_dim_div: return term->div->n_row;
3289 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3290 default: return 0;
3291 }
3292 }
3293
3294 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3295 {
3296 return term ? term->dim->ctx : NULL;
3297 }
3298
3299 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3300 {
3301 if (!term)
3302 return;
3303 isl_int_set(*n, term->n);
3304 }
3305
3306 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3307 {
3308 if (!term)
3309 return;
3310 isl_int_set(*d, term->d);
3311 }
3312
3313 int isl_term_get_exp(__isl_keep isl_term *term,
3314 enum isl_dim_type type, unsigned pos)
3315 {
3316 if (!term)
3317 return -1;
3318
3319 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3320
3321 if (type >= isl_dim_set)
3322 pos += isl_dim_size(term->dim, isl_dim_param);
3323 if (type >= isl_dim_div)
3324 pos += isl_dim_size(term->dim, isl_dim_set);
3325
3326 return term->pow[pos];
3327 }
3328
3329 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3330 {
3331 isl_basic_map *bmap;
3332 unsigned total;
3333 int k;
3334
3335 if (!term)
3336 return NULL;
3337
3338 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3339 return NULL);
3340
3341 total = term->div->n_col - term->div->n_row - 2;
3342 /* No nested divs for now */
3343 isl_assert(term->dim->ctx,
3344 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3345 term->div->n_row) == -1,
3346 return NULL);
3347
3348 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3349 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3350 goto error;
3351
3352 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3353
3354 return isl_basic_map_div(bmap, k);
3355 error:
3356 isl_basic_map_free(bmap);
3357 return NULL;
3358 }
3359
3360 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3361 int (*fn)(__isl_take isl_term *term, void *user),
3362 __isl_take isl_term *term, void *user)
3363 {
3364 int i;
3365 struct isl_upoly_rec *rec;
3366
3367 if (!up || !term)
3368 goto error;
3369
3370 if (isl_upoly_is_zero(up))
3371 return term;
3372
3373 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3374 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3375 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3376
3377 if (isl_upoly_is_cst(up)) {
3378 struct isl_upoly_cst *cst;
3379 cst = isl_upoly_as_cst(up);
3380 if (!cst)
3381 goto error;
3382 term = isl_term_cow(term);
3383 if (!term)
3384 goto error;
3385 isl_int_set(term->n, cst->n);
3386 isl_int_set(term->d, cst->d);
3387 if (fn(isl_term_copy(term), user) < 0)
3388 goto error;
3389 return term;
3390 }
3391
3392 rec = isl_upoly_as_rec(up);
3393 if (!rec)
3394 goto error;
3395
3396 for (i = 0; i < rec->n; ++i) {
3397 term = isl_term_cow(term);
3398 if (!term)
3399 goto error;
3400 term->pow[up->var] = i;
3401 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3402 if (!term)
3403 goto error;
3404 }
3405 term->pow[up->var] = 0;
3406
3407 return term;
3408 error:
3409 isl_term_free(term);
3410 return NULL;
3411 }
3412
3413 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3414 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3415 {
3416 isl_term *term;
3417
3418 if (!qp)
3419 return -1;
3420
3421 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3422 if (!term)
3423 return -1;
3424
3425 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3426
3427 isl_term_free(term);
3428
3429 return term ? 0 : -1;
3430 }
3431
3432 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3433 {
3434 struct isl_upoly *up;
3435 isl_qpolynomial *qp;
3436 int i, n;
3437
3438 if (!term)
3439 return NULL;
3440
3441 n = isl_dim_total(term->dim) + term->div->n_row;
3442
3443 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3444 for (i = 0; i < n; ++i) {
3445 if (!term->pow[i])
3446 continue;
3447 up = isl_upoly_mul(up,
3448 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3449 }
3450
3451 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3452 if (!qp)
3453 goto error;
3454 isl_mat_free(qp->div);
3455 qp->div = isl_mat_copy(term->div);
3456 if (!qp->div)
3457 goto error;
3458
3459 isl_term_free(term);
3460 return qp;
3461 error:
3462 isl_qpolynomial_free(qp);
3463 isl_term_free(term);
3464 return NULL;
3465 }
3466
3467 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3468 __isl_take isl_dim *dim)
3469 {
3470 int i;
3471 int extra;
3472 unsigned total;
3473
3474 if (!qp || !dim)
3475 goto error;
3476
3477 if (isl_dim_equal(qp->dim, dim)) {
3478 isl_dim_free(dim);
3479 return qp;
3480 }
3481
3482 qp = isl_qpolynomial_cow(qp);
3483 if (!qp)
3484 goto error;
3485
3486 extra = isl_dim_size(dim, isl_dim_set) -
3487 isl_dim_size(qp->dim, isl_dim_set);
3488 total = isl_dim_total(qp->dim);
3489 if (qp->div->n_row) {
3490 int *exp;
3491
3492 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3493 if (!exp)
3494 goto error;
3495 for (i = 0; i < qp->div->n_row; ++i)
3496 exp[i] = extra + i;
3497 qp->upoly = expand(qp->upoly, exp, total);
3498 free(exp);
3499 if (!qp->upoly)
3500 goto error;
3501 }
3502 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3503 if (!qp->div)
3504 goto error;
3505 for (i = 0; i < qp->div->n_row; ++i)
3506 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3507
3508 isl_dim_free(qp->dim);
3509 qp->dim = dim;
3510
3511 return qp;
3512 error:
3513 isl_dim_free(dim);
3514 isl_qpolynomial_free(qp);
3515 return NULL;
3516 }
3517
3518 /* For each parameter or variable that does not appear in qp,
3519 * first eliminate the variable from all constraints and then set it to zero.
3520 */
3521 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3522 __isl_keep isl_qpolynomial *qp)
3523 {
3524 int *active = NULL;
3525 int i;
3526 int d;
3527 unsigned nparam;
3528 unsigned nvar;
3529
3530 if (!set || !qp)
3531 goto error;
3532
3533 d = isl_dim_total(set->dim);
3534 active = isl_calloc_array(set->ctx, int, d);
3535 if (set_active(qp, active) < 0)
3536 goto error;
3537
3538 for (i = 0; i < d; ++i)
3539 if (!active[i])
3540 break;
3541
3542 if (i == d) {
3543 free(active);
3544 return set;
3545 }
3546
3547 nparam = isl_dim_size(set->dim, isl_dim_param);
3548 nvar = isl_dim_size(set->dim, isl_dim_set);
3549 for (i = 0; i < nparam; ++i) {
3550 if (active[i])
3551 continue;
3552 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3553 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3554 }
3555 for (i = 0; i < nvar; ++i) {
3556 if (active[nparam + i])
3557 continue;
3558 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3559 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3560 }
3561
3562 free(active);
3563
3564 return set;
3565 error:
3566 free(active);
3567 isl_set_free(set);
3568 return NULL;
3569 }
3570
3571 struct isl_opt_data {
3572 isl_qpolynomial *qp;
3573 int first;
3574 isl_qpolynomial *opt;
3575 int max;
3576 };
3577
3578 static int opt_fn(__isl_take isl_point *pnt, void *user)
3579 {
3580 struct isl_opt_data *data = (struct isl_opt_data *)user;
3581 isl_qpolynomial *val;
3582
3583 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3584 if (data->first) {
3585 data->first = 0;
3586 data->opt = val;
3587 } else if (data->max) {
3588 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3589 } else {
3590 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3591 }
3592
3593 return 0;
3594 }
3595
3596 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3597 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3598 {
3599 struct isl_opt_data data = { NULL, 1, NULL, max };
3600
3601 if (!set || !qp)
3602 goto error;
3603
3604 if (isl_upoly_is_cst(qp->upoly)) {
3605 isl_set_free(set);
3606 return qp;
3607 }
3608
3609 set = fix_inactive(set, qp);
3610
3611 data.qp = qp;
3612 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3613 goto error;
3614
3615 if (data.first)
3616 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3617
3618 isl_set_free(set);
3619 isl_qpolynomial_free(qp);
3620 return data.opt;
3621 error:
3622 isl_set_free(set);
3623 isl_qpolynomial_free(qp);
3624 isl_qpolynomial_free(data.opt);
3625 return NULL;
3626 }
3627
3628 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3629 __isl_take isl_morph *morph)
3630 {
3631 int i;
3632 int n_sub;
3633 isl_ctx *ctx;
3634 struct isl_upoly *up;
3635 unsigned n_div;
3636 struct isl_upoly **subs;
3637 isl_mat *mat;
3638
3639 qp = isl_qpolynomial_cow(qp);
3640 if (!qp || !morph)
3641 goto error;
3642
3643 ctx = qp->dim->ctx;
3644 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3645
3646 n_sub = morph->inv->n_row - 1;
3647 if (morph->inv->n_row != morph->inv->n_col)
3648 n_sub += qp->div->n_row;
3649 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3650 if (!subs)
3651 goto error;
3652
3653 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3654 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3655 morph->inv->row[0][0], morph->inv->n_col);
3656 if (morph->inv->n_row != morph->inv->n_col)
3657 for (i = 0; i < qp->div->n_row; ++i)
3658 subs[morph->inv->n_row - 1 + i] =
3659 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3660
3661 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3662
3663 for (i = 0; i < n_sub; ++i)
3664 isl_upoly_free(subs[i]);
3665 free(subs);
3666
3667 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3668 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3669 qp->div = isl_mat_product(qp->div, mat);
3670 isl_dim_free(qp->dim);
3671 qp->dim = isl_dim_copy(morph->ran->dim);
3672
3673 if (!qp->upoly || !qp->div || !qp->dim)
3674 goto error;
3675
3676 isl_morph_free(morph);
3677
3678 return qp;
3679 error:
3680 isl_qpolynomial_free(qp);
3681 isl_morph_free(morph);
3682 return NULL;
3683 }
3684
3685 static int neg_entry(void **entry, void *user)
3686 {
3687 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3688
3689 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3690
3691 return *pwqp ? 0 : -1;
3692 }
3693
3694 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3695 __isl_take isl_union_pw_qpolynomial *upwqp)
3696 {
3697 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3698 if (!upwqp)
3699 return NULL;
3700
3701 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3702 &neg_entry, NULL) < 0)
3703 goto error;
3704
3705 return upwqp;
3706 error:
3707 isl_union_pw_qpolynomial_free(upwqp);
3708 return NULL;
3709 }
3710
3711 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3712 __isl_take isl_union_pw_qpolynomial *upwqp1,
3713 __isl_take isl_union_pw_qpolynomial *upwqp2)
3714 {
3715 return isl_union_pw_qpolynomial_add(upwqp1,
3716 isl_union_pw_qpolynomial_neg(upwqp2));
3717 }
3718
3719 static int mul_entry(void **entry, void *user)
3720 {
3721 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3722 uint32_t hash;
3723 struct isl_hash_table_entry *entry2;
3724 isl_pw_qpolynomial *pwpq = *entry;
3725 int empty;
3726
3727 hash = isl_dim_get_hash(pwpq->dim);
3728 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3729 hash, &has_dim, pwpq->dim, 0);
3730 if (!entry2)
3731 return 0;
3732
3733 pwpq = isl_pw_qpolynomial_copy(pwpq);
3734 pwpq = isl_pw_qpolynomial_mul(pwpq,
3735 isl_pw_qpolynomial_copy(entry2->data));
3736
3737 empty = isl_pw_qpolynomial_is_zero(pwpq);
3738 if (empty < 0) {
3739 isl_pw_qpolynomial_free(pwpq);
3740 return -1;
3741 }
3742 if (empty) {
3743 isl_pw_qpolynomial_free(pwpq);
3744 return 0;
3745 }
3746
3747 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3748
3749 return 0;
3750 }
3751
3752 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3753 __isl_take isl_union_pw_qpolynomial *upwqp1,
3754 __isl_take isl_union_pw_qpolynomial *upwqp2)
3755 {
3756 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3757 }
3758
3759 /* Reorder the columns of the given div definitions according to the
3760 * given reordering.
3761 */
3762 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3763 __isl_take isl_reordering *r)
3764 {
3765 int i, j;
3766 isl_mat *mat;
3767 int extra;
3768
3769 if (!div || !r)
3770 goto error;
3771
3772 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3773 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3774 if (!mat)
3775 goto error;
3776
3777 for (i = 0; i < div->n_row; ++i) {
3778 isl_seq_cpy(mat->row[i], div->row[i], 2);
3779 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3780 for (j = 0; j < r->len; ++j)
3781 isl_int_set(mat->row[i][2 + r->pos[j]],
3782 div->row[i][2 + j]);
3783 }
3784
3785 isl_reordering_free(r);
3786 isl_mat_free(div);
3787 return mat;
3788 error:
3789 isl_reordering_free(r);
3790 isl_mat_free(div);
3791 return NULL;
3792 }
3793
3794 /* Reorder the dimension of "qp" according to the given reordering.
3795 */
3796 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3797 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3798 {
3799 qp = isl_qpolynomial_cow(qp);
3800 if (!qp)
3801 goto error;
3802
3803 r = isl_reordering_extend(r, qp->div->n_row);
3804 if (!r)
3805 goto error;
3806
3807 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3808 if (!qp->div)
3809 goto error;
3810
3811 qp->upoly = reorder(qp->upoly, r->pos);
3812 if (!qp->upoly)
3813 goto error;
3814
3815 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3816
3817 isl_reordering_free(r);
3818 return qp;
3819 error:
3820 isl_qpolynomial_free(qp);
3821 isl_reordering_free(r);
3822 return NULL;
3823 }
3824
3825 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3826 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3827 {
3828 if (!qp || !model)
3829 goto error;
3830
3831 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
3832 isl_reordering *exp;
3833
3834 model = isl_dim_drop(model, isl_dim_in,
3835 0, isl_dim_size(model, isl_dim_in));
3836 model = isl_dim_drop(model, isl_dim_out,
3837 0, isl_dim_size(model, isl_dim_out));
3838 exp = isl_parameter_alignment_reordering(qp->dim, model);
3839 exp = isl_reordering_extend_dim(exp,
3840 isl_qpolynomial_get_dim(qp));
3841 qp = isl_qpolynomial_realign(qp, exp);
3842 }
3843
3844 isl_dim_free(model);
3845 return qp;
3846 error:
3847 isl_dim_free(model);
3848 isl_qpolynomial_free(qp);
3849 return NULL;
3850 }
3851
3852 struct isl_split_periods_data {
3853 int max_periods;
3854 isl_pw_qpolynomial *res;
3855 };
3856
3857 /* Create a slice where the integer division "div" has the fixed value "v".
3858 * In particular, if "div" refers to floor(f/m), then create a slice
3859 *
3860 * m v <= f <= m v + (m - 1)
3861 *
3862 * or
3863 *
3864 * f - m v >= 0
3865 * -f + m v + (m - 1) >= 0
3866 */
3867 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3868 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3869 {
3870 int total;
3871 isl_basic_set *bset = NULL;
3872 int k;
3873
3874 if (!dim || !qp)
3875 goto error;
3876
3877 total = isl_dim_total(dim);
3878 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3879
3880 k = isl_basic_set_alloc_inequality(bset);
3881 if (k < 0)
3882 goto error;
3883 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3884 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3885
3886 k = isl_basic_set_alloc_inequality(bset);
3887 if (k < 0)
3888 goto error;
3889 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3890 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3891 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3892 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3893
3894 isl_dim_free(dim);
3895 return isl_set_from_basic_set(bset);
3896 error:
3897 isl_basic_set_free(bset);
3898 isl_dim_free(dim);
3899 return NULL;
3900 }
3901
3902 static int split_periods(__isl_take isl_set *set,
3903 __isl_take isl_qpolynomial *qp, void *user);
3904
3905 /* Create a slice of the domain "set" such that integer division "div"
3906 * has the fixed value "v" and add the results to data->res,
3907 * replacing the integer division by "v" in "qp".
3908 */
3909 static int set_div(__isl_take isl_set *set,
3910 __isl_take isl_qpolynomial *qp, int div, isl_int v,
3911 struct isl_split_periods_data *data)
3912 {
3913 int i;
3914 int total;
3915 isl_set *slice;
3916 struct isl_upoly *cst;
3917
3918 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
3919 set = isl_set_intersect(set, slice);
3920
3921 if (!qp)
3922 goto error;
3923
3924 total = isl_dim_total(qp->dim);
3925
3926 for (i = div + 1; i < qp->div->n_row; ++i) {
3927 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
3928 continue;
3929 isl_int_addmul(qp->div->row[i][1],
3930 qp->div->row[i][2 + total + div], v);
3931 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
3932 }
3933
3934 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
3935 qp = substitute_div(qp, div, cst);
3936
3937 return split_periods(set, qp, data);
3938 error:
3939 isl_set_free(set);
3940 isl_qpolynomial_free(qp);
3941 return -1;
3942 }
3943
3944 /* Split the domain "set" such that integer division "div"
3945 * has a fixed value (ranging from "min" to "max") on each slice
3946 * and add the results to data->res.
3947 */
3948 static int split_div(__isl_take isl_set *set,
3949 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
3950 struct isl_split_periods_data *data)
3951 {
3952 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
3953 isl_set *set_i = isl_set_copy(set);
3954 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
3955
3956 if (set_div(set_i, qp_i, div, min, data) < 0)
3957 goto error;
3958 }
3959 isl_set_free(set);
3960 isl_qpolynomial_free(qp);
3961 return 0;
3962 error:
3963 isl_set_free(set);
3964 isl_qpolynomial_free(qp);
3965 return -1;
3966 }
3967
3968 /* If "qp" refers to any integer division
3969 * that can only attain "max_periods" distinct values on "set"
3970 * then split the domain along those distinct values.
3971 * Add the results (or the original if no splitting occurs)
3972 * to data->res.
3973 */
3974 static int split_periods(__isl_take isl_set *set,
3975 __isl_take isl_qpolynomial *qp, void *user)
3976 {
3977 int i;
3978 isl_pw_qpolynomial *pwqp;
3979 struct isl_split_periods_data *data;
3980 isl_int min, max;
3981 int total;
3982 int r = 0;
3983
3984 data = (struct isl_split_periods_data *)user;
3985
3986 if (!set || !qp)
3987 goto error;
3988
3989 if (qp->div->n_row == 0) {
3990 pwqp = isl_pw_qpolynomial_alloc(set, qp);
3991 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
3992 return 0;
3993 }
3994
3995 isl_int_init(min);
3996 isl_int_init(max);
3997 total = isl_dim_total(qp->dim);
3998 for (i = 0; i < qp->div->n_row; ++i) {
3999 enum isl_lp_result lp_res;
4000
4001 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4002 qp->div->n_row) != -1)
4003 continue;
4004
4005 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4006 set->ctx->one, &min, NULL, NULL);
4007 if (lp_res == isl_lp_error)
4008 goto error2;
4009 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4010 continue;
4011 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4012
4013 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4014 set->ctx->one, &max, 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(max, max, qp->div->row[i][0]);
4020
4021 isl_int_sub(max, max, min);
4022 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4023 isl_int_add(max, max, min);
4024 break;
4025 }
4026 }
4027
4028 if (i < qp->div->n_row) {
4029 r = split_div(set, qp, i, min, max, data);
4030 } else {
4031 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4032 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4033 }
4034
4035 isl_int_clear(max);
4036 isl_int_clear(min);
4037
4038 return r;
4039 error2:
4040 isl_int_clear(max);
4041 isl_int_clear(min);
4042 error:
4043 isl_set_free(set);
4044 isl_qpolynomial_free(qp);
4045 return -1;
4046 }
4047
4048 /* If any quasi-polynomial in pwqp refers to any integer division
4049 * that can only attain "max_periods" distinct values on its domain
4050 * then split the domain along those distinct values.
4051 */
4052 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4053 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4054 {
4055 struct isl_split_periods_data data;
4056
4057 data.max_periods = max_periods;
4058 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4059
4060 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4061 goto error;
4062
4063 isl_pw_qpolynomial_free(pwqp);
4064
4065 return data.res;
4066 error:
4067 isl_pw_qpolynomial_free(data.res);
4068 isl_pw_qpolynomial_free(pwqp);
4069 return NULL;
4070 }
4071
4072 /* Construct a piecewise quasipolynomial that is constant on the given
4073 * domain. In particular, it is
4074 * 0 if cst == 0
4075 * 1 if cst == 1
4076 * infinity if cst == -1
4077 */
4078 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4079 __isl_take isl_basic_set *bset, int cst)
4080 {
4081 isl_dim *dim;
4082 isl_qpolynomial *qp;
4083
4084 if (!bset)
4085 return NULL;
4086
4087 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4088 dim = isl_basic_set_get_dim(bset);
4089 if (cst < 0)
4090 qp = isl_qpolynomial_infty(dim);
4091 else if (cst == 0)
4092 qp = isl_qpolynomial_zero(dim);
4093 else
4094 qp = isl_qpolynomial_one(dim);
4095 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4096 }
4097
4098 /* Factor bset, call fn on each of the factors and return the product.
4099 *
4100 * If no factors can be found, simply call fn on the input.
4101 * Otherwise, construct the factors based on the factorizer,
4102 * call fn on each factor and compute the product.
4103 */
4104 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4105 __isl_take isl_basic_set *bset,
4106 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4107 {
4108 int i, n;
4109 isl_dim *dim;
4110 isl_set *set;
4111 isl_factorizer *f;
4112 isl_qpolynomial *qp;
4113 isl_pw_qpolynomial *pwqp;
4114 unsigned nparam;
4115 unsigned nvar;
4116
4117 f = isl_basic_set_factorizer(bset);
4118 if (!f)
4119 goto error;
4120 if (f->n_group == 0) {
4121 isl_factorizer_free(f);
4122 return fn(bset);
4123 }
4124
4125 nparam = isl_basic_set_dim(bset, isl_dim_param);
4126 nvar = isl_basic_set_dim(bset, isl_dim_set);
4127
4128 dim = isl_basic_set_get_dim(bset);
4129 dim = isl_dim_domain(dim);
4130 set = isl_set_universe(isl_dim_copy(dim));
4131 qp = isl_qpolynomial_one(dim);
4132 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4133
4134 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4135
4136 for (i = 0, n = 0; i < f->n_group; ++i) {
4137 isl_basic_set *bset_i;
4138 isl_pw_qpolynomial *pwqp_i;
4139
4140 bset_i = isl_basic_set_copy(bset);
4141 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4142 nparam + n + f->len[i], nvar - n - f->len[i]);
4143 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4144 nparam, n);
4145 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4146 n + f->len[i], nvar - n - f->len[i]);
4147 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4148
4149 pwqp_i = fn(bset_i);
4150 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4151
4152 n += f->len[i];
4153 }
4154
4155 isl_basic_set_free(bset);
4156 isl_factorizer_free(f);
4157
4158 return pwqp;
4159 error:
4160 isl_basic_set_free(bset);
4161 return NULL;
4162 }
4163
4164 /* Factor bset, call fn on each of the factors and return the product.
4165 * The function is assumed to evaluate to zero on empty domains,
4166 * to one on zero-dimensional domains and to infinity on unbounded domains
4167 * and will not be called explicitly on zero-dimensional or unbounded domains.
4168 *
4169 * We first check for some special cases and remove all equalities.
4170 * Then we hand over control to compressed_multiplicative_call.
4171 */
4172 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4173 __isl_take isl_basic_set *bset,
4174 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4175 {
4176 int bounded;
4177 isl_morph *morph;
4178 isl_pw_qpolynomial *pwqp;
4179 unsigned orig_nvar, final_nvar;
4180
4181 if (!bset)
4182 return NULL;
4183
4184 if (isl_basic_set_plain_is_empty(bset))
4185 return constant_on_domain(bset, 0);
4186
4187 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4188
4189 if (orig_nvar == 0)
4190 return constant_on_domain(bset, 1);
4191
4192 bounded = isl_basic_set_is_bounded(bset);
4193 if (bounded < 0)
4194 goto error;
4195 if (!bounded)
4196 return constant_on_domain(bset, -1);
4197
4198 if (bset->n_eq == 0)
4199 return compressed_multiplicative_call(bset, fn);
4200
4201 morph = isl_basic_set_full_compression(bset);
4202 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4203
4204 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4205
4206 pwqp = compressed_multiplicative_call(bset, fn);
4207
4208 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4209 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4210 morph = isl_morph_inverse(morph);
4211
4212 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4213
4214 return pwqp;
4215 error:
4216 isl_basic_set_free(bset);
4217 return NULL;
4218 }
4219
4220 /* Drop all floors in "qp", turning each integer division [a/m] into
4221 * a rational division a/m. If "down" is set, then the integer division
4222 * is replaces by (a-(m-1))/m instead.
4223 */
4224 static __isl_give isl_qpolynomial *qp_drop_floors(
4225 __isl_take isl_qpolynomial *qp, int down)
4226 {
4227 int i;
4228 struct isl_upoly *s;
4229
4230 if (!qp)
4231 return NULL;
4232 if (qp->div->n_row == 0)
4233 return qp;
4234
4235 qp = isl_qpolynomial_cow(qp);
4236 if (!qp)
4237 return NULL;
4238
4239 for (i = qp->div->n_row - 1; i >= 0; --i) {
4240 if (down) {
4241 isl_int_sub(qp->div->row[i][1],
4242 qp->div->row[i][1], qp->div->row[i][0]);
4243 isl_int_add_ui(qp->div->row[i][1],
4244 qp->div->row[i][1], 1);
4245 }
4246 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4247 qp->div->row[i][0], qp->div->n_col - 1);
4248 qp = substitute_div(qp, i, s);
4249 if (!qp)
4250 return NULL;
4251 }
4252
4253 return qp;
4254 }
4255
4256 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4257 * a rational division a/m.
4258 */
4259 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4260 __isl_take isl_pw_qpolynomial *pwqp)
4261 {
4262 int i;
4263
4264 if (!pwqp)
4265 return NULL;
4266
4267 if (isl_pw_qpolynomial_is_zero(pwqp))
4268 return pwqp;
4269
4270 pwqp = isl_pw_qpolynomial_cow(pwqp);
4271 if (!pwqp)
4272 return NULL;
4273
4274 for (i = 0; i < pwqp->n; ++i) {
4275 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4276 if (!pwqp->p[i].qp)
4277 goto error;
4278 }
4279
4280 return pwqp;
4281 error:
4282 isl_pw_qpolynomial_free(pwqp);
4283 return NULL;
4284 }
4285
4286 /* Adjust all the integer divisions in "qp" such that they are at least
4287 * one over the given orthant (identified by "signs"). This ensures
4288 * that they will still be non-negative even after subtracting (m-1)/m.
4289 *
4290 * In particular, f is replaced by f' + v, changing f = [a/m]
4291 * to f' = [(a - m v)/m].
4292 * If the constant term k in a is smaller than m,
4293 * the constant term of v is set to floor(k/m) - 1.
4294 * For any other term, if the coefficient c and the variable x have
4295 * the same sign, then no changes are needed.
4296 * Otherwise, if the variable is positive (and c is negative),
4297 * then the coefficient of x in v is set to floor(c/m).
4298 * If the variable is negative (and c is positive),
4299 * then the coefficient of x in v is set to ceil(c/m).
4300 */
4301 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4302 int *signs)
4303 {
4304 int i, j;
4305 int total;
4306 isl_vec *v = NULL;
4307 struct isl_upoly *s;
4308
4309 qp = isl_qpolynomial_cow(qp);
4310 if (!qp)
4311 return NULL;
4312 qp->div = isl_mat_cow(qp->div);
4313 if (!qp->div)
4314 goto error;
4315
4316 total = isl_dim_total(qp->dim);
4317 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4318
4319 for (i = 0; i < qp->div->n_row; ++i) {
4320 isl_int *row = qp->div->row[i];
4321 v = isl_vec_clr(v);
4322 if (!v)
4323 goto error;
4324 if (isl_int_lt(row[1], row[0])) {
4325 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4326 isl_int_sub_ui(v->el[0], v->el[0], 1);
4327 isl_int_submul(row[1], row[0], v->el[0]);
4328 }
4329 for (j = 0; j < total; ++j) {
4330 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4331 continue;
4332 if (signs[j] < 0)
4333 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4334 else
4335 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4336 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4337 }
4338 for (j = 0; j < i; ++j) {
4339 if (isl_int_sgn(row[2 + total + j]) >= 0)
4340 continue;
4341 isl_int_fdiv_q(v->el[1 + total + j],
4342 row[2 + total + j], row[0]);
4343 isl_int_submul(row[2 + total + j],
4344 row[0], v->el[1 + total + j]);
4345 }
4346 for (j = i + 1; j < qp->div->n_row; ++j) {
4347 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4348 continue;
4349 isl_seq_combine(qp->div->row[j] + 1,
4350 qp->div->ctx->one, qp->div->row[j] + 1,
4351 qp->div->row[j][2 + total + i], v->el, v->size);
4352 }
4353 isl_int_set_si(v->el[1 + total + i], 1);
4354 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4355 qp->div->ctx->one, v->size);
4356 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4357 isl_upoly_free(s);
4358 if (!qp->upoly)
4359 goto error;
4360 }
4361
4362 isl_vec_free(v);
4363 return qp;
4364 error:
4365 isl_vec_free(v);
4366 isl_qpolynomial_free(qp);
4367 return NULL;
4368 }
4369
4370 struct isl_to_poly_data {
4371 int sign;
4372 isl_pw_qpolynomial *res;
4373 isl_qpolynomial *qp;
4374 };
4375
4376 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4377 * We first make all integer divisions positive and then split the
4378 * quasipolynomials into terms with sign data->sign (the direction
4379 * of the requested approximation) and terms with the opposite sign.
4380 * In the first set of terms, each integer division [a/m] is
4381 * overapproximated by a/m, while in the second it is underapproximated
4382 * by (a-(m-1))/m.
4383 */
4384 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4385 void *user)
4386 {
4387 struct isl_to_poly_data *data = user;
4388 isl_pw_qpolynomial *t;
4389 isl_qpolynomial *qp, *up, *down;
4390
4391 qp = isl_qpolynomial_copy(data->qp);
4392 qp = make_divs_pos(qp, signs);
4393
4394 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4395 up = qp_drop_floors(up, 0);
4396 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4397 down = qp_drop_floors(down, 1);
4398
4399 isl_qpolynomial_free(qp);
4400 qp = isl_qpolynomial_add(up, down);
4401
4402 t = isl_pw_qpolynomial_alloc(orthant, qp);
4403 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4404
4405 return 0;
4406 }
4407
4408 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4409 * the polynomial will be an overapproximation. If "sign" is negative,
4410 * it will be an underapproximation. If "sign" is zero, the approximation
4411 * will lie somewhere in between.
4412 *
4413 * In particular, is sign == 0, we simply drop the floors, turning
4414 * the integer divisions into rational divisions.
4415 * Otherwise, we split the domains into orthants, make all integer divisions
4416 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4417 * depending on the requested sign and the sign of the term in which
4418 * the integer division appears.
4419 */
4420 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4421 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4422 {
4423 int i;
4424 struct isl_to_poly_data data;
4425
4426 if (sign == 0)
4427 return pwqp_drop_floors(pwqp);
4428
4429 if (!pwqp)
4430 return NULL;
4431
4432 data.sign = sign;
4433 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4434
4435 for (i = 0; i < pwqp->n; ++i) {
4436 if (pwqp->p[i].qp->div->n_row == 0) {
4437 isl_pw_qpolynomial *t;
4438 t = isl_pw_qpolynomial_alloc(
4439 isl_set_copy(pwqp->p[i].set),
4440 isl_qpolynomial_copy(pwqp->p[i].qp));
4441 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4442 continue;
4443 }
4444 data.qp = pwqp->p[i].qp;
4445 if (isl_set_foreach_orthant(pwqp->p[i].set,
4446 &to_polynomial_on_orthant, &data) < 0)
4447 goto error;
4448 }
4449
4450 isl_pw_qpolynomial_free(pwqp);
4451
4452 return data.res;
4453 error:
4454 isl_pw_qpolynomial_free(pwqp);
4455 isl_pw_qpolynomial_free(data.res);
4456 return NULL;
4457 }
4458
4459 static int poly_entry(void **entry, void *user)
4460 {
4461 int *sign = user;
4462 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4463
4464 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4465
4466 return *pwqp ? 0 : -1;
4467 }
4468
4469 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4470 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4471 {
4472 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4473 if (!upwqp)
4474 return NULL;
4475
4476 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4477 &poly_entry, &sign) < 0)
4478 goto error;
4479
4480 return upwqp;
4481 error:
4482 isl_union_pw_qpolynomial_free(upwqp);
4483 return NULL;
4484 }
4485
4486 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4487 __isl_take isl_qpolynomial *qp)
4488 {
4489 int i, k;
4490 isl_dim *dim;
4491 isl_vec *aff = NULL;
4492 isl_basic_map *bmap = NULL;
4493 unsigned pos;
4494 unsigned n_div;
4495
4496 if (!qp)
4497 return NULL;
4498 if (!isl_upoly_is_affine(qp->upoly))
4499 isl_die(qp->dim->ctx, isl_error_invalid,
4500 "input quasi-polynomial not affine", goto error);
4501 aff = isl_qpolynomial_extract_affine(qp);
4502 if (!aff)
4503 goto error;
4504 dim = isl_qpolynomial_get_dim(qp);
4505 dim = isl_dim_from_domain(dim);
4506 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4507 dim = isl_dim_add(dim, isl_dim_out, 1);
4508 n_div = qp->div->n_row;
4509 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4510
4511 for (i = 0; i < n_div; ++i) {
4512 k = isl_basic_map_alloc_div(bmap);
4513 if (k < 0)
4514 goto error;
4515 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4516 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4517 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4518 goto error;
4519 }
4520 k = isl_basic_map_alloc_equality(bmap);
4521 if (k < 0)
4522 goto error;
4523 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4524 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4525 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4526
4527 isl_vec_free(aff);
4528 isl_qpolynomial_free(qp);
4529 bmap = isl_basic_map_finalize(bmap);
4530 return bmap;
4531 error:
4532 isl_vec_free(aff);
4533 isl_qpolynomial_free(qp);
4534 isl_basic_map_free(bmap);
4535 return NULL;
4536 }
Integer set library