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scheduling: optionally split parallel rows in non-tilable bands
[isl.git] / isl_polynomial.c
blob6f3be323d7da05803bbb66f80a1715f4feda8f48
1 /*
2 * Copyright 2010 INRIA Saclay
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
8 * 91893 Orsay, France
9 */
10
11 #include <stdlib.h>
12 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl_factorization.h>
15 #include <isl/lp.h>
16 #include <isl/seq.h>
17 #include <isl_union_map_private.h>
18 #include <isl_polynomial_private.h>
19 #include <isl_point_private.h>
20 #include <isl_dim_private.h>
21 #include <isl_div_private.h>
22 #include <isl_mat_private.h>
23 #include <isl_range.h>
24 #include <isl_local_space_private.h>
25 #include <isl_aff_private.h>
26 #include <isl_config.h>
27
28 static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
29 {
30 switch (type) {
31 case isl_dim_param: return 0;
32 case isl_dim_in: return dim->nparam;
33 case isl_dim_out: return dim->nparam + dim->n_in;
34 default: return 0;
35 }
36 }
37
38 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
39 {
40 if (!up)
41 return -1;
42
43 return up->var < 0;
44 }
45
46 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
47 {
48 if (!up)
49 return NULL;
50
51 isl_assert(up->ctx, up->var < 0, return NULL);
52
53 return (struct isl_upoly_cst *)up;
54 }
55
56 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
57 {
58 if (!up)
59 return NULL;
60
61 isl_assert(up->ctx, up->var >= 0, return NULL);
62
63 return (struct isl_upoly_rec *)up;
64 }
65
66 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
67 __isl_keep struct isl_upoly *up2)
68 {
69 int i;
70 struct isl_upoly_rec *rec1, *rec2;
71
72 if (!up1 || !up2)
73 return -1;
74 if (up1 == up2)
75 return 1;
76 if (up1->var != up2->var)
77 return 0;
78 if (isl_upoly_is_cst(up1)) {
79 struct isl_upoly_cst *cst1, *cst2;
80 cst1 = isl_upoly_as_cst(up1);
81 cst2 = isl_upoly_as_cst(up2);
82 if (!cst1 || !cst2)
83 return -1;
84 return isl_int_eq(cst1->n, cst2->n) &&
85 isl_int_eq(cst1->d, cst2->d);
86 }
87
88 rec1 = isl_upoly_as_rec(up1);
89 rec2 = isl_upoly_as_rec(up2);
90 if (!rec1 || !rec2)
91 return -1;
92
93 if (rec1->n != rec2->n)
94 return 0;
95
96 for (i = 0; i < rec1->n; ++i) {
97 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
98 if (eq < 0 || !eq)
99 return eq;
100 }
101
102 return 1;
103 }
104
105 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
106 {
107 struct isl_upoly_cst *cst;
108
109 if (!up)
110 return -1;
111 if (!isl_upoly_is_cst(up))
112 return 0;
113
114 cst = isl_upoly_as_cst(up);
115 if (!cst)
116 return -1;
117
118 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
119 }
120
121 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
122 {
123 struct isl_upoly_cst *cst;
124
125 if (!up)
126 return 0;
127 if (!isl_upoly_is_cst(up))
128 return 0;
129
130 cst = isl_upoly_as_cst(up);
131 if (!cst)
132 return 0;
133
134 return isl_int_sgn(cst->n);
135 }
136
137 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
138 {
139 struct isl_upoly_cst *cst;
140
141 if (!up)
142 return -1;
143 if (!isl_upoly_is_cst(up))
144 return 0;
145
146 cst = isl_upoly_as_cst(up);
147 if (!cst)
148 return -1;
149
150 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
151 }
152
153 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
154 {
155 struct isl_upoly_cst *cst;
156
157 if (!up)
158 return -1;
159 if (!isl_upoly_is_cst(up))
160 return 0;
161
162 cst = isl_upoly_as_cst(up);
163 if (!cst)
164 return -1;
165
166 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
167 }
168
169 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
170 {
171 struct isl_upoly_cst *cst;
172
173 if (!up)
174 return -1;
175 if (!isl_upoly_is_cst(up))
176 return 0;
177
178 cst = isl_upoly_as_cst(up);
179 if (!cst)
180 return -1;
181
182 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
183 }
184
185 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
186 {
187 struct isl_upoly_cst *cst;
188
189 if (!up)
190 return -1;
191 if (!isl_upoly_is_cst(up))
192 return 0;
193
194 cst = isl_upoly_as_cst(up);
195 if (!cst)
196 return -1;
197
198 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
199 }
200
201 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
202 {
203 struct isl_upoly_cst *cst;
204
205 if (!up)
206 return -1;
207 if (!isl_upoly_is_cst(up))
208 return 0;
209
210 cst = isl_upoly_as_cst(up);
211 if (!cst)
212 return -1;
213
214 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
215 }
216
217 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
218 {
219 struct isl_upoly_cst *cst;
220
221 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
222 if (!cst)
223 return NULL;
224
225 cst->up.ref = 1;
226 cst->up.ctx = ctx;
227 isl_ctx_ref(ctx);
228 cst->up.var = -1;
229
230 isl_int_init(cst->n);
231 isl_int_init(cst->d);
232
233 return cst;
234 }
235
236 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
237 {
238 struct isl_upoly_cst *cst;
239
240 cst = isl_upoly_cst_alloc(ctx);
241 if (!cst)
242 return NULL;
243
244 isl_int_set_si(cst->n, 0);
245 isl_int_set_si(cst->d, 1);
246
247 return &cst->up;
248 }
249
250 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
251 {
252 struct isl_upoly_cst *cst;
253
254 cst = isl_upoly_cst_alloc(ctx);
255 if (!cst)
256 return NULL;
257
258 isl_int_set_si(cst->n, 1);
259 isl_int_set_si(cst->d, 1);
260
261 return &cst->up;
262 }
263
264 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
265 {
266 struct isl_upoly_cst *cst;
267
268 cst = isl_upoly_cst_alloc(ctx);
269 if (!cst)
270 return NULL;
271
272 isl_int_set_si(cst->n, 1);
273 isl_int_set_si(cst->d, 0);
274
275 return &cst->up;
276 }
277
278 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
279 {
280 struct isl_upoly_cst *cst;
281
282 cst = isl_upoly_cst_alloc(ctx);
283 if (!cst)
284 return NULL;
285
286 isl_int_set_si(cst->n, -1);
287 isl_int_set_si(cst->d, 0);
288
289 return &cst->up;
290 }
291
292 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
293 {
294 struct isl_upoly_cst *cst;
295
296 cst = isl_upoly_cst_alloc(ctx);
297 if (!cst)
298 return NULL;
299
300 isl_int_set_si(cst->n, 0);
301 isl_int_set_si(cst->d, 0);
302
303 return &cst->up;
304 }
305
306 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
307 isl_int n, isl_int d)
308 {
309 struct isl_upoly_cst *cst;
310
311 cst = isl_upoly_cst_alloc(ctx);
312 if (!cst)
313 return NULL;
314
315 isl_int_set(cst->n, n);
316 isl_int_set(cst->d, d);
317
318 return &cst->up;
319 }
320
321 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
322 int var, int size)
323 {
324 struct isl_upoly_rec *rec;
325
326 isl_assert(ctx, var >= 0, return NULL);
327 isl_assert(ctx, size >= 0, return NULL);
328 rec = isl_calloc(ctx, struct isl_upoly_rec,
329 sizeof(struct isl_upoly_rec) +
330 size * sizeof(struct isl_upoly *));
331 if (!rec)
332 return NULL;
333
334 rec->up.ref = 1;
335 rec->up.ctx = ctx;
336 isl_ctx_ref(ctx);
337 rec->up.var = var;
338
339 rec->n = 0;
340 rec->size = size;
341
342 return rec;
343 }
344
345 __isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
346 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
347 {
348 qp = isl_qpolynomial_cow(qp);
349 if (!qp || !dim)
350 goto error;
351
352 isl_dim_free(qp->dim);
353 qp->dim = dim;
354
355 return qp;
356 error:
357 isl_qpolynomial_free(qp);
358 isl_dim_free(dim);
359 return NULL;
360 }
361
362 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
363 {
364 return qp ? qp->dim->ctx : NULL;
365 }
366
367 __isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
368 {
369 return qp ? isl_dim_copy(qp->dim) : NULL;
370 }
371
372 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
373 enum isl_dim_type type)
374 {
375 return qp ? isl_dim_size(qp->dim, type) : 0;
376 }
377
378 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
379 {
380 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
381 }
382
383 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
384 {
385 return qp ? isl_upoly_is_one(qp->upoly) : -1;
386 }
387
388 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
389 {
390 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
391 }
392
393 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
394 {
395 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
396 }
397
398 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
399 {
400 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
401 }
402
403 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
404 {
405 return qp ? isl_upoly_sgn(qp->upoly) : 0;
406 }
407
408 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
409 {
410 isl_int_clear(cst->n);
411 isl_int_clear(cst->d);
412 }
413
414 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
415 {
416 int i;
417
418 for (i = 0; i < rec->n; ++i)
419 isl_upoly_free(rec->p[i]);
420 }
421
422 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
423 {
424 if (!up)
425 return NULL;
426
427 up->ref++;
428 return up;
429 }
430
431 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
432 {
433 struct isl_upoly_cst *cst;
434 struct isl_upoly_cst *dup;
435
436 cst = isl_upoly_as_cst(up);
437 if (!cst)
438 return NULL;
439
440 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
441 if (!dup)
442 return NULL;
443 isl_int_set(dup->n, cst->n);
444 isl_int_set(dup->d, cst->d);
445
446 return &dup->up;
447 }
448
449 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
450 {
451 int i;
452 struct isl_upoly_rec *rec;
453 struct isl_upoly_rec *dup;
454
455 rec = isl_upoly_as_rec(up);
456 if (!rec)
457 return NULL;
458
459 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
460 if (!dup)
461 return NULL;
462
463 for (i = 0; i < rec->n; ++i) {
464 dup->p[i] = isl_upoly_copy(rec->p[i]);
465 if (!dup->p[i])
466 goto error;
467 dup->n++;
468 }
469
470 return &dup->up;
471 error:
472 isl_upoly_free(&dup->up);
473 return NULL;
474 }
475
476 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
477 {
478 if (!up)
479 return NULL;
480
481 if (isl_upoly_is_cst(up))
482 return isl_upoly_dup_cst(up);
483 else
484 return isl_upoly_dup_rec(up);
485 }
486
487 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
488 {
489 if (!up)
490 return NULL;
491
492 if (up->ref == 1)
493 return up;
494 up->ref--;
495 return isl_upoly_dup(up);
496 }
497
498 void isl_upoly_free(__isl_take struct isl_upoly *up)
499 {
500 if (!up)
501 return;
502
503 if (--up->ref > 0)
504 return;
505
506 if (up->var < 0)
507 upoly_free_cst((struct isl_upoly_cst *)up);
508 else
509 upoly_free_rec((struct isl_upoly_rec *)up);
510
511 isl_ctx_deref(up->ctx);
512 free(up);
513 }
514
515 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
516 {
517 isl_int gcd;
518
519 isl_int_init(gcd);
520 isl_int_gcd(gcd, cst->n, cst->d);
521 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
522 isl_int_divexact(cst->n, cst->n, gcd);
523 isl_int_divexact(cst->d, cst->d, gcd);
524 }
525 isl_int_clear(gcd);
526 }
527
528 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
529 __isl_take struct isl_upoly *up2)
530 {
531 struct isl_upoly_cst *cst1;
532 struct isl_upoly_cst *cst2;
533
534 up1 = isl_upoly_cow(up1);
535 if (!up1 || !up2)
536 goto error;
537
538 cst1 = isl_upoly_as_cst(up1);
539 cst2 = isl_upoly_as_cst(up2);
540
541 if (isl_int_eq(cst1->d, cst2->d))
542 isl_int_add(cst1->n, cst1->n, cst2->n);
543 else {
544 isl_int_mul(cst1->n, cst1->n, cst2->d);
545 isl_int_addmul(cst1->n, cst2->n, cst1->d);
546 isl_int_mul(cst1->d, cst1->d, cst2->d);
547 }
548
549 isl_upoly_cst_reduce(cst1);
550
551 isl_upoly_free(up2);
552 return up1;
553 error:
554 isl_upoly_free(up1);
555 isl_upoly_free(up2);
556 return NULL;
557 }
558
559 static __isl_give struct isl_upoly *replace_by_zero(
560 __isl_take struct isl_upoly *up)
561 {
562 struct isl_ctx *ctx;
563
564 if (!up)
565 return NULL;
566 ctx = up->ctx;
567 isl_upoly_free(up);
568 return isl_upoly_zero(ctx);
569 }
570
571 static __isl_give struct isl_upoly *replace_by_constant_term(
572 __isl_take struct isl_upoly *up)
573 {
574 struct isl_upoly_rec *rec;
575 struct isl_upoly *cst;
576
577 if (!up)
578 return NULL;
579
580 rec = isl_upoly_as_rec(up);
581 if (!rec)
582 goto error;
583 cst = isl_upoly_copy(rec->p[0]);
584 isl_upoly_free(up);
585 return cst;
586 error:
587 isl_upoly_free(up);
588 return NULL;
589 }
590
591 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
592 __isl_take struct isl_upoly *up2)
593 {
594 int i;
595 struct isl_upoly_rec *rec1, *rec2;
596
597 if (!up1 || !up2)
598 goto error;
599
600 if (isl_upoly_is_nan(up1)) {
601 isl_upoly_free(up2);
602 return up1;
603 }
604
605 if (isl_upoly_is_nan(up2)) {
606 isl_upoly_free(up1);
607 return up2;
608 }
609
610 if (isl_upoly_is_zero(up1)) {
611 isl_upoly_free(up1);
612 return up2;
613 }
614
615 if (isl_upoly_is_zero(up2)) {
616 isl_upoly_free(up2);
617 return up1;
618 }
619
620 if (up1->var < up2->var)
621 return isl_upoly_sum(up2, up1);
622
623 if (up2->var < up1->var) {
624 struct isl_upoly_rec *rec;
625 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
626 isl_upoly_free(up1);
627 return up2;
628 }
629 up1 = isl_upoly_cow(up1);
630 rec = isl_upoly_as_rec(up1);
631 if (!rec)
632 goto error;
633 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
634 if (rec->n == 1)
635 up1 = replace_by_constant_term(up1);
636 return up1;
637 }
638
639 if (isl_upoly_is_cst(up1))
640 return isl_upoly_sum_cst(up1, up2);
641
642 rec1 = isl_upoly_as_rec(up1);
643 rec2 = isl_upoly_as_rec(up2);
644 if (!rec1 || !rec2)
645 goto error;
646
647 if (rec1->n < rec2->n)
648 return isl_upoly_sum(up2, up1);
649
650 up1 = isl_upoly_cow(up1);
651 rec1 = isl_upoly_as_rec(up1);
652 if (!rec1)
653 goto error;
654
655 for (i = rec2->n - 1; i >= 0; --i) {
656 rec1->p[i] = isl_upoly_sum(rec1->p[i],
657 isl_upoly_copy(rec2->p[i]));
658 if (!rec1->p[i])
659 goto error;
660 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
661 isl_upoly_free(rec1->p[i]);
662 rec1->n--;
663 }
664 }
665
666 if (rec1->n == 0)
667 up1 = replace_by_zero(up1);
668 else if (rec1->n == 1)
669 up1 = replace_by_constant_term(up1);
670
671 isl_upoly_free(up2);
672
673 return up1;
674 error:
675 isl_upoly_free(up1);
676 isl_upoly_free(up2);
677 return NULL;
678 }
679
680 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
681 __isl_take struct isl_upoly *up, isl_int v)
682 {
683 struct isl_upoly_cst *cst;
684
685 up = isl_upoly_cow(up);
686 if (!up)
687 return NULL;
688
689 cst = isl_upoly_as_cst(up);
690
691 isl_int_addmul(cst->n, cst->d, v);
692
693 return up;
694 }
695
696 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
697 __isl_take struct isl_upoly *up, isl_int v)
698 {
699 struct isl_upoly_rec *rec;
700
701 if (!up)
702 return NULL;
703
704 if (isl_upoly_is_cst(up))
705 return isl_upoly_cst_add_isl_int(up, v);
706
707 up = isl_upoly_cow(up);
708 rec = isl_upoly_as_rec(up);
709 if (!rec)
710 goto error;
711
712 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
713 if (!rec->p[0])
714 goto error;
715
716 return up;
717 error:
718 isl_upoly_free(up);
719 return NULL;
720 }
721
722 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
723 __isl_take struct isl_upoly *up, isl_int v)
724 {
725 struct isl_upoly_cst *cst;
726
727 if (isl_upoly_is_zero(up))
728 return up;
729
730 up = isl_upoly_cow(up);
731 if (!up)
732 return NULL;
733
734 cst = isl_upoly_as_cst(up);
735
736 isl_int_mul(cst->n, cst->n, v);
737
738 return up;
739 }
740
741 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
742 __isl_take struct isl_upoly *up, isl_int v)
743 {
744 int i;
745 struct isl_upoly_rec *rec;
746
747 if (!up)
748 return NULL;
749
750 if (isl_upoly_is_cst(up))
751 return isl_upoly_cst_mul_isl_int(up, v);
752
753 up = isl_upoly_cow(up);
754 rec = isl_upoly_as_rec(up);
755 if (!rec)
756 goto error;
757
758 for (i = 0; i < rec->n; ++i) {
759 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
760 if (!rec->p[i])
761 goto error;
762 }
763
764 return up;
765 error:
766 isl_upoly_free(up);
767 return NULL;
768 }
769
770 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
771 __isl_take struct isl_upoly *up2)
772 {
773 struct isl_upoly_cst *cst1;
774 struct isl_upoly_cst *cst2;
775
776 up1 = isl_upoly_cow(up1);
777 if (!up1 || !up2)
778 goto error;
779
780 cst1 = isl_upoly_as_cst(up1);
781 cst2 = isl_upoly_as_cst(up2);
782
783 isl_int_mul(cst1->n, cst1->n, cst2->n);
784 isl_int_mul(cst1->d, cst1->d, cst2->d);
785
786 isl_upoly_cst_reduce(cst1);
787
788 isl_upoly_free(up2);
789 return up1;
790 error:
791 isl_upoly_free(up1);
792 isl_upoly_free(up2);
793 return NULL;
794 }
795
796 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
797 __isl_take struct isl_upoly *up2)
798 {
799 struct isl_upoly_rec *rec1;
800 struct isl_upoly_rec *rec2;
801 struct isl_upoly_rec *res = NULL;
802 int i, j;
803 int size;
804
805 rec1 = isl_upoly_as_rec(up1);
806 rec2 = isl_upoly_as_rec(up2);
807 if (!rec1 || !rec2)
808 goto error;
809 size = rec1->n + rec2->n - 1;
810 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
811 if (!res)
812 goto error;
813
814 for (i = 0; i < rec1->n; ++i) {
815 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
816 isl_upoly_copy(rec1->p[i]));
817 if (!res->p[i])
818 goto error;
819 res->n++;
820 }
821 for (; i < size; ++i) {
822 res->p[i] = isl_upoly_zero(up1->ctx);
823 if (!res->p[i])
824 goto error;
825 res->n++;
826 }
827 for (i = 0; i < rec1->n; ++i) {
828 for (j = 1; j < rec2->n; ++j) {
829 struct isl_upoly *up;
830 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
831 isl_upoly_copy(rec1->p[i]));
832 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
833 if (!res->p[i + j])
834 goto error;
835 }
836 }
837
838 isl_upoly_free(up1);
839 isl_upoly_free(up2);
840
841 return &res->up;
842 error:
843 isl_upoly_free(up1);
844 isl_upoly_free(up2);
845 isl_upoly_free(&res->up);
846 return NULL;
847 }
848
849 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
850 __isl_take struct isl_upoly *up2)
851 {
852 if (!up1 || !up2)
853 goto error;
854
855 if (isl_upoly_is_nan(up1)) {
856 isl_upoly_free(up2);
857 return up1;
858 }
859
860 if (isl_upoly_is_nan(up2)) {
861 isl_upoly_free(up1);
862 return up2;
863 }
864
865 if (isl_upoly_is_zero(up1)) {
866 isl_upoly_free(up2);
867 return up1;
868 }
869
870 if (isl_upoly_is_zero(up2)) {
871 isl_upoly_free(up1);
872 return up2;
873 }
874
875 if (isl_upoly_is_one(up1)) {
876 isl_upoly_free(up1);
877 return up2;
878 }
879
880 if (isl_upoly_is_one(up2)) {
881 isl_upoly_free(up2);
882 return up1;
883 }
884
885 if (up1->var < up2->var)
886 return isl_upoly_mul(up2, up1);
887
888 if (up2->var < up1->var) {
889 int i;
890 struct isl_upoly_rec *rec;
891 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
892 isl_ctx *ctx = up1->ctx;
893 isl_upoly_free(up1);
894 isl_upoly_free(up2);
895 return isl_upoly_nan(ctx);
896 }
897 up1 = isl_upoly_cow(up1);
898 rec = isl_upoly_as_rec(up1);
899 if (!rec)
900 goto error;
901
902 for (i = 0; i < rec->n; ++i) {
903 rec->p[i] = isl_upoly_mul(rec->p[i],
904 isl_upoly_copy(up2));
905 if (!rec->p[i])
906 goto error;
907 }
908 isl_upoly_free(up2);
909 return up1;
910 }
911
912 if (isl_upoly_is_cst(up1))
913 return isl_upoly_mul_cst(up1, up2);
914
915 return isl_upoly_mul_rec(up1, up2);
916 error:
917 isl_upoly_free(up1);
918 isl_upoly_free(up2);
919 return NULL;
920 }
921
922 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
923 unsigned power)
924 {
925 struct isl_upoly *res;
926
927 if (!up)
928 return NULL;
929 if (power == 1)
930 return up;
931
932 if (power % 2)
933 res = isl_upoly_copy(up);
934 else
935 res = isl_upoly_one(up->ctx);
936
937 while (power >>= 1) {
938 up = isl_upoly_mul(up, isl_upoly_copy(up));
939 if (power % 2)
940 res = isl_upoly_mul(res, isl_upoly_copy(up));
941 }
942
943 isl_upoly_free(up);
944 return res;
945 }
946
947 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
948 unsigned n_div, __isl_take struct isl_upoly *up)
949 {
950 struct isl_qpolynomial *qp = NULL;
951 unsigned total;
952
953 if (!dim || !up)
954 goto error;
955
956 total = isl_dim_total(dim);
957
958 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
959 if (!qp)
960 goto error;
961
962 qp->ref = 1;
963 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
964 if (!qp->div)
965 goto error;
966
967 qp->dim = dim;
968 qp->upoly = up;
969
970 return qp;
971 error:
972 isl_dim_free(dim);
973 isl_upoly_free(up);
974 isl_qpolynomial_free(qp);
975 return NULL;
976 }
977
978 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
979 {
980 if (!qp)
981 return NULL;
982
983 qp->ref++;
984 return qp;
985 }
986
987 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
988 {
989 struct isl_qpolynomial *dup;
990
991 if (!qp)
992 return NULL;
993
994 dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
995 isl_upoly_copy(qp->upoly));
996 if (!dup)
997 return NULL;
998 isl_mat_free(dup->div);
999 dup->div = isl_mat_copy(qp->div);
1000 if (!dup->div)
1001 goto error;
1002
1003 return dup;
1004 error:
1005 isl_qpolynomial_free(dup);
1006 return NULL;
1007 }
1008
1009 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1010 {
1011 if (!qp)
1012 return NULL;
1013
1014 if (qp->ref == 1)
1015 return qp;
1016 qp->ref--;
1017 return isl_qpolynomial_dup(qp);
1018 }
1019
1020 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1021 {
1022 if (!qp)
1023 return;
1024
1025 if (--qp->ref > 0)
1026 return;
1027
1028 isl_dim_free(qp->dim);
1029 isl_mat_free(qp->div);
1030 isl_upoly_free(qp->upoly);
1031
1032 free(qp);
1033 }
1034
1035 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1036 {
1037 int i;
1038 struct isl_upoly_rec *rec;
1039 struct isl_upoly_cst *cst;
1040
1041 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1042 if (!rec)
1043 return NULL;
1044 for (i = 0; i < 1 + power; ++i) {
1045 rec->p[i] = isl_upoly_zero(ctx);
1046 if (!rec->p[i])
1047 goto error;
1048 rec->n++;
1049 }
1050 cst = isl_upoly_as_cst(rec->p[power]);
1051 isl_int_set_si(cst->n, 1);
1052
1053 return &rec->up;
1054 error:
1055 isl_upoly_free(&rec->up);
1056 return NULL;
1057 }
1058
1059 /* r array maps original positions to new positions.
1060 */
1061 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1062 int *r)
1063 {
1064 int i;
1065 struct isl_upoly_rec *rec;
1066 struct isl_upoly *base;
1067 struct isl_upoly *res;
1068
1069 if (isl_upoly_is_cst(up))
1070 return up;
1071
1072 rec = isl_upoly_as_rec(up);
1073 if (!rec)
1074 goto error;
1075
1076 isl_assert(up->ctx, rec->n >= 1, goto error);
1077
1078 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1079 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1080
1081 for (i = rec->n - 2; i >= 0; --i) {
1082 res = isl_upoly_mul(res, isl_upoly_copy(base));
1083 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1084 }
1085
1086 isl_upoly_free(base);
1087 isl_upoly_free(up);
1088
1089 return res;
1090 error:
1091 isl_upoly_free(up);
1092 return NULL;
1093 }
1094
1095 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1096 {
1097 int n_row, n_col;
1098 int equal;
1099
1100 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1101 div1->n_col >= div2->n_col, return -1);
1102
1103 if (div1->n_row == div2->n_row)
1104 return isl_mat_is_equal(div1, div2);
1105
1106 n_row = div1->n_row;
1107 n_col = div1->n_col;
1108 div1->n_row = div2->n_row;
1109 div1->n_col = div2->n_col;
1110
1111 equal = isl_mat_is_equal(div1, div2);
1112
1113 div1->n_row = n_row;
1114 div1->n_col = n_col;
1115
1116 return equal;
1117 }
1118
1119 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1120 {
1121 int li, lj;
1122
1123 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1124 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1125
1126 if (li != lj)
1127 return li - lj;
1128
1129 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1130 }
1131
1132 struct isl_div_sort_info {
1133 isl_mat *div;
1134 int row;
1135 };
1136
1137 static int div_sort_cmp(const void *p1, const void *p2)
1138 {
1139 const struct isl_div_sort_info *i1, *i2;
1140 i1 = (const struct isl_div_sort_info *) p1;
1141 i2 = (const struct isl_div_sort_info *) p2;
1142
1143 return cmp_row(i1->div, i1->row, i2->row);
1144 }
1145
1146 /* Sort divs and remove duplicates.
1147 */
1148 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1149 {
1150 int i;
1151 int skip;
1152 int len;
1153 struct isl_div_sort_info *array = NULL;
1154 int *pos = NULL, *at = NULL;
1155 int *reordering = NULL;
1156 unsigned div_pos;
1157
1158 if (!qp)
1159 return NULL;
1160 if (qp->div->n_row <= 1)
1161 return qp;
1162
1163 div_pos = isl_dim_total(qp->dim);
1164
1165 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1166 qp->div->n_row);
1167 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1168 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1169 len = qp->div->n_col - 2;
1170 reordering = isl_alloc_array(qp->div->ctx, int, len);
1171 if (!array || !pos || !at || !reordering)
1172 goto error;
1173
1174 for (i = 0; i < qp->div->n_row; ++i) {
1175 array[i].div = qp->div;
1176 array[i].row = i;
1177 pos[i] = i;
1178 at[i] = i;
1179 }
1180
1181 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1182 div_sort_cmp);
1183
1184 for (i = 0; i < div_pos; ++i)
1185 reordering[i] = i;
1186
1187 for (i = 0; i < qp->div->n_row; ++i) {
1188 if (pos[array[i].row] == i)
1189 continue;
1190 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1191 pos[at[i]] = pos[array[i].row];
1192 at[pos[array[i].row]] = at[i];
1193 at[i] = array[i].row;
1194 pos[array[i].row] = i;
1195 }
1196
1197 skip = 0;
1198 for (i = 0; i < len - div_pos; ++i) {
1199 if (i > 0 &&
1200 isl_seq_eq(qp->div->row[i - skip - 1],
1201 qp->div->row[i - skip], qp->div->n_col)) {
1202 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1203 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1204 2 + div_pos + i - skip);
1205 qp->div = isl_mat_drop_cols(qp->div,
1206 2 + div_pos + i - skip, 1);
1207 skip++;
1208 }
1209 reordering[div_pos + array[i].row] = div_pos + i - skip;
1210 }
1211
1212 qp->upoly = reorder(qp->upoly, reordering);
1213
1214 if (!qp->upoly || !qp->div)
1215 goto error;
1216
1217 free(at);
1218 free(pos);
1219 free(array);
1220 free(reordering);
1221
1222 return qp;
1223 error:
1224 free(at);
1225 free(pos);
1226 free(array);
1227 free(reordering);
1228 isl_qpolynomial_free(qp);
1229 return NULL;
1230 }
1231
1232 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1233 int *exp, int first)
1234 {
1235 int i;
1236 struct isl_upoly_rec *rec;
1237
1238 if (isl_upoly_is_cst(up))
1239 return up;
1240
1241 if (up->var < first)
1242 return up;
1243
1244 if (exp[up->var - first] == up->var - first)
1245 return up;
1246
1247 up = isl_upoly_cow(up);
1248 if (!up)
1249 goto error;
1250
1251 up->var = exp[up->var - first] + first;
1252
1253 rec = isl_upoly_as_rec(up);
1254 if (!rec)
1255 goto error;
1256
1257 for (i = 0; i < rec->n; ++i) {
1258 rec->p[i] = expand(rec->p[i], exp, first);
1259 if (!rec->p[i])
1260 goto error;
1261 }
1262
1263 return up;
1264 error:
1265 isl_upoly_free(up);
1266 return NULL;
1267 }
1268
1269 static __isl_give isl_qpolynomial *with_merged_divs(
1270 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1271 __isl_take isl_qpolynomial *qp2),
1272 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1273 {
1274 int *exp1 = NULL;
1275 int *exp2 = NULL;
1276 isl_mat *div = NULL;
1277
1278 qp1 = isl_qpolynomial_cow(qp1);
1279 qp2 = isl_qpolynomial_cow(qp2);
1280
1281 if (!qp1 || !qp2)
1282 goto error;
1283
1284 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1285 qp1->div->n_col >= qp2->div->n_col, goto error);
1286
1287 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1288 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1289 if (!exp1 || !exp2)
1290 goto error;
1291
1292 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1293 if (!div)
1294 goto error;
1295
1296 isl_mat_free(qp1->div);
1297 qp1->div = isl_mat_copy(div);
1298 isl_mat_free(qp2->div);
1299 qp2->div = isl_mat_copy(div);
1300
1301 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1302 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1303
1304 if (!qp1->upoly || !qp2->upoly)
1305 goto error;
1306
1307 isl_mat_free(div);
1308 free(exp1);
1309 free(exp2);
1310
1311 return fn(qp1, qp2);
1312 error:
1313 isl_mat_free(div);
1314 free(exp1);
1315 free(exp2);
1316 isl_qpolynomial_free(qp1);
1317 isl_qpolynomial_free(qp2);
1318 return NULL;
1319 }
1320
1321 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1322 __isl_take isl_qpolynomial *qp2)
1323 {
1324 qp1 = isl_qpolynomial_cow(qp1);
1325
1326 if (!qp1 || !qp2)
1327 goto error;
1328
1329 if (qp1->div->n_row < qp2->div->n_row)
1330 return isl_qpolynomial_add(qp2, qp1);
1331
1332 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1333 if (!compatible_divs(qp1->div, qp2->div))
1334 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1335
1336 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1337 if (!qp1->upoly)
1338 goto error;
1339
1340 isl_qpolynomial_free(qp2);
1341
1342 return qp1;
1343 error:
1344 isl_qpolynomial_free(qp1);
1345 isl_qpolynomial_free(qp2);
1346 return NULL;
1347 }
1348
1349 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1350 __isl_keep isl_set *dom,
1351 __isl_take isl_qpolynomial *qp1,
1352 __isl_take isl_qpolynomial *qp2)
1353 {
1354 qp1 = isl_qpolynomial_add(qp1, qp2);
1355 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1356 return qp1;
1357 }
1358
1359 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1360 __isl_take isl_qpolynomial *qp2)
1361 {
1362 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1363 }
1364
1365 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1366 __isl_take isl_qpolynomial *qp, isl_int v)
1367 {
1368 if (isl_int_is_zero(v))
1369 return qp;
1370
1371 qp = isl_qpolynomial_cow(qp);
1372 if (!qp)
1373 return NULL;
1374
1375 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1376 if (!qp->upoly)
1377 goto error;
1378
1379 return qp;
1380 error:
1381 isl_qpolynomial_free(qp);
1382 return NULL;
1383
1384 }
1385
1386 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1387 {
1388 if (!qp)
1389 return NULL;
1390
1391 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1392 }
1393
1394 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1395 __isl_take isl_qpolynomial *qp, isl_int v)
1396 {
1397 if (isl_int_is_one(v))
1398 return qp;
1399
1400 if (qp && isl_int_is_zero(v)) {
1401 isl_qpolynomial *zero;
1402 zero = isl_qpolynomial_zero(isl_dim_copy(qp->dim));
1403 isl_qpolynomial_free(qp);
1404 return zero;
1405 }
1406
1407 qp = isl_qpolynomial_cow(qp);
1408 if (!qp)
1409 return NULL;
1410
1411 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1412 if (!qp->upoly)
1413 goto error;
1414
1415 return qp;
1416 error:
1417 isl_qpolynomial_free(qp);
1418 return NULL;
1419 }
1420
1421 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1422 __isl_take isl_qpolynomial *qp2)
1423 {
1424 qp1 = isl_qpolynomial_cow(qp1);
1425
1426 if (!qp1 || !qp2)
1427 goto error;
1428
1429 if (qp1->div->n_row < qp2->div->n_row)
1430 return isl_qpolynomial_mul(qp2, qp1);
1431
1432 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1433 if (!compatible_divs(qp1->div, qp2->div))
1434 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1435
1436 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1437 if (!qp1->upoly)
1438 goto error;
1439
1440 isl_qpolynomial_free(qp2);
1441
1442 return qp1;
1443 error:
1444 isl_qpolynomial_free(qp1);
1445 isl_qpolynomial_free(qp2);
1446 return NULL;
1447 }
1448
1449 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1450 unsigned power)
1451 {
1452 qp = isl_qpolynomial_cow(qp);
1453
1454 if (!qp)
1455 return NULL;
1456
1457 qp->upoly = isl_upoly_pow(qp->upoly, power);
1458 if (!qp->upoly)
1459 goto error;
1460
1461 return qp;
1462 error:
1463 isl_qpolynomial_free(qp);
1464 return NULL;
1465 }
1466
1467 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1468 {
1469 if (!dim)
1470 return NULL;
1471 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1472 }
1473
1474 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1475 {
1476 if (!dim)
1477 return NULL;
1478 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1479 }
1480
1481 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1482 {
1483 if (!dim)
1484 return NULL;
1485 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1486 }
1487
1488 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1489 {
1490 if (!dim)
1491 return NULL;
1492 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1493 }
1494
1495 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1496 {
1497 if (!dim)
1498 return NULL;
1499 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1500 }
1501
1502 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1503 isl_int v)
1504 {
1505 struct isl_qpolynomial *qp;
1506 struct isl_upoly_cst *cst;
1507
1508 if (!dim)
1509 return NULL;
1510
1511 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1512 if (!qp)
1513 return NULL;
1514
1515 cst = isl_upoly_as_cst(qp->upoly);
1516 isl_int_set(cst->n, v);
1517
1518 return qp;
1519 }
1520
1521 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1522 isl_int *n, isl_int *d)
1523 {
1524 struct isl_upoly_cst *cst;
1525
1526 if (!qp)
1527 return -1;
1528
1529 if (!isl_upoly_is_cst(qp->upoly))
1530 return 0;
1531
1532 cst = isl_upoly_as_cst(qp->upoly);
1533 if (!cst)
1534 return -1;
1535
1536 if (n)
1537 isl_int_set(*n, cst->n);
1538 if (d)
1539 isl_int_set(*d, cst->d);
1540
1541 return 1;
1542 }
1543
1544 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1545 {
1546 int is_cst;
1547 struct isl_upoly_rec *rec;
1548
1549 if (!up)
1550 return -1;
1551
1552 if (up->var < 0)
1553 return 1;
1554
1555 rec = isl_upoly_as_rec(up);
1556 if (!rec)
1557 return -1;
1558
1559 if (rec->n > 2)
1560 return 0;
1561
1562 isl_assert(up->ctx, rec->n > 1, return -1);
1563
1564 is_cst = isl_upoly_is_cst(rec->p[1]);
1565 if (is_cst < 0)
1566 return -1;
1567 if (!is_cst)
1568 return 0;
1569
1570 return isl_upoly_is_affine(rec->p[0]);
1571 }
1572
1573 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1574 {
1575 if (!qp)
1576 return -1;
1577
1578 if (qp->div->n_row > 0)
1579 return 0;
1580
1581 return isl_upoly_is_affine(qp->upoly);
1582 }
1583
1584 static void update_coeff(__isl_keep isl_vec *aff,
1585 __isl_keep struct isl_upoly_cst *cst, int pos)
1586 {
1587 isl_int gcd;
1588 isl_int f;
1589
1590 if (isl_int_is_zero(cst->n))
1591 return;
1592
1593 isl_int_init(gcd);
1594 isl_int_init(f);
1595 isl_int_gcd(gcd, cst->d, aff->el[0]);
1596 isl_int_divexact(f, cst->d, gcd);
1597 isl_int_divexact(gcd, aff->el[0], gcd);
1598 isl_seq_scale(aff->el, aff->el, f, aff->size);
1599 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1600 isl_int_clear(gcd);
1601 isl_int_clear(f);
1602 }
1603
1604 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1605 __isl_keep isl_vec *aff)
1606 {
1607 struct isl_upoly_cst *cst;
1608 struct isl_upoly_rec *rec;
1609
1610 if (!up || !aff)
1611 return -1;
1612
1613 if (up->var < 0) {
1614 struct isl_upoly_cst *cst;
1615
1616 cst = isl_upoly_as_cst(up);
1617 if (!cst)
1618 return -1;
1619 update_coeff(aff, cst, 0);
1620 return 0;
1621 }
1622
1623 rec = isl_upoly_as_rec(up);
1624 if (!rec)
1625 return -1;
1626 isl_assert(up->ctx, rec->n == 2, return -1);
1627
1628 cst = isl_upoly_as_cst(rec->p[1]);
1629 if (!cst)
1630 return -1;
1631 update_coeff(aff, cst, 1 + up->var);
1632
1633 return isl_upoly_update_affine(rec->p[0], aff);
1634 }
1635
1636 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1637 __isl_keep isl_qpolynomial *qp)
1638 {
1639 isl_vec *aff;
1640 unsigned d;
1641
1642 if (!qp)
1643 return NULL;
1644
1645 d = isl_dim_total(qp->dim);
1646 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1647 if (!aff)
1648 return NULL;
1649
1650 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1651 isl_int_set_si(aff->el[0], 1);
1652
1653 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1654 goto error;
1655
1656 return aff;
1657 error:
1658 isl_vec_free(aff);
1659 return NULL;
1660 }
1661
1662 int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
1663 __isl_keep isl_qpolynomial *qp2)
1664 {
1665 if (!qp1 || !qp2)
1666 return -1;
1667
1668 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1669 }
1670
1671 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1672 {
1673 int i;
1674 struct isl_upoly_rec *rec;
1675
1676 if (isl_upoly_is_cst(up)) {
1677 struct isl_upoly_cst *cst;
1678 cst = isl_upoly_as_cst(up);
1679 if (!cst)
1680 return;
1681 isl_int_lcm(*d, *d, cst->d);
1682 return;
1683 }
1684
1685 rec = isl_upoly_as_rec(up);
1686 if (!rec)
1687 return;
1688
1689 for (i = 0; i < rec->n; ++i)
1690 upoly_update_den(rec->p[i], d);
1691 }
1692
1693 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1694 {
1695 isl_int_set_si(*d, 1);
1696 if (!qp)
1697 return;
1698 upoly_update_den(qp->upoly, d);
1699 }
1700
1701 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1702 int pos, int power)
1703 {
1704 struct isl_ctx *ctx;
1705
1706 if (!dim)
1707 return NULL;
1708
1709 ctx = dim->ctx;
1710
1711 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1712 }
1713
1714 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1715 enum isl_dim_type type, unsigned pos)
1716 {
1717 if (!dim)
1718 return NULL;
1719
1720 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1721 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1722
1723 if (type == isl_dim_set)
1724 pos += isl_dim_size(dim, isl_dim_param);
1725
1726 return isl_qpolynomial_var_pow(dim, pos, 1);
1727 error:
1728 isl_dim_free(dim);
1729 return NULL;
1730 }
1731
1732 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1733 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1734 {
1735 int i;
1736 struct isl_upoly_rec *rec;
1737 struct isl_upoly *base, *res;
1738
1739 if (!up)
1740 return NULL;
1741
1742 if (isl_upoly_is_cst(up))
1743 return up;
1744
1745 if (up->var < first)
1746 return up;
1747
1748 rec = isl_upoly_as_rec(up);
1749 if (!rec)
1750 goto error;
1751
1752 isl_assert(up->ctx, rec->n >= 1, goto error);
1753
1754 if (up->var >= first + n)
1755 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1756 else
1757 base = isl_upoly_copy(subs[up->var - first]);
1758
1759 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1760 for (i = rec->n - 2; i >= 0; --i) {
1761 struct isl_upoly *t;
1762 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1763 res = isl_upoly_mul(res, isl_upoly_copy(base));
1764 res = isl_upoly_sum(res, t);
1765 }
1766
1767 isl_upoly_free(base);
1768 isl_upoly_free(up);
1769
1770 return res;
1771 error:
1772 isl_upoly_free(up);
1773 return NULL;
1774 }
1775
1776 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1777 isl_int denom, unsigned len)
1778 {
1779 int i;
1780 struct isl_upoly *up;
1781
1782 isl_assert(ctx, len >= 1, return NULL);
1783
1784 up = isl_upoly_rat_cst(ctx, f[0], denom);
1785 for (i = 0; i < len - 1; ++i) {
1786 struct isl_upoly *t;
1787 struct isl_upoly *c;
1788
1789 if (isl_int_is_zero(f[1 + i]))
1790 continue;
1791
1792 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1793 t = isl_upoly_var_pow(ctx, i, 1);
1794 t = isl_upoly_mul(c, t);
1795 up = isl_upoly_sum(up, t);
1796 }
1797
1798 return up;
1799 }
1800
1801 /* Remove common factor of non-constant terms and denominator.
1802 */
1803 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1804 {
1805 isl_ctx *ctx = qp->div->ctx;
1806 unsigned total = qp->div->n_col - 2;
1807
1808 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1809 isl_int_gcd(ctx->normalize_gcd,
1810 ctx->normalize_gcd, qp->div->row[div][0]);
1811 if (isl_int_is_one(ctx->normalize_gcd))
1812 return;
1813
1814 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1815 ctx->normalize_gcd, total);
1816 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1817 ctx->normalize_gcd);
1818 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1819 ctx->normalize_gcd);
1820 }
1821
1822 /* Replace the integer division identified by "div" by the polynomial "s".
1823 * The integer division is assumed not to appear in the definition
1824 * of any other integer divisions.
1825 */
1826 static __isl_give isl_qpolynomial *substitute_div(
1827 __isl_take isl_qpolynomial *qp,
1828 int div, __isl_take struct isl_upoly *s)
1829 {
1830 int i;
1831 int total;
1832 int *reordering;
1833
1834 if (!qp || !s)
1835 goto error;
1836
1837 qp = isl_qpolynomial_cow(qp);
1838 if (!qp)
1839 goto error;
1840
1841 total = isl_dim_total(qp->dim);
1842 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1843 if (!qp->upoly)
1844 goto error;
1845
1846 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1847 if (!reordering)
1848 goto error;
1849 for (i = 0; i < total + div; ++i)
1850 reordering[i] = i;
1851 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1852 reordering[i] = i - 1;
1853 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1854 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1855 qp->upoly = reorder(qp->upoly, reordering);
1856 free(reordering);
1857
1858 if (!qp->upoly || !qp->div)
1859 goto error;
1860
1861 isl_upoly_free(s);
1862 return qp;
1863 error:
1864 isl_qpolynomial_free(qp);
1865 isl_upoly_free(s);
1866 return NULL;
1867 }
1868
1869 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1870 * divisions because d is equal to 1 by their definition, i.e., e.
1871 */
1872 static __isl_give isl_qpolynomial *substitute_non_divs(
1873 __isl_take isl_qpolynomial *qp)
1874 {
1875 int i, j;
1876 int total;
1877 struct isl_upoly *s;
1878
1879 if (!qp)
1880 return NULL;
1881
1882 total = isl_dim_total(qp->dim);
1883 for (i = 0; qp && i < qp->div->n_row; ++i) {
1884 if (!isl_int_is_one(qp->div->row[i][0]))
1885 continue;
1886 for (j = i + 1; j < qp->div->n_row; ++j) {
1887 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1888 continue;
1889 isl_seq_combine(qp->div->row[j] + 1,
1890 qp->div->ctx->one, qp->div->row[j] + 1,
1891 qp->div->row[j][2 + total + i],
1892 qp->div->row[i] + 1, 1 + total + i);
1893 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1894 normalize_div(qp, j);
1895 }
1896 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1897 qp->div->row[i][0], qp->div->n_col - 1);
1898 qp = substitute_div(qp, i, s);
1899 --i;
1900 }
1901
1902 return qp;
1903 }
1904
1905 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1906 * with d the denominator. When replacing the coefficient e of x by
1907 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1908 * inside the division, so we need to add floor(e/d) * x outside.
1909 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1910 * to adjust the coefficient of x in each later div that depends on the
1911 * current div "div" and also in the affine expression "aff"
1912 * (if it too depends on "div").
1913 */
1914 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1915 __isl_keep isl_vec *aff)
1916 {
1917 int i, j;
1918 isl_int v;
1919 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1920
1921 isl_int_init(v);
1922 for (i = 0; i < 1 + total + div; ++i) {
1923 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1924 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1925 continue;
1926 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1927 isl_int_fdiv_r(qp->div->row[div][1 + i],
1928 qp->div->row[div][1 + i], qp->div->row[div][0]);
1929 if (!isl_int_is_zero(aff->el[1 + total + div]))
1930 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1931 for (j = div + 1; j < qp->div->n_row; ++j) {
1932 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1933 continue;
1934 isl_int_addmul(qp->div->row[j][1 + i],
1935 v, qp->div->row[j][2 + total + div]);
1936 }
1937 }
1938 isl_int_clear(v);
1939 }
1940
1941 /* Check if the last non-zero coefficient is bigger that half of the
1942 * denominator. If so, we will invert the div to further reduce the number
1943 * of distinct divs that may appear.
1944 * If the last non-zero coefficient is exactly half the denominator,
1945 * then we continue looking for earlier coefficients that are bigger
1946 * than half the denominator.
1947 */
1948 static int needs_invert(__isl_keep isl_mat *div, int row)
1949 {
1950 int i;
1951 int cmp;
1952
1953 for (i = div->n_col - 1; i >= 1; --i) {
1954 if (isl_int_is_zero(div->row[row][i]))
1955 continue;
1956 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1957 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1958 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1959 if (cmp)
1960 return cmp > 0;
1961 if (i == 1)
1962 return 1;
1963 }
1964
1965 return 0;
1966 }
1967
1968 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1969 * We only invert the coefficients of e (and the coefficient of q in
1970 * later divs and in "aff"). After calling this function, the
1971 * coefficients of e should be reduced again.
1972 */
1973 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1974 __isl_keep isl_vec *aff)
1975 {
1976 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1977
1978 isl_seq_neg(qp->div->row[div] + 1,
1979 qp->div->row[div] + 1, qp->div->n_col - 1);
1980 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
1981 isl_int_add(qp->div->row[div][1],
1982 qp->div->row[div][1], qp->div->row[div][0]);
1983 if (!isl_int_is_zero(aff->el[1 + total + div]))
1984 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
1985 isl_mat_col_mul(qp->div, 2 + total + div,
1986 qp->div->ctx->negone, 2 + total + div);
1987 }
1988
1989 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
1990 * in the interval [0, d-1], with d the denominator and such that the
1991 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
1992 *
1993 * After the reduction, some divs may have become redundant or identical,
1994 * so we call substitute_non_divs and sort_divs. If these functions
1995 * eliminate divs or merge two or more divs into one, the coefficients
1996 * of the enclosing divs may have to be reduced again, so we call
1997 * ourselves recursively if the number of divs decreases.
1998 */
1999 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2000 {
2001 int i;
2002 isl_vec *aff = NULL;
2003 struct isl_upoly *s;
2004 unsigned n_div;
2005
2006 if (!qp)
2007 return NULL;
2008
2009 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2010 aff = isl_vec_clr(aff);
2011 if (!aff)
2012 goto error;
2013
2014 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2015
2016 for (i = 0; i < qp->div->n_row; ++i) {
2017 normalize_div(qp, i);
2018 reduce_div(qp, i, aff);
2019 if (needs_invert(qp->div, i)) {
2020 invert_div(qp, i, aff);
2021 reduce_div(qp, i, aff);
2022 }
2023 }
2024
2025 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2026 qp->div->ctx->one, aff->size);
2027 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2028 isl_upoly_free(s);
2029 if (!qp->upoly)
2030 goto error;
2031
2032 isl_vec_free(aff);
2033
2034 n_div = qp->div->n_row;
2035 qp = substitute_non_divs(qp);
2036 qp = sort_divs(qp);
2037 if (qp && qp->div->n_row < n_div)
2038 return reduce_divs(qp);
2039
2040 return qp;
2041 error:
2042 isl_qpolynomial_free(qp);
2043 isl_vec_free(aff);
2044 return NULL;
2045 }
2046
2047 /* Assumes each div only depends on earlier divs.
2048 */
2049 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2050 int power)
2051 {
2052 struct isl_qpolynomial *qp = NULL;
2053 struct isl_upoly_rec *rec;
2054 struct isl_upoly_cst *cst;
2055 int i, d;
2056 int pos;
2057
2058 if (!div)
2059 return NULL;
2060
2061 d = div->line - div->bmap->div;
2062
2063 pos = isl_dim_total(div->bmap->dim) + d;
2064 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2065 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2066 div->bmap->n_div, &rec->up);
2067 if (!qp)
2068 goto error;
2069
2070 for (i = 0; i < div->bmap->n_div; ++i)
2071 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2072
2073 for (i = 0; i < 1 + power; ++i) {
2074 rec->p[i] = isl_upoly_zero(div->ctx);
2075 if (!rec->p[i])
2076 goto error;
2077 rec->n++;
2078 }
2079 cst = isl_upoly_as_cst(rec->p[power]);
2080 isl_int_set_si(cst->n, 1);
2081
2082 isl_div_free(div);
2083
2084 qp = reduce_divs(qp);
2085
2086 return qp;
2087 error:
2088 isl_qpolynomial_free(qp);
2089 isl_div_free(div);
2090 return NULL;
2091 }
2092
2093 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2094 {
2095 return isl_qpolynomial_div_pow(div, 1);
2096 }
2097
2098 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2099 const isl_int n, const isl_int d)
2100 {
2101 struct isl_qpolynomial *qp;
2102 struct isl_upoly_cst *cst;
2103
2104 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2105 if (!qp)
2106 return NULL;
2107
2108 cst = isl_upoly_as_cst(qp->upoly);
2109 isl_int_set(cst->n, n);
2110 isl_int_set(cst->d, d);
2111
2112 return qp;
2113 }
2114
2115 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2116 {
2117 struct isl_upoly_rec *rec;
2118 int i;
2119
2120 if (!up)
2121 return -1;
2122
2123 if (isl_upoly_is_cst(up))
2124 return 0;
2125
2126 if (up->var < d)
2127 active[up->var] = 1;
2128
2129 rec = isl_upoly_as_rec(up);
2130 for (i = 0; i < rec->n; ++i)
2131 if (up_set_active(rec->p[i], active, d) < 0)
2132 return -1;
2133
2134 return 0;
2135 }
2136
2137 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2138 {
2139 int i, j;
2140 int d = isl_dim_total(qp->dim);
2141
2142 if (!qp || !active)
2143 return -1;
2144
2145 for (i = 0; i < d; ++i)
2146 for (j = 0; j < qp->div->n_row; ++j) {
2147 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2148 continue;
2149 active[i] = 1;
2150 break;
2151 }
2152
2153 return up_set_active(qp->upoly, active, d);
2154 }
2155
2156 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2157 enum isl_dim_type type, unsigned first, unsigned n)
2158 {
2159 int i;
2160 int *active = NULL;
2161 int involves = 0;
2162
2163 if (!qp)
2164 return -1;
2165 if (n == 0)
2166 return 0;
2167
2168 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2169 return -1);
2170 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2171 type == isl_dim_set, return -1);
2172
2173 active = isl_calloc_array(qp->dim->ctx, int, isl_dim_total(qp->dim));
2174 if (set_active(qp, active) < 0)
2175 goto error;
2176
2177 if (type == isl_dim_set)
2178 first += isl_dim_size(qp->dim, isl_dim_param);
2179 for (i = 0; i < n; ++i)
2180 if (active[first + i]) {
2181 involves = 1;
2182 break;
2183 }
2184
2185 free(active);
2186
2187 return involves;
2188 error:
2189 free(active);
2190 return -1;
2191 }
2192
2193 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2194 * of the divs that do appear in the quasi-polynomial.
2195 */
2196 static __isl_give isl_qpolynomial *remove_redundant_divs(
2197 __isl_take isl_qpolynomial *qp)
2198 {
2199 int i, j;
2200 int d;
2201 int len;
2202 int skip;
2203 int *active = NULL;
2204 int *reordering = NULL;
2205 int redundant = 0;
2206 int n_div;
2207
2208 if (!qp)
2209 return NULL;
2210 if (qp->div->n_row == 0)
2211 return qp;
2212
2213 d = isl_dim_total(qp->dim);
2214 len = qp->div->n_col - 2;
2215 active = isl_calloc_array(qp->ctx, int, len);
2216 if (!active)
2217 goto error;
2218
2219 if (up_set_active(qp->upoly, active, len) < 0)
2220 goto error;
2221
2222 for (i = qp->div->n_row - 1; i >= 0; --i) {
2223 if (!active[d + i]) {
2224 redundant = 1;
2225 continue;
2226 }
2227 for (j = 0; j < i; ++j) {
2228 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2229 continue;
2230 active[d + j] = 1;
2231 break;
2232 }
2233 }
2234
2235 if (!redundant) {
2236 free(active);
2237 return qp;
2238 }
2239
2240 reordering = isl_alloc_array(qp->div->ctx, int, len);
2241 if (!reordering)
2242 goto error;
2243
2244 for (i = 0; i < d; ++i)
2245 reordering[i] = i;
2246
2247 skip = 0;
2248 n_div = qp->div->n_row;
2249 for (i = 0; i < n_div; ++i) {
2250 if (!active[d + i]) {
2251 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2252 qp->div = isl_mat_drop_cols(qp->div,
2253 2 + d + i - skip, 1);
2254 skip++;
2255 }
2256 reordering[d + i] = d + i - skip;
2257 }
2258
2259 qp->upoly = reorder(qp->upoly, reordering);
2260
2261 if (!qp->upoly || !qp->div)
2262 goto error;
2263
2264 free(active);
2265 free(reordering);
2266
2267 return qp;
2268 error:
2269 free(active);
2270 free(reordering);
2271 isl_qpolynomial_free(qp);
2272 return NULL;
2273 }
2274
2275 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2276 unsigned first, unsigned n)
2277 {
2278 int i;
2279 struct isl_upoly_rec *rec;
2280
2281 if (!up)
2282 return NULL;
2283 if (n == 0 || up->var < 0 || up->var < first)
2284 return up;
2285 if (up->var < first + n) {
2286 up = replace_by_constant_term(up);
2287 return isl_upoly_drop(up, first, n);
2288 }
2289 up = isl_upoly_cow(up);
2290 if (!up)
2291 return NULL;
2292 up->var -= n;
2293 rec = isl_upoly_as_rec(up);
2294 if (!rec)
2295 goto error;
2296
2297 for (i = 0; i < rec->n; ++i) {
2298 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2299 if (!rec->p[i])
2300 goto error;
2301 }
2302
2303 return up;
2304 error:
2305 isl_upoly_free(up);
2306 return NULL;
2307 }
2308
2309 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2310 __isl_take isl_qpolynomial *qp,
2311 enum isl_dim_type type, unsigned pos, const char *s)
2312 {
2313 qp = isl_qpolynomial_cow(qp);
2314 if (!qp)
2315 return NULL;
2316 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2317 if (!qp->dim)
2318 goto error;
2319 return qp;
2320 error:
2321 isl_qpolynomial_free(qp);
2322 return NULL;
2323 }
2324
2325 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2326 __isl_take isl_qpolynomial *qp,
2327 enum isl_dim_type type, unsigned first, unsigned n)
2328 {
2329 if (!qp)
2330 return NULL;
2331 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
2332 return qp;
2333
2334 qp = isl_qpolynomial_cow(qp);
2335 if (!qp)
2336 return NULL;
2337
2338 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2339 goto error);
2340 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2341 type == isl_dim_set, goto error);
2342
2343 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2344 if (!qp->dim)
2345 goto error;
2346
2347 if (type == isl_dim_set)
2348 first += isl_dim_size(qp->dim, isl_dim_param);
2349
2350 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2351 if (!qp->div)
2352 goto error;
2353
2354 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2355 if (!qp->upoly)
2356 goto error;
2357
2358 return qp;
2359 error:
2360 isl_qpolynomial_free(qp);
2361 return NULL;
2362 }
2363
2364 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2365 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2366 {
2367 int i, j, k;
2368 isl_int denom;
2369 unsigned total;
2370 unsigned n_div;
2371 struct isl_upoly *up;
2372
2373 if (!eq)
2374 goto error;
2375 if (eq->n_eq == 0) {
2376 isl_basic_set_free(eq);
2377 return qp;
2378 }
2379
2380 qp = isl_qpolynomial_cow(qp);
2381 if (!qp)
2382 goto error;
2383 qp->div = isl_mat_cow(qp->div);
2384 if (!qp->div)
2385 goto error;
2386
2387 total = 1 + isl_dim_total(eq->dim);
2388 n_div = eq->n_div;
2389 isl_int_init(denom);
2390 for (i = 0; i < eq->n_eq; ++i) {
2391 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2392 if (j < 0 || j == 0 || j >= total)
2393 continue;
2394
2395 for (k = 0; k < qp->div->n_row; ++k) {
2396 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2397 continue;
2398 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2399 &qp->div->row[k][0]);
2400 normalize_div(qp, k);
2401 }
2402
2403 if (isl_int_is_pos(eq->eq[i][j]))
2404 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2405 isl_int_abs(denom, eq->eq[i][j]);
2406 isl_int_set_si(eq->eq[i][j], 0);
2407
2408 up = isl_upoly_from_affine(qp->dim->ctx,
2409 eq->eq[i], denom, total);
2410 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2411 isl_upoly_free(up);
2412 }
2413 isl_int_clear(denom);
2414
2415 if (!qp->upoly)
2416 goto error;
2417
2418 isl_basic_set_free(eq);
2419
2420 qp = substitute_non_divs(qp);
2421 qp = sort_divs(qp);
2422
2423 return qp;
2424 error:
2425 isl_basic_set_free(eq);
2426 isl_qpolynomial_free(qp);
2427 return NULL;
2428 }
2429
2430 static __isl_give isl_basic_set *add_div_constraints(
2431 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2432 {
2433 int i;
2434 unsigned total;
2435
2436 if (!bset || !div)
2437 goto error;
2438
2439 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2440 if (!bset)
2441 goto error;
2442 total = isl_basic_set_total_dim(bset);
2443 for (i = 0; i < div->n_row; ++i)
2444 if (isl_basic_set_add_div_constraints_var(bset,
2445 total - div->n_row + i, div->row[i]) < 0)
2446 goto error;
2447
2448 isl_mat_free(div);
2449 return bset;
2450 error:
2451 isl_mat_free(div);
2452 isl_basic_set_free(bset);
2453 return NULL;
2454 }
2455
2456 /* Look for equalities among the variables shared by context and qp
2457 * and the integer divisions of qp, if any.
2458 * The equalities are then used to eliminate variables and/or integer
2459 * divisions from qp.
2460 */
2461 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2462 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2463 {
2464 isl_basic_set *aff;
2465
2466 if (!qp)
2467 goto error;
2468 if (qp->div->n_row > 0) {
2469 isl_basic_set *bset;
2470 context = isl_set_add_dims(context, isl_dim_set,
2471 qp->div->n_row);
2472 bset = isl_basic_set_universe(isl_set_get_dim(context));
2473 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2474 context = isl_set_intersect(context,
2475 isl_set_from_basic_set(bset));
2476 }
2477
2478 aff = isl_set_affine_hull(context);
2479 return isl_qpolynomial_substitute_equalities(qp, aff);
2480 error:
2481 isl_qpolynomial_free(qp);
2482 isl_set_free(context);
2483 return NULL;
2484 }
2485
2486 #undef PW
2487 #define PW isl_pw_qpolynomial
2488 #undef EL
2489 #define EL isl_qpolynomial
2490 #undef IS_ZERO
2491 #define IS_ZERO is_zero
2492 #undef FIELD
2493 #define FIELD qp
2494
2495 #include <isl_pw_templ.c>
2496
2497 #undef UNION
2498 #define UNION isl_union_pw_qpolynomial
2499 #undef PART
2500 #define PART isl_pw_qpolynomial
2501 #undef PARTS
2502 #define PARTS pw_qpolynomial
2503
2504 #include <isl_union_templ.c>
2505
2506 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2507 {
2508 if (!pwqp)
2509 return -1;
2510
2511 if (pwqp->n != -1)
2512 return 0;
2513
2514 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2515 return 0;
2516
2517 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2518 }
2519
2520 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2521 __isl_take isl_pw_qpolynomial *pwqp1,
2522 __isl_take isl_pw_qpolynomial *pwqp2)
2523 {
2524 int i, j, n;
2525 struct isl_pw_qpolynomial *res;
2526
2527 if (!pwqp1 || !pwqp2)
2528 goto error;
2529
2530 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2531 goto error);
2532
2533 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2534 isl_pw_qpolynomial_free(pwqp2);
2535 return pwqp1;
2536 }
2537
2538 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2539 isl_pw_qpolynomial_free(pwqp1);
2540 return pwqp2;
2541 }
2542
2543 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2544 isl_pw_qpolynomial_free(pwqp1);
2545 return pwqp2;
2546 }
2547
2548 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2549 isl_pw_qpolynomial_free(pwqp2);
2550 return pwqp1;
2551 }
2552
2553 n = pwqp1->n * pwqp2->n;
2554 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2555
2556 for (i = 0; i < pwqp1->n; ++i) {
2557 for (j = 0; j < pwqp2->n; ++j) {
2558 struct isl_set *common;
2559 struct isl_qpolynomial *prod;
2560 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2561 isl_set_copy(pwqp2->p[j].set));
2562 if (isl_set_plain_is_empty(common)) {
2563 isl_set_free(common);
2564 continue;
2565 }
2566
2567 prod = isl_qpolynomial_mul(
2568 isl_qpolynomial_copy(pwqp1->p[i].qp),
2569 isl_qpolynomial_copy(pwqp2->p[j].qp));
2570
2571 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2572 }
2573 }
2574
2575 isl_pw_qpolynomial_free(pwqp1);
2576 isl_pw_qpolynomial_free(pwqp2);
2577
2578 return res;
2579 error:
2580 isl_pw_qpolynomial_free(pwqp1);
2581 isl_pw_qpolynomial_free(pwqp2);
2582 return NULL;
2583 }
2584
2585 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2586 __isl_take isl_pw_qpolynomial *pwqp)
2587 {
2588 int i;
2589
2590 if (!pwqp)
2591 return NULL;
2592
2593 if (isl_pw_qpolynomial_is_zero(pwqp))
2594 return pwqp;
2595
2596 pwqp = isl_pw_qpolynomial_cow(pwqp);
2597 if (!pwqp)
2598 return NULL;
2599
2600 for (i = 0; i < pwqp->n; ++i) {
2601 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2602 if (!pwqp->p[i].qp)
2603 goto error;
2604 }
2605
2606 return pwqp;
2607 error:
2608 isl_pw_qpolynomial_free(pwqp);
2609 return NULL;
2610 }
2611
2612 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2613 __isl_take isl_pw_qpolynomial *pwqp1,
2614 __isl_take isl_pw_qpolynomial *pwqp2)
2615 {
2616 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2617 }
2618
2619 __isl_give struct isl_upoly *isl_upoly_eval(
2620 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2621 {
2622 int i;
2623 struct isl_upoly_rec *rec;
2624 struct isl_upoly *res;
2625 struct isl_upoly *base;
2626
2627 if (isl_upoly_is_cst(up)) {
2628 isl_vec_free(vec);
2629 return up;
2630 }
2631
2632 rec = isl_upoly_as_rec(up);
2633 if (!rec)
2634 goto error;
2635
2636 isl_assert(up->ctx, rec->n >= 1, goto error);
2637
2638 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2639
2640 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2641 isl_vec_copy(vec));
2642
2643 for (i = rec->n - 2; i >= 0; --i) {
2644 res = isl_upoly_mul(res, isl_upoly_copy(base));
2645 res = isl_upoly_sum(res,
2646 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2647 isl_vec_copy(vec)));
2648 }
2649
2650 isl_upoly_free(base);
2651 isl_upoly_free(up);
2652 isl_vec_free(vec);
2653 return res;
2654 error:
2655 isl_upoly_free(up);
2656 isl_vec_free(vec);
2657 return NULL;
2658 }
2659
2660 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2661 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2662 {
2663 isl_vec *ext;
2664 struct isl_upoly *up;
2665 isl_dim *dim;
2666
2667 if (!qp || !pnt)
2668 goto error;
2669 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2670
2671 if (qp->div->n_row == 0)
2672 ext = isl_vec_copy(pnt->vec);
2673 else {
2674 int i;
2675 unsigned dim = isl_dim_total(qp->dim);
2676 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2677 if (!ext)
2678 goto error;
2679
2680 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2681 for (i = 0; i < qp->div->n_row; ++i) {
2682 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2683 1 + dim + i, &ext->el[1+dim+i]);
2684 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2685 qp->div->row[i][0]);
2686 }
2687 }
2688
2689 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2690 if (!up)
2691 goto error;
2692
2693 dim = isl_dim_copy(qp->dim);
2694 isl_qpolynomial_free(qp);
2695 isl_point_free(pnt);
2696
2697 return isl_qpolynomial_alloc(dim, 0, up);
2698 error:
2699 isl_qpolynomial_free(qp);
2700 isl_point_free(pnt);
2701 return NULL;
2702 }
2703
2704 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2705 __isl_keep struct isl_upoly_cst *cst2)
2706 {
2707 int cmp;
2708 isl_int t;
2709 isl_int_init(t);
2710 isl_int_mul(t, cst1->n, cst2->d);
2711 isl_int_submul(t, cst2->n, cst1->d);
2712 cmp = isl_int_sgn(t);
2713 isl_int_clear(t);
2714 return cmp;
2715 }
2716
2717 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2718 __isl_keep isl_qpolynomial *qp2)
2719 {
2720 struct isl_upoly_cst *cst1, *cst2;
2721
2722 if (!qp1 || !qp2)
2723 return -1;
2724 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2725 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2726 if (isl_qpolynomial_is_nan(qp1))
2727 return -1;
2728 if (isl_qpolynomial_is_nan(qp2))
2729 return -1;
2730 cst1 = isl_upoly_as_cst(qp1->upoly);
2731 cst2 = isl_upoly_as_cst(qp2->upoly);
2732
2733 return isl_upoly_cmp(cst1, cst2) <= 0;
2734 }
2735
2736 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2737 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2738 {
2739 struct isl_upoly_cst *cst1, *cst2;
2740 int cmp;
2741
2742 if (!qp1 || !qp2)
2743 goto error;
2744 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2745 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2746 cst1 = isl_upoly_as_cst(qp1->upoly);
2747 cst2 = isl_upoly_as_cst(qp2->upoly);
2748 cmp = isl_upoly_cmp(cst1, cst2);
2749
2750 if (cmp <= 0) {
2751 isl_qpolynomial_free(qp2);
2752 } else {
2753 isl_qpolynomial_free(qp1);
2754 qp1 = qp2;
2755 }
2756 return qp1;
2757 error:
2758 isl_qpolynomial_free(qp1);
2759 isl_qpolynomial_free(qp2);
2760 return NULL;
2761 }
2762
2763 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2764 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2765 {
2766 struct isl_upoly_cst *cst1, *cst2;
2767 int cmp;
2768
2769 if (!qp1 || !qp2)
2770 goto error;
2771 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2772 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2773 cst1 = isl_upoly_as_cst(qp1->upoly);
2774 cst2 = isl_upoly_as_cst(qp2->upoly);
2775 cmp = isl_upoly_cmp(cst1, cst2);
2776
2777 if (cmp >= 0) {
2778 isl_qpolynomial_free(qp2);
2779 } else {
2780 isl_qpolynomial_free(qp1);
2781 qp1 = qp2;
2782 }
2783 return qp1;
2784 error:
2785 isl_qpolynomial_free(qp1);
2786 isl_qpolynomial_free(qp2);
2787 return NULL;
2788 }
2789
2790 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2791 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2792 unsigned first, unsigned n)
2793 {
2794 unsigned total;
2795 unsigned g_pos;
2796 int *exp;
2797
2798 if (n == 0)
2799 return qp;
2800
2801 qp = isl_qpolynomial_cow(qp);
2802 if (!qp)
2803 return NULL;
2804
2805 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2806 goto error);
2807
2808 g_pos = pos(qp->dim, type) + first;
2809
2810 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2811 if (!qp->div)
2812 goto error;
2813
2814 total = qp->div->n_col - 2;
2815 if (total > g_pos) {
2816 int i;
2817 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2818 if (!exp)
2819 goto error;
2820 for (i = 0; i < total - g_pos; ++i)
2821 exp[i] = i + n;
2822 qp->upoly = expand(qp->upoly, exp, g_pos);
2823 free(exp);
2824 if (!qp->upoly)
2825 goto error;
2826 }
2827
2828 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2829 if (!qp->dim)
2830 goto error;
2831
2832 return qp;
2833 error:
2834 isl_qpolynomial_free(qp);
2835 return NULL;
2836 }
2837
2838 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2839 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2840 {
2841 unsigned pos;
2842
2843 pos = isl_qpolynomial_dim(qp, type);
2844
2845 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2846 }
2847
2848 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2849 __isl_take isl_pw_qpolynomial *pwqp,
2850 enum isl_dim_type type, unsigned n)
2851 {
2852 unsigned pos;
2853
2854 pos = isl_pw_qpolynomial_dim(pwqp, type);
2855
2856 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2857 }
2858
2859 static int *reordering_move(isl_ctx *ctx,
2860 unsigned len, unsigned dst, unsigned src, unsigned n)
2861 {
2862 int i;
2863 int *reordering;
2864
2865 reordering = isl_alloc_array(ctx, int, len);
2866 if (!reordering)
2867 return NULL;
2868
2869 if (dst <= src) {
2870 for (i = 0; i < dst; ++i)
2871 reordering[i] = i;
2872 for (i = 0; i < n; ++i)
2873 reordering[src + i] = dst + i;
2874 for (i = 0; i < src - dst; ++i)
2875 reordering[dst + i] = dst + n + i;
2876 for (i = 0; i < len - src - n; ++i)
2877 reordering[src + n + i] = src + n + i;
2878 } else {
2879 for (i = 0; i < src; ++i)
2880 reordering[i] = i;
2881 for (i = 0; i < n; ++i)
2882 reordering[src + i] = dst + i;
2883 for (i = 0; i < dst - src; ++i)
2884 reordering[src + n + i] = src + i;
2885 for (i = 0; i < len - dst - n; ++i)
2886 reordering[dst + n + i] = dst + n + i;
2887 }
2888
2889 return reordering;
2890 }
2891
2892 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2893 __isl_take isl_qpolynomial *qp,
2894 enum isl_dim_type dst_type, unsigned dst_pos,
2895 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2896 {
2897 unsigned g_dst_pos;
2898 unsigned g_src_pos;
2899 int *reordering;
2900
2901 qp = isl_qpolynomial_cow(qp);
2902 if (!qp)
2903 return NULL;
2904
2905 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2906 goto error);
2907
2908 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2909 g_src_pos = pos(qp->dim, src_type) + src_pos;
2910 if (dst_type > src_type)
2911 g_dst_pos -= n;
2912
2913 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2914 if (!qp->div)
2915 goto error;
2916 qp = sort_divs(qp);
2917 if (!qp)
2918 goto error;
2919
2920 reordering = reordering_move(qp->dim->ctx,
2921 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2922 if (!reordering)
2923 goto error;
2924
2925 qp->upoly = reorder(qp->upoly, reordering);
2926 free(reordering);
2927 if (!qp->upoly)
2928 goto error;
2929
2930 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2931 if (!qp->dim)
2932 goto error;
2933
2934 return qp;
2935 error:
2936 isl_qpolynomial_free(qp);
2937 return NULL;
2938 }
2939
2940 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2941 isl_int *f, isl_int denom)
2942 {
2943 struct isl_upoly *up;
2944
2945 if (!dim)
2946 return NULL;
2947
2948 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2949
2950 return isl_qpolynomial_alloc(dim, 0, up);
2951 }
2952
2953 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
2954 {
2955 isl_ctx *ctx;
2956 struct isl_upoly *up;
2957 isl_qpolynomial *qp;
2958
2959 if (!aff)
2960 return NULL;
2961
2962 ctx = isl_aff_get_ctx(aff);
2963 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
2964 aff->v->size - 1);
2965
2966 qp = isl_qpolynomial_alloc(isl_aff_get_dim(aff),
2967 aff->ls->div->n_row, up);
2968 if (!qp)
2969 goto error;
2970
2971 isl_mat_free(qp->div);
2972 qp->div = isl_mat_copy(aff->ls->div);
2973 qp->div = isl_mat_cow(qp->div);
2974 if (!qp->div)
2975 goto error;
2976
2977 isl_aff_free(aff);
2978 qp = reduce_divs(qp);
2979 qp = remove_redundant_divs(qp);
2980 return qp;
2981 error:
2982 isl_aff_free(aff);
2983 return NULL;
2984 }
2985
2986 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2987 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2988 {
2989 isl_int denom;
2990 isl_dim *dim;
2991 struct isl_upoly *up;
2992 isl_qpolynomial *qp;
2993 int sgn;
2994
2995 if (!c)
2996 return NULL;
2997
2998 isl_int_init(denom);
2999
3000 isl_constraint_get_coefficient(c, type, pos, &denom);
3001 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
3002 sgn = isl_int_sgn(denom);
3003 isl_int_abs(denom, denom);
3004 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
3005 1 + isl_constraint_dim(c, isl_dim_all));
3006 if (sgn < 0)
3007 isl_int_neg(denom, denom);
3008 isl_constraint_set_coefficient(c, type, pos, denom);
3009
3010 dim = isl_dim_copy(c->bmap->dim);
3011
3012 isl_int_clear(denom);
3013 isl_constraint_free(c);
3014
3015 qp = isl_qpolynomial_alloc(dim, 0, up);
3016 if (sgn > 0)
3017 qp = isl_qpolynomial_neg(qp);
3018 return qp;
3019 }
3020
3021 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3022 * in "qp" by subs[i].
3023 */
3024 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3025 __isl_take isl_qpolynomial *qp,
3026 enum isl_dim_type type, unsigned first, unsigned n,
3027 __isl_keep isl_qpolynomial **subs)
3028 {
3029 int i;
3030 struct isl_upoly **ups;
3031
3032 if (n == 0)
3033 return qp;
3034
3035 qp = isl_qpolynomial_cow(qp);
3036 if (!qp)
3037 return NULL;
3038 for (i = 0; i < n; ++i)
3039 if (!subs[i])
3040 goto error;
3041
3042 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
3043 goto error);
3044
3045 for (i = 0; i < n; ++i)
3046 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
3047 goto error);
3048
3049 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3050 for (i = 0; i < n; ++i)
3051 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3052
3053 first += pos(qp->dim, type);
3054
3055 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3056 if (!ups)
3057 goto error;
3058 for (i = 0; i < n; ++i)
3059 ups[i] = subs[i]->upoly;
3060
3061 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3062
3063 free(ups);
3064
3065 if (!qp->upoly)
3066 goto error;
3067
3068 return qp;
3069 error:
3070 isl_qpolynomial_free(qp);
3071 return NULL;
3072 }
3073
3074 /* Extend "bset" with extra set dimensions for each integer division
3075 * in "qp" and then call "fn" with the extended bset and the polynomial
3076 * that results from replacing each of the integer divisions by the
3077 * corresponding extra set dimension.
3078 */
3079 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3080 __isl_keep isl_basic_set *bset,
3081 int (*fn)(__isl_take isl_basic_set *bset,
3082 __isl_take isl_qpolynomial *poly, void *user), void *user)
3083 {
3084 isl_dim *dim;
3085 isl_mat *div;
3086 isl_qpolynomial *poly;
3087
3088 if (!qp || !bset)
3089 goto error;
3090 if (qp->div->n_row == 0)
3091 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3092 user);
3093
3094 div = isl_mat_copy(qp->div);
3095 dim = isl_dim_copy(qp->dim);
3096 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3097 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3098 bset = isl_basic_set_copy(bset);
3099 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3100 bset = add_div_constraints(bset, div);
3101
3102 return fn(bset, poly, user);
3103 error:
3104 return -1;
3105 }
3106
3107 /* Return total degree in variables first (inclusive) up to last (exclusive).
3108 */
3109 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3110 {
3111 int deg = -1;
3112 int i;
3113 struct isl_upoly_rec *rec;
3114
3115 if (!up)
3116 return -2;
3117 if (isl_upoly_is_zero(up))
3118 return -1;
3119 if (isl_upoly_is_cst(up) || up->var < first)
3120 return 0;
3121
3122 rec = isl_upoly_as_rec(up);
3123 if (!rec)
3124 return -2;
3125
3126 for (i = 0; i < rec->n; ++i) {
3127 int d;
3128
3129 if (isl_upoly_is_zero(rec->p[i]))
3130 continue;
3131 d = isl_upoly_degree(rec->p[i], first, last);
3132 if (up->var < last)
3133 d += i;
3134 if (d > deg)
3135 deg = d;
3136 }
3137
3138 return deg;
3139 }
3140
3141 /* Return total degree in set variables.
3142 */
3143 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3144 {
3145 unsigned ovar;
3146 unsigned nvar;
3147
3148 if (!poly)
3149 return -2;
3150
3151 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3152 nvar = isl_dim_size(poly->dim, isl_dim_set);
3153 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3154 }
3155
3156 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3157 unsigned pos, int deg)
3158 {
3159 int i;
3160 struct isl_upoly_rec *rec;
3161
3162 if (!up)
3163 return NULL;
3164
3165 if (isl_upoly_is_cst(up) || up->var < pos) {
3166 if (deg == 0)
3167 return isl_upoly_copy(up);
3168 else
3169 return isl_upoly_zero(up->ctx);
3170 }
3171
3172 rec = isl_upoly_as_rec(up);
3173 if (!rec)
3174 return NULL;
3175
3176 if (up->var == pos) {
3177 if (deg < rec->n)
3178 return isl_upoly_copy(rec->p[deg]);
3179 else
3180 return isl_upoly_zero(up->ctx);
3181 }
3182
3183 up = isl_upoly_copy(up);
3184 up = isl_upoly_cow(up);
3185 rec = isl_upoly_as_rec(up);
3186 if (!rec)
3187 goto error;
3188
3189 for (i = 0; i < rec->n; ++i) {
3190 struct isl_upoly *t;
3191 t = isl_upoly_coeff(rec->p[i], pos, deg);
3192 if (!t)
3193 goto error;
3194 isl_upoly_free(rec->p[i]);
3195 rec->p[i] = t;
3196 }
3197
3198 return up;
3199 error:
3200 isl_upoly_free(up);
3201 return NULL;
3202 }
3203
3204 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3205 */
3206 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3207 __isl_keep isl_qpolynomial *qp,
3208 enum isl_dim_type type, unsigned t_pos, int deg)
3209 {
3210 unsigned g_pos;
3211 struct isl_upoly *up;
3212 isl_qpolynomial *c;
3213
3214 if (!qp)
3215 return NULL;
3216
3217 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3218 return NULL);
3219
3220 g_pos = pos(qp->dim, type) + t_pos;
3221 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3222
3223 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3224 if (!c)
3225 return NULL;
3226 isl_mat_free(c->div);
3227 c->div = isl_mat_copy(qp->div);
3228 if (!c->div)
3229 goto error;
3230 return c;
3231 error:
3232 isl_qpolynomial_free(c);
3233 return NULL;
3234 }
3235
3236 /* Homogenize the polynomial in the variables first (inclusive) up to
3237 * last (exclusive) by inserting powers of variable first.
3238 * Variable first is assumed not to appear in the input.
3239 */
3240 __isl_give struct isl_upoly *isl_upoly_homogenize(
3241 __isl_take struct isl_upoly *up, int deg, int target,
3242 int first, int last)
3243 {
3244 int i;
3245 struct isl_upoly_rec *rec;
3246
3247 if (!up)
3248 return NULL;
3249 if (isl_upoly_is_zero(up))
3250 return up;
3251 if (deg == target)
3252 return up;
3253 if (isl_upoly_is_cst(up) || up->var < first) {
3254 struct isl_upoly *hom;
3255
3256 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3257 if (!hom)
3258 goto error;
3259 rec = isl_upoly_as_rec(hom);
3260 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3261
3262 return hom;
3263 }
3264
3265 up = isl_upoly_cow(up);
3266 rec = isl_upoly_as_rec(up);
3267 if (!rec)
3268 goto error;
3269
3270 for (i = 0; i < rec->n; ++i) {
3271 if (isl_upoly_is_zero(rec->p[i]))
3272 continue;
3273 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3274 up->var < last ? deg + i : i, target,
3275 first, last);
3276 if (!rec->p[i])
3277 goto error;
3278 }
3279
3280 return up;
3281 error:
3282 isl_upoly_free(up);
3283 return NULL;
3284 }
3285
3286 /* Homogenize the polynomial in the set variables by introducing
3287 * powers of an extra set variable at position 0.
3288 */
3289 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3290 __isl_take isl_qpolynomial *poly)
3291 {
3292 unsigned ovar;
3293 unsigned nvar;
3294 int deg = isl_qpolynomial_degree(poly);
3295
3296 if (deg < -1)
3297 goto error;
3298
3299 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3300 poly = isl_qpolynomial_cow(poly);
3301 if (!poly)
3302 goto error;
3303
3304 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3305 nvar = isl_dim_size(poly->dim, isl_dim_set);
3306 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3307 ovar, ovar + nvar);
3308 if (!poly->upoly)
3309 goto error;
3310
3311 return poly;
3312 error:
3313 isl_qpolynomial_free(poly);
3314 return NULL;
3315 }
3316
3317 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3318 __isl_take isl_mat *div)
3319 {
3320 isl_term *term;
3321 int n;
3322
3323 if (!dim || !div)
3324 goto error;
3325
3326 n = isl_dim_total(dim) + div->n_row;
3327
3328 term = isl_calloc(dim->ctx, struct isl_term,
3329 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3330 if (!term)
3331 goto error;
3332
3333 term->ref = 1;
3334 term->dim = dim;
3335 term->div = div;
3336 isl_int_init(term->n);
3337 isl_int_init(term->d);
3338
3339 return term;
3340 error:
3341 isl_dim_free(dim);
3342 isl_mat_free(div);
3343 return NULL;
3344 }
3345
3346 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3347 {
3348 if (!term)
3349 return NULL;
3350
3351 term->ref++;
3352 return term;
3353 }
3354
3355 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3356 {
3357 int i;
3358 isl_term *dup;
3359 unsigned total;
3360
3361 if (term)
3362 return NULL;
3363
3364 total = isl_dim_total(term->dim) + term->div->n_row;
3365
3366 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3367 if (!dup)
3368 return NULL;
3369
3370 isl_int_set(dup->n, term->n);
3371 isl_int_set(dup->d, term->d);
3372
3373 for (i = 0; i < total; ++i)
3374 dup->pow[i] = term->pow[i];
3375
3376 return dup;
3377 }
3378
3379 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3380 {
3381 if (!term)
3382 return NULL;
3383
3384 if (term->ref == 1)
3385 return term;
3386 term->ref--;
3387 return isl_term_dup(term);
3388 }
3389
3390 void isl_term_free(__isl_take isl_term *term)
3391 {
3392 if (!term)
3393 return;
3394
3395 if (--term->ref > 0)
3396 return;
3397
3398 isl_dim_free(term->dim);
3399 isl_mat_free(term->div);
3400 isl_int_clear(term->n);
3401 isl_int_clear(term->d);
3402 free(term);
3403 }
3404
3405 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3406 {
3407 if (!term)
3408 return 0;
3409
3410 switch (type) {
3411 case isl_dim_param:
3412 case isl_dim_in:
3413 case isl_dim_out: return isl_dim_size(term->dim, type);
3414 case isl_dim_div: return term->div->n_row;
3415 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3416 default: return 0;
3417 }
3418 }
3419
3420 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3421 {
3422 return term ? term->dim->ctx : NULL;
3423 }
3424
3425 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3426 {
3427 if (!term)
3428 return;
3429 isl_int_set(*n, term->n);
3430 }
3431
3432 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3433 {
3434 if (!term)
3435 return;
3436 isl_int_set(*d, term->d);
3437 }
3438
3439 int isl_term_get_exp(__isl_keep isl_term *term,
3440 enum isl_dim_type type, unsigned pos)
3441 {
3442 if (!term)
3443 return -1;
3444
3445 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3446
3447 if (type >= isl_dim_set)
3448 pos += isl_dim_size(term->dim, isl_dim_param);
3449 if (type >= isl_dim_div)
3450 pos += isl_dim_size(term->dim, isl_dim_set);
3451
3452 return term->pow[pos];
3453 }
3454
3455 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3456 {
3457 isl_basic_map *bmap;
3458 unsigned total;
3459 int k;
3460
3461 if (!term)
3462 return NULL;
3463
3464 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3465 return NULL);
3466
3467 total = term->div->n_col - term->div->n_row - 2;
3468 /* No nested divs for now */
3469 isl_assert(term->dim->ctx,
3470 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3471 term->div->n_row) == -1,
3472 return NULL);
3473
3474 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3475 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3476 goto error;
3477
3478 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3479
3480 return isl_basic_map_div(bmap, k);
3481 error:
3482 isl_basic_map_free(bmap);
3483 return NULL;
3484 }
3485
3486 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3487 int (*fn)(__isl_take isl_term *term, void *user),
3488 __isl_take isl_term *term, void *user)
3489 {
3490 int i;
3491 struct isl_upoly_rec *rec;
3492
3493 if (!up || !term)
3494 goto error;
3495
3496 if (isl_upoly_is_zero(up))
3497 return term;
3498
3499 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3500 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3501 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3502
3503 if (isl_upoly_is_cst(up)) {
3504 struct isl_upoly_cst *cst;
3505 cst = isl_upoly_as_cst(up);
3506 if (!cst)
3507 goto error;
3508 term = isl_term_cow(term);
3509 if (!term)
3510 goto error;
3511 isl_int_set(term->n, cst->n);
3512 isl_int_set(term->d, cst->d);
3513 if (fn(isl_term_copy(term), user) < 0)
3514 goto error;
3515 return term;
3516 }
3517
3518 rec = isl_upoly_as_rec(up);
3519 if (!rec)
3520 goto error;
3521
3522 for (i = 0; i < rec->n; ++i) {
3523 term = isl_term_cow(term);
3524 if (!term)
3525 goto error;
3526 term->pow[up->var] = i;
3527 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3528 if (!term)
3529 goto error;
3530 }
3531 term->pow[up->var] = 0;
3532
3533 return term;
3534 error:
3535 isl_term_free(term);
3536 return NULL;
3537 }
3538
3539 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3540 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3541 {
3542 isl_term *term;
3543
3544 if (!qp)
3545 return -1;
3546
3547 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3548 if (!term)
3549 return -1;
3550
3551 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3552
3553 isl_term_free(term);
3554
3555 return term ? 0 : -1;
3556 }
3557
3558 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3559 {
3560 struct isl_upoly *up;
3561 isl_qpolynomial *qp;
3562 int i, n;
3563
3564 if (!term)
3565 return NULL;
3566
3567 n = isl_dim_total(term->dim) + term->div->n_row;
3568
3569 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3570 for (i = 0; i < n; ++i) {
3571 if (!term->pow[i])
3572 continue;
3573 up = isl_upoly_mul(up,
3574 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3575 }
3576
3577 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3578 if (!qp)
3579 goto error;
3580 isl_mat_free(qp->div);
3581 qp->div = isl_mat_copy(term->div);
3582 if (!qp->div)
3583 goto error;
3584
3585 isl_term_free(term);
3586 return qp;
3587 error:
3588 isl_qpolynomial_free(qp);
3589 isl_term_free(term);
3590 return NULL;
3591 }
3592
3593 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3594 __isl_take isl_dim *dim)
3595 {
3596 int i;
3597 int extra;
3598 unsigned total;
3599
3600 if (!qp || !dim)
3601 goto error;
3602
3603 if (isl_dim_equal(qp->dim, dim)) {
3604 isl_dim_free(dim);
3605 return qp;
3606 }
3607
3608 qp = isl_qpolynomial_cow(qp);
3609 if (!qp)
3610 goto error;
3611
3612 extra = isl_dim_size(dim, isl_dim_set) -
3613 isl_dim_size(qp->dim, isl_dim_set);
3614 total = isl_dim_total(qp->dim);
3615 if (qp->div->n_row) {
3616 int *exp;
3617
3618 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3619 if (!exp)
3620 goto error;
3621 for (i = 0; i < qp->div->n_row; ++i)
3622 exp[i] = extra + i;
3623 qp->upoly = expand(qp->upoly, exp, total);
3624 free(exp);
3625 if (!qp->upoly)
3626 goto error;
3627 }
3628 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3629 if (!qp->div)
3630 goto error;
3631 for (i = 0; i < qp->div->n_row; ++i)
3632 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3633
3634 isl_dim_free(qp->dim);
3635 qp->dim = dim;
3636
3637 return qp;
3638 error:
3639 isl_dim_free(dim);
3640 isl_qpolynomial_free(qp);
3641 return NULL;
3642 }
3643
3644 /* For each parameter or variable that does not appear in qp,
3645 * first eliminate the variable from all constraints and then set it to zero.
3646 */
3647 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3648 __isl_keep isl_qpolynomial *qp)
3649 {
3650 int *active = NULL;
3651 int i;
3652 int d;
3653 unsigned nparam;
3654 unsigned nvar;
3655
3656 if (!set || !qp)
3657 goto error;
3658
3659 d = isl_dim_total(set->dim);
3660 active = isl_calloc_array(set->ctx, int, d);
3661 if (set_active(qp, active) < 0)
3662 goto error;
3663
3664 for (i = 0; i < d; ++i)
3665 if (!active[i])
3666 break;
3667
3668 if (i == d) {
3669 free(active);
3670 return set;
3671 }
3672
3673 nparam = isl_dim_size(set->dim, isl_dim_param);
3674 nvar = isl_dim_size(set->dim, isl_dim_set);
3675 for (i = 0; i < nparam; ++i) {
3676 if (active[i])
3677 continue;
3678 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3679 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3680 }
3681 for (i = 0; i < nvar; ++i) {
3682 if (active[nparam + i])
3683 continue;
3684 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3685 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3686 }
3687
3688 free(active);
3689
3690 return set;
3691 error:
3692 free(active);
3693 isl_set_free(set);
3694 return NULL;
3695 }
3696
3697 struct isl_opt_data {
3698 isl_qpolynomial *qp;
3699 int first;
3700 isl_qpolynomial *opt;
3701 int max;
3702 };
3703
3704 static int opt_fn(__isl_take isl_point *pnt, void *user)
3705 {
3706 struct isl_opt_data *data = (struct isl_opt_data *)user;
3707 isl_qpolynomial *val;
3708
3709 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3710 if (data->first) {
3711 data->first = 0;
3712 data->opt = val;
3713 } else if (data->max) {
3714 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3715 } else {
3716 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3717 }
3718
3719 return 0;
3720 }
3721
3722 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3723 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3724 {
3725 struct isl_opt_data data = { NULL, 1, NULL, max };
3726
3727 if (!set || !qp)
3728 goto error;
3729
3730 if (isl_upoly_is_cst(qp->upoly)) {
3731 isl_set_free(set);
3732 return qp;
3733 }
3734
3735 set = fix_inactive(set, qp);
3736
3737 data.qp = qp;
3738 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3739 goto error;
3740
3741 if (data.first)
3742 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3743
3744 isl_set_free(set);
3745 isl_qpolynomial_free(qp);
3746 return data.opt;
3747 error:
3748 isl_set_free(set);
3749 isl_qpolynomial_free(qp);
3750 isl_qpolynomial_free(data.opt);
3751 return NULL;
3752 }
3753
3754 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3755 __isl_take isl_morph *morph)
3756 {
3757 int i;
3758 int n_sub;
3759 isl_ctx *ctx;
3760 struct isl_upoly **subs;
3761 isl_mat *mat;
3762
3763 qp = isl_qpolynomial_cow(qp);
3764 if (!qp || !morph)
3765 goto error;
3766
3767 ctx = qp->dim->ctx;
3768 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3769
3770 n_sub = morph->inv->n_row - 1;
3771 if (morph->inv->n_row != morph->inv->n_col)
3772 n_sub += qp->div->n_row;
3773 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3774 if (!subs)
3775 goto error;
3776
3777 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3778 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3779 morph->inv->row[0][0], morph->inv->n_col);
3780 if (morph->inv->n_row != morph->inv->n_col)
3781 for (i = 0; i < qp->div->n_row; ++i)
3782 subs[morph->inv->n_row - 1 + i] =
3783 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3784
3785 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3786
3787 for (i = 0; i < n_sub; ++i)
3788 isl_upoly_free(subs[i]);
3789 free(subs);
3790
3791 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3792 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3793 qp->div = isl_mat_product(qp->div, mat);
3794 isl_dim_free(qp->dim);
3795 qp->dim = isl_dim_copy(morph->ran->dim);
3796
3797 if (!qp->upoly || !qp->div || !qp->dim)
3798 goto error;
3799
3800 isl_morph_free(morph);
3801
3802 return qp;
3803 error:
3804 isl_qpolynomial_free(qp);
3805 isl_morph_free(morph);
3806 return NULL;
3807 }
3808
3809 static int neg_entry(void **entry, void *user)
3810 {
3811 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3812
3813 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3814
3815 return *pwqp ? 0 : -1;
3816 }
3817
3818 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3819 __isl_take isl_union_pw_qpolynomial *upwqp)
3820 {
3821 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3822 if (!upwqp)
3823 return NULL;
3824
3825 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3826 &neg_entry, NULL) < 0)
3827 goto error;
3828
3829 return upwqp;
3830 error:
3831 isl_union_pw_qpolynomial_free(upwqp);
3832 return NULL;
3833 }
3834
3835 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3836 __isl_take isl_union_pw_qpolynomial *upwqp1,
3837 __isl_take isl_union_pw_qpolynomial *upwqp2)
3838 {
3839 return isl_union_pw_qpolynomial_add(upwqp1,
3840 isl_union_pw_qpolynomial_neg(upwqp2));
3841 }
3842
3843 static int mul_entry(void **entry, void *user)
3844 {
3845 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3846 uint32_t hash;
3847 struct isl_hash_table_entry *entry2;
3848 isl_pw_qpolynomial *pwpq = *entry;
3849 int empty;
3850
3851 hash = isl_dim_get_hash(pwpq->dim);
3852 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3853 hash, &has_dim, pwpq->dim, 0);
3854 if (!entry2)
3855 return 0;
3856
3857 pwpq = isl_pw_qpolynomial_copy(pwpq);
3858 pwpq = isl_pw_qpolynomial_mul(pwpq,
3859 isl_pw_qpolynomial_copy(entry2->data));
3860
3861 empty = isl_pw_qpolynomial_is_zero(pwpq);
3862 if (empty < 0) {
3863 isl_pw_qpolynomial_free(pwpq);
3864 return -1;
3865 }
3866 if (empty) {
3867 isl_pw_qpolynomial_free(pwpq);
3868 return 0;
3869 }
3870
3871 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3872
3873 return 0;
3874 }
3875
3876 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3877 __isl_take isl_union_pw_qpolynomial *upwqp1,
3878 __isl_take isl_union_pw_qpolynomial *upwqp2)
3879 {
3880 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3881 }
3882
3883 /* Reorder the columns of the given div definitions according to the
3884 * given reordering.
3885 */
3886 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3887 __isl_take isl_reordering *r)
3888 {
3889 int i, j;
3890 isl_mat *mat;
3891 int extra;
3892
3893 if (!div || !r)
3894 goto error;
3895
3896 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3897 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3898 if (!mat)
3899 goto error;
3900
3901 for (i = 0; i < div->n_row; ++i) {
3902 isl_seq_cpy(mat->row[i], div->row[i], 2);
3903 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3904 for (j = 0; j < r->len; ++j)
3905 isl_int_set(mat->row[i][2 + r->pos[j]],
3906 div->row[i][2 + j]);
3907 }
3908
3909 isl_reordering_free(r);
3910 isl_mat_free(div);
3911 return mat;
3912 error:
3913 isl_reordering_free(r);
3914 isl_mat_free(div);
3915 return NULL;
3916 }
3917
3918 /* Reorder the dimension of "qp" according to the given reordering.
3919 */
3920 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3921 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3922 {
3923 qp = isl_qpolynomial_cow(qp);
3924 if (!qp)
3925 goto error;
3926
3927 r = isl_reordering_extend(r, qp->div->n_row);
3928 if (!r)
3929 goto error;
3930
3931 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3932 if (!qp->div)
3933 goto error;
3934
3935 qp->upoly = reorder(qp->upoly, r->pos);
3936 if (!qp->upoly)
3937 goto error;
3938
3939 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3940
3941 isl_reordering_free(r);
3942 return qp;
3943 error:
3944 isl_qpolynomial_free(qp);
3945 isl_reordering_free(r);
3946 return NULL;
3947 }
3948
3949 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3950 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3951 {
3952 if (!qp || !model)
3953 goto error;
3954
3955 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
3956 isl_reordering *exp;
3957
3958 model = isl_dim_drop(model, isl_dim_in,
3959 0, isl_dim_size(model, isl_dim_in));
3960 model = isl_dim_drop(model, isl_dim_out,
3961 0, isl_dim_size(model, isl_dim_out));
3962 exp = isl_parameter_alignment_reordering(qp->dim, model);
3963 exp = isl_reordering_extend_dim(exp,
3964 isl_qpolynomial_get_dim(qp));
3965 qp = isl_qpolynomial_realign(qp, exp);
3966 }
3967
3968 isl_dim_free(model);
3969 return qp;
3970 error:
3971 isl_dim_free(model);
3972 isl_qpolynomial_free(qp);
3973 return NULL;
3974 }
3975
3976 struct isl_split_periods_data {
3977 int max_periods;
3978 isl_pw_qpolynomial *res;
3979 };
3980
3981 /* Create a slice where the integer division "div" has the fixed value "v".
3982 * In particular, if "div" refers to floor(f/m), then create a slice
3983 *
3984 * m v <= f <= m v + (m - 1)
3985 *
3986 * or
3987 *
3988 * f - m v >= 0
3989 * -f + m v + (m - 1) >= 0
3990 */
3991 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3992 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3993 {
3994 int total;
3995 isl_basic_set *bset = NULL;
3996 int k;
3997
3998 if (!dim || !qp)
3999 goto error;
4000
4001 total = isl_dim_total(dim);
4002 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
4003
4004 k = isl_basic_set_alloc_inequality(bset);
4005 if (k < 0)
4006 goto error;
4007 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4008 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4009
4010 k = isl_basic_set_alloc_inequality(bset);
4011 if (k < 0)
4012 goto error;
4013 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4014 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4015 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4016 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4017
4018 isl_dim_free(dim);
4019 return isl_set_from_basic_set(bset);
4020 error:
4021 isl_basic_set_free(bset);
4022 isl_dim_free(dim);
4023 return NULL;
4024 }
4025
4026 static int split_periods(__isl_take isl_set *set,
4027 __isl_take isl_qpolynomial *qp, void *user);
4028
4029 /* Create a slice of the domain "set" such that integer division "div"
4030 * has the fixed value "v" and add the results to data->res,
4031 * replacing the integer division by "v" in "qp".
4032 */
4033 static int set_div(__isl_take isl_set *set,
4034 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4035 struct isl_split_periods_data *data)
4036 {
4037 int i;
4038 int total;
4039 isl_set *slice;
4040 struct isl_upoly *cst;
4041
4042 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
4043 set = isl_set_intersect(set, slice);
4044
4045 if (!qp)
4046 goto error;
4047
4048 total = isl_dim_total(qp->dim);
4049
4050 for (i = div + 1; i < qp->div->n_row; ++i) {
4051 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4052 continue;
4053 isl_int_addmul(qp->div->row[i][1],
4054 qp->div->row[i][2 + total + div], v);
4055 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4056 }
4057
4058 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4059 qp = substitute_div(qp, div, cst);
4060
4061 return split_periods(set, qp, data);
4062 error:
4063 isl_set_free(set);
4064 isl_qpolynomial_free(qp);
4065 return -1;
4066 }
4067
4068 /* Split the domain "set" such that integer division "div"
4069 * has a fixed value (ranging from "min" to "max") on each slice
4070 * and add the results to data->res.
4071 */
4072 static int split_div(__isl_take isl_set *set,
4073 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4074 struct isl_split_periods_data *data)
4075 {
4076 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4077 isl_set *set_i = isl_set_copy(set);
4078 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4079
4080 if (set_div(set_i, qp_i, div, min, data) < 0)
4081 goto error;
4082 }
4083 isl_set_free(set);
4084 isl_qpolynomial_free(qp);
4085 return 0;
4086 error:
4087 isl_set_free(set);
4088 isl_qpolynomial_free(qp);
4089 return -1;
4090 }
4091
4092 /* If "qp" refers to any integer division
4093 * that can only attain "max_periods" distinct values on "set"
4094 * then split the domain along those distinct values.
4095 * Add the results (or the original if no splitting occurs)
4096 * to data->res.
4097 */
4098 static int split_periods(__isl_take isl_set *set,
4099 __isl_take isl_qpolynomial *qp, void *user)
4100 {
4101 int i;
4102 isl_pw_qpolynomial *pwqp;
4103 struct isl_split_periods_data *data;
4104 isl_int min, max;
4105 int total;
4106 int r = 0;
4107
4108 data = (struct isl_split_periods_data *)user;
4109
4110 if (!set || !qp)
4111 goto error;
4112
4113 if (qp->div->n_row == 0) {
4114 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4115 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4116 return 0;
4117 }
4118
4119 isl_int_init(min);
4120 isl_int_init(max);
4121 total = isl_dim_total(qp->dim);
4122 for (i = 0; i < qp->div->n_row; ++i) {
4123 enum isl_lp_result lp_res;
4124
4125 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4126 qp->div->n_row) != -1)
4127 continue;
4128
4129 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4130 set->ctx->one, &min, NULL, NULL);
4131 if (lp_res == isl_lp_error)
4132 goto error2;
4133 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4134 continue;
4135 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4136
4137 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4138 set->ctx->one, &max, NULL, NULL);
4139 if (lp_res == isl_lp_error)
4140 goto error2;
4141 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4142 continue;
4143 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4144
4145 isl_int_sub(max, max, min);
4146 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4147 isl_int_add(max, max, min);
4148 break;
4149 }
4150 }
4151
4152 if (i < qp->div->n_row) {
4153 r = split_div(set, qp, i, min, max, data);
4154 } else {
4155 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4156 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4157 }
4158
4159 isl_int_clear(max);
4160 isl_int_clear(min);
4161
4162 return r;
4163 error2:
4164 isl_int_clear(max);
4165 isl_int_clear(min);
4166 error:
4167 isl_set_free(set);
4168 isl_qpolynomial_free(qp);
4169 return -1;
4170 }
4171
4172 /* If any quasi-polynomial in pwqp refers to any integer division
4173 * that can only attain "max_periods" distinct values on its domain
4174 * then split the domain along those distinct values.
4175 */
4176 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4177 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4178 {
4179 struct isl_split_periods_data data;
4180
4181 data.max_periods = max_periods;
4182 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4183
4184 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4185 goto error;
4186
4187 isl_pw_qpolynomial_free(pwqp);
4188
4189 return data.res;
4190 error:
4191 isl_pw_qpolynomial_free(data.res);
4192 isl_pw_qpolynomial_free(pwqp);
4193 return NULL;
4194 }
4195
4196 /* Construct a piecewise quasipolynomial that is constant on the given
4197 * domain. In particular, it is
4198 * 0 if cst == 0
4199 * 1 if cst == 1
4200 * infinity if cst == -1
4201 */
4202 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4203 __isl_take isl_basic_set *bset, int cst)
4204 {
4205 isl_dim *dim;
4206 isl_qpolynomial *qp;
4207
4208 if (!bset)
4209 return NULL;
4210
4211 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4212 dim = isl_basic_set_get_dim(bset);
4213 if (cst < 0)
4214 qp = isl_qpolynomial_infty(dim);
4215 else if (cst == 0)
4216 qp = isl_qpolynomial_zero(dim);
4217 else
4218 qp = isl_qpolynomial_one(dim);
4219 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4220 }
4221
4222 /* Factor bset, call fn on each of the factors and return the product.
4223 *
4224 * If no factors can be found, simply call fn on the input.
4225 * Otherwise, construct the factors based on the factorizer,
4226 * call fn on each factor and compute the product.
4227 */
4228 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4229 __isl_take isl_basic_set *bset,
4230 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4231 {
4232 int i, n;
4233 isl_dim *dim;
4234 isl_set *set;
4235 isl_factorizer *f;
4236 isl_qpolynomial *qp;
4237 isl_pw_qpolynomial *pwqp;
4238 unsigned nparam;
4239 unsigned nvar;
4240
4241 f = isl_basic_set_factorizer(bset);
4242 if (!f)
4243 goto error;
4244 if (f->n_group == 0) {
4245 isl_factorizer_free(f);
4246 return fn(bset);
4247 }
4248
4249 nparam = isl_basic_set_dim(bset, isl_dim_param);
4250 nvar = isl_basic_set_dim(bset, isl_dim_set);
4251
4252 dim = isl_basic_set_get_dim(bset);
4253 dim = isl_dim_domain(dim);
4254 set = isl_set_universe(isl_dim_copy(dim));
4255 qp = isl_qpolynomial_one(dim);
4256 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4257
4258 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4259
4260 for (i = 0, n = 0; i < f->n_group; ++i) {
4261 isl_basic_set *bset_i;
4262 isl_pw_qpolynomial *pwqp_i;
4263
4264 bset_i = isl_basic_set_copy(bset);
4265 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4266 nparam + n + f->len[i], nvar - n - f->len[i]);
4267 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4268 nparam, n);
4269 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4270 n + f->len[i], nvar - n - f->len[i]);
4271 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4272
4273 pwqp_i = fn(bset_i);
4274 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4275
4276 n += f->len[i];
4277 }
4278
4279 isl_basic_set_free(bset);
4280 isl_factorizer_free(f);
4281
4282 return pwqp;
4283 error:
4284 isl_basic_set_free(bset);
4285 return NULL;
4286 }
4287
4288 /* Factor bset, call fn on each of the factors and return the product.
4289 * The function is assumed to evaluate to zero on empty domains,
4290 * to one on zero-dimensional domains and to infinity on unbounded domains
4291 * and will not be called explicitly on zero-dimensional or unbounded domains.
4292 *
4293 * We first check for some special cases and remove all equalities.
4294 * Then we hand over control to compressed_multiplicative_call.
4295 */
4296 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4297 __isl_take isl_basic_set *bset,
4298 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4299 {
4300 int bounded;
4301 isl_morph *morph;
4302 isl_pw_qpolynomial *pwqp;
4303 unsigned orig_nvar, final_nvar;
4304
4305 if (!bset)
4306 return NULL;
4307
4308 if (isl_basic_set_plain_is_empty(bset))
4309 return constant_on_domain(bset, 0);
4310
4311 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4312
4313 if (orig_nvar == 0)
4314 return constant_on_domain(bset, 1);
4315
4316 bounded = isl_basic_set_is_bounded(bset);
4317 if (bounded < 0)
4318 goto error;
4319 if (!bounded)
4320 return constant_on_domain(bset, -1);
4321
4322 if (bset->n_eq == 0)
4323 return compressed_multiplicative_call(bset, fn);
4324
4325 morph = isl_basic_set_full_compression(bset);
4326 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4327
4328 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4329
4330 pwqp = compressed_multiplicative_call(bset, fn);
4331
4332 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4333 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4334 morph = isl_morph_inverse(morph);
4335
4336 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4337
4338 return pwqp;
4339 error:
4340 isl_basic_set_free(bset);
4341 return NULL;
4342 }
4343
4344 /* Drop all floors in "qp", turning each integer division [a/m] into
4345 * a rational division a/m. If "down" is set, then the integer division
4346 * is replaces by (a-(m-1))/m instead.
4347 */
4348 static __isl_give isl_qpolynomial *qp_drop_floors(
4349 __isl_take isl_qpolynomial *qp, int down)
4350 {
4351 int i;
4352 struct isl_upoly *s;
4353
4354 if (!qp)
4355 return NULL;
4356 if (qp->div->n_row == 0)
4357 return qp;
4358
4359 qp = isl_qpolynomial_cow(qp);
4360 if (!qp)
4361 return NULL;
4362
4363 for (i = qp->div->n_row - 1; i >= 0; --i) {
4364 if (down) {
4365 isl_int_sub(qp->div->row[i][1],
4366 qp->div->row[i][1], qp->div->row[i][0]);
4367 isl_int_add_ui(qp->div->row[i][1],
4368 qp->div->row[i][1], 1);
4369 }
4370 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4371 qp->div->row[i][0], qp->div->n_col - 1);
4372 qp = substitute_div(qp, i, s);
4373 if (!qp)
4374 return NULL;
4375 }
4376
4377 return qp;
4378 }
4379
4380 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4381 * a rational division a/m.
4382 */
4383 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4384 __isl_take isl_pw_qpolynomial *pwqp)
4385 {
4386 int i;
4387
4388 if (!pwqp)
4389 return NULL;
4390
4391 if (isl_pw_qpolynomial_is_zero(pwqp))
4392 return pwqp;
4393
4394 pwqp = isl_pw_qpolynomial_cow(pwqp);
4395 if (!pwqp)
4396 return NULL;
4397
4398 for (i = 0; i < pwqp->n; ++i) {
4399 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4400 if (!pwqp->p[i].qp)
4401 goto error;
4402 }
4403
4404 return pwqp;
4405 error:
4406 isl_pw_qpolynomial_free(pwqp);
4407 return NULL;
4408 }
4409
4410 /* Adjust all the integer divisions in "qp" such that they are at least
4411 * one over the given orthant (identified by "signs"). This ensures
4412 * that they will still be non-negative even after subtracting (m-1)/m.
4413 *
4414 * In particular, f is replaced by f' + v, changing f = [a/m]
4415 * to f' = [(a - m v)/m].
4416 * If the constant term k in a is smaller than m,
4417 * the constant term of v is set to floor(k/m) - 1.
4418 * For any other term, if the coefficient c and the variable x have
4419 * the same sign, then no changes are needed.
4420 * Otherwise, if the variable is positive (and c is negative),
4421 * then the coefficient of x in v is set to floor(c/m).
4422 * If the variable is negative (and c is positive),
4423 * then the coefficient of x in v is set to ceil(c/m).
4424 */
4425 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4426 int *signs)
4427 {
4428 int i, j;
4429 int total;
4430 isl_vec *v = NULL;
4431 struct isl_upoly *s;
4432
4433 qp = isl_qpolynomial_cow(qp);
4434 if (!qp)
4435 return NULL;
4436 qp->div = isl_mat_cow(qp->div);
4437 if (!qp->div)
4438 goto error;
4439
4440 total = isl_dim_total(qp->dim);
4441 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4442
4443 for (i = 0; i < qp->div->n_row; ++i) {
4444 isl_int *row = qp->div->row[i];
4445 v = isl_vec_clr(v);
4446 if (!v)
4447 goto error;
4448 if (isl_int_lt(row[1], row[0])) {
4449 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4450 isl_int_sub_ui(v->el[0], v->el[0], 1);
4451 isl_int_submul(row[1], row[0], v->el[0]);
4452 }
4453 for (j = 0; j < total; ++j) {
4454 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4455 continue;
4456 if (signs[j] < 0)
4457 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4458 else
4459 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4460 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4461 }
4462 for (j = 0; j < i; ++j) {
4463 if (isl_int_sgn(row[2 + total + j]) >= 0)
4464 continue;
4465 isl_int_fdiv_q(v->el[1 + total + j],
4466 row[2 + total + j], row[0]);
4467 isl_int_submul(row[2 + total + j],
4468 row[0], v->el[1 + total + j]);
4469 }
4470 for (j = i + 1; j < qp->div->n_row; ++j) {
4471 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4472 continue;
4473 isl_seq_combine(qp->div->row[j] + 1,
4474 qp->div->ctx->one, qp->div->row[j] + 1,
4475 qp->div->row[j][2 + total + i], v->el, v->size);
4476 }
4477 isl_int_set_si(v->el[1 + total + i], 1);
4478 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4479 qp->div->ctx->one, v->size);
4480 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4481 isl_upoly_free(s);
4482 if (!qp->upoly)
4483 goto error;
4484 }
4485
4486 isl_vec_free(v);
4487 return qp;
4488 error:
4489 isl_vec_free(v);
4490 isl_qpolynomial_free(qp);
4491 return NULL;
4492 }
4493
4494 struct isl_to_poly_data {
4495 int sign;
4496 isl_pw_qpolynomial *res;
4497 isl_qpolynomial *qp;
4498 };
4499
4500 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4501 * We first make all integer divisions positive and then split the
4502 * quasipolynomials into terms with sign data->sign (the direction
4503 * of the requested approximation) and terms with the opposite sign.
4504 * In the first set of terms, each integer division [a/m] is
4505 * overapproximated by a/m, while in the second it is underapproximated
4506 * by (a-(m-1))/m.
4507 */
4508 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4509 void *user)
4510 {
4511 struct isl_to_poly_data *data = user;
4512 isl_pw_qpolynomial *t;
4513 isl_qpolynomial *qp, *up, *down;
4514
4515 qp = isl_qpolynomial_copy(data->qp);
4516 qp = make_divs_pos(qp, signs);
4517
4518 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4519 up = qp_drop_floors(up, 0);
4520 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4521 down = qp_drop_floors(down, 1);
4522
4523 isl_qpolynomial_free(qp);
4524 qp = isl_qpolynomial_add(up, down);
4525
4526 t = isl_pw_qpolynomial_alloc(orthant, qp);
4527 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4528
4529 return 0;
4530 }
4531
4532 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4533 * the polynomial will be an overapproximation. If "sign" is negative,
4534 * it will be an underapproximation. If "sign" is zero, the approximation
4535 * will lie somewhere in between.
4536 *
4537 * In particular, is sign == 0, we simply drop the floors, turning
4538 * the integer divisions into rational divisions.
4539 * Otherwise, we split the domains into orthants, make all integer divisions
4540 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4541 * depending on the requested sign and the sign of the term in which
4542 * the integer division appears.
4543 */
4544 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4545 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4546 {
4547 int i;
4548 struct isl_to_poly_data data;
4549
4550 if (sign == 0)
4551 return pwqp_drop_floors(pwqp);
4552
4553 if (!pwqp)
4554 return NULL;
4555
4556 data.sign = sign;
4557 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4558
4559 for (i = 0; i < pwqp->n; ++i) {
4560 if (pwqp->p[i].qp->div->n_row == 0) {
4561 isl_pw_qpolynomial *t;
4562 t = isl_pw_qpolynomial_alloc(
4563 isl_set_copy(pwqp->p[i].set),
4564 isl_qpolynomial_copy(pwqp->p[i].qp));
4565 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4566 continue;
4567 }
4568 data.qp = pwqp->p[i].qp;
4569 if (isl_set_foreach_orthant(pwqp->p[i].set,
4570 &to_polynomial_on_orthant, &data) < 0)
4571 goto error;
4572 }
4573
4574 isl_pw_qpolynomial_free(pwqp);
4575
4576 return data.res;
4577 error:
4578 isl_pw_qpolynomial_free(pwqp);
4579 isl_pw_qpolynomial_free(data.res);
4580 return NULL;
4581 }
4582
4583 static int poly_entry(void **entry, void *user)
4584 {
4585 int *sign = user;
4586 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4587
4588 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4589
4590 return *pwqp ? 0 : -1;
4591 }
4592
4593 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4594 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4595 {
4596 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4597 if (!upwqp)
4598 return NULL;
4599
4600 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4601 &poly_entry, &sign) < 0)
4602 goto error;
4603
4604 return upwqp;
4605 error:
4606 isl_union_pw_qpolynomial_free(upwqp);
4607 return NULL;
4608 }
4609
4610 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4611 __isl_take isl_qpolynomial *qp)
4612 {
4613 int i, k;
4614 isl_dim *dim;
4615 isl_vec *aff = NULL;
4616 isl_basic_map *bmap = NULL;
4617 unsigned pos;
4618 unsigned n_div;
4619
4620 if (!qp)
4621 return NULL;
4622 if (!isl_upoly_is_affine(qp->upoly))
4623 isl_die(qp->dim->ctx, isl_error_invalid,
4624 "input quasi-polynomial not affine", goto error);
4625 aff = isl_qpolynomial_extract_affine(qp);
4626 if (!aff)
4627 goto error;
4628 dim = isl_qpolynomial_get_dim(qp);
4629 dim = isl_dim_from_domain(dim);
4630 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4631 dim = isl_dim_add(dim, isl_dim_out, 1);
4632 n_div = qp->div->n_row;
4633 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4634
4635 for (i = 0; i < n_div; ++i) {
4636 k = isl_basic_map_alloc_div(bmap);
4637 if (k < 0)
4638 goto error;
4639 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4640 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4641 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4642 goto error;
4643 }
4644 k = isl_basic_map_alloc_equality(bmap);
4645 if (k < 0)
4646 goto error;
4647 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4648 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4649 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4650
4651 isl_vec_free(aff);
4652 isl_qpolynomial_free(qp);
4653 bmap = isl_basic_map_finalize(bmap);
4654 return bmap;
4655 error:
4656 isl_vec_free(aff);
4657 isl_qpolynomial_free(qp);
4658 isl_basic_map_free(bmap);
4659 return NULL;
4660 }
Integer set library