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add isl_aff_scale_down_ui
[isl.git] / isl_polynomial.c
blobee32b387b736e7e9d4c6c927c91d3a00e267198a
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_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1663 __isl_keep isl_qpolynomial *qp2)
1664 {
1665 int equal;
1666
1667 if (!qp1 || !qp2)
1668 return -1;
1669
1670 equal = isl_dim_equal(qp1->dim, qp2->dim);
1671 if (equal < 0 || !equal)
1672 return equal;
1673
1674 equal = isl_mat_is_equal(qp1->div, qp2->div);
1675 if (equal < 0 || !equal)
1676 return equal;
1677
1678 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1679 }
1680
1681 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1682 {
1683 int i;
1684 struct isl_upoly_rec *rec;
1685
1686 if (isl_upoly_is_cst(up)) {
1687 struct isl_upoly_cst *cst;
1688 cst = isl_upoly_as_cst(up);
1689 if (!cst)
1690 return;
1691 isl_int_lcm(*d, *d, cst->d);
1692 return;
1693 }
1694
1695 rec = isl_upoly_as_rec(up);
1696 if (!rec)
1697 return;
1698
1699 for (i = 0; i < rec->n; ++i)
1700 upoly_update_den(rec->p[i], d);
1701 }
1702
1703 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1704 {
1705 isl_int_set_si(*d, 1);
1706 if (!qp)
1707 return;
1708 upoly_update_den(qp->upoly, d);
1709 }
1710
1711 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1712 int pos, int power)
1713 {
1714 struct isl_ctx *ctx;
1715
1716 if (!dim)
1717 return NULL;
1718
1719 ctx = dim->ctx;
1720
1721 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1722 }
1723
1724 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1725 enum isl_dim_type type, unsigned pos)
1726 {
1727 if (!dim)
1728 return NULL;
1729
1730 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1731 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1732
1733 if (type == isl_dim_set)
1734 pos += isl_dim_size(dim, isl_dim_param);
1735
1736 return isl_qpolynomial_var_pow(dim, pos, 1);
1737 error:
1738 isl_dim_free(dim);
1739 return NULL;
1740 }
1741
1742 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1743 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1744 {
1745 int i;
1746 struct isl_upoly_rec *rec;
1747 struct isl_upoly *base, *res;
1748
1749 if (!up)
1750 return NULL;
1751
1752 if (isl_upoly_is_cst(up))
1753 return up;
1754
1755 if (up->var < first)
1756 return up;
1757
1758 rec = isl_upoly_as_rec(up);
1759 if (!rec)
1760 goto error;
1761
1762 isl_assert(up->ctx, rec->n >= 1, goto error);
1763
1764 if (up->var >= first + n)
1765 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1766 else
1767 base = isl_upoly_copy(subs[up->var - first]);
1768
1769 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1770 for (i = rec->n - 2; i >= 0; --i) {
1771 struct isl_upoly *t;
1772 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1773 res = isl_upoly_mul(res, isl_upoly_copy(base));
1774 res = isl_upoly_sum(res, t);
1775 }
1776
1777 isl_upoly_free(base);
1778 isl_upoly_free(up);
1779
1780 return res;
1781 error:
1782 isl_upoly_free(up);
1783 return NULL;
1784 }
1785
1786 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1787 isl_int denom, unsigned len)
1788 {
1789 int i;
1790 struct isl_upoly *up;
1791
1792 isl_assert(ctx, len >= 1, return NULL);
1793
1794 up = isl_upoly_rat_cst(ctx, f[0], denom);
1795 for (i = 0; i < len - 1; ++i) {
1796 struct isl_upoly *t;
1797 struct isl_upoly *c;
1798
1799 if (isl_int_is_zero(f[1 + i]))
1800 continue;
1801
1802 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1803 t = isl_upoly_var_pow(ctx, i, 1);
1804 t = isl_upoly_mul(c, t);
1805 up = isl_upoly_sum(up, t);
1806 }
1807
1808 return up;
1809 }
1810
1811 /* Remove common factor of non-constant terms and denominator.
1812 */
1813 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1814 {
1815 isl_ctx *ctx = qp->div->ctx;
1816 unsigned total = qp->div->n_col - 2;
1817
1818 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1819 isl_int_gcd(ctx->normalize_gcd,
1820 ctx->normalize_gcd, qp->div->row[div][0]);
1821 if (isl_int_is_one(ctx->normalize_gcd))
1822 return;
1823
1824 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1825 ctx->normalize_gcd, total);
1826 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1827 ctx->normalize_gcd);
1828 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1829 ctx->normalize_gcd);
1830 }
1831
1832 /* Replace the integer division identified by "div" by the polynomial "s".
1833 * The integer division is assumed not to appear in the definition
1834 * of any other integer divisions.
1835 */
1836 static __isl_give isl_qpolynomial *substitute_div(
1837 __isl_take isl_qpolynomial *qp,
1838 int div, __isl_take struct isl_upoly *s)
1839 {
1840 int i;
1841 int total;
1842 int *reordering;
1843
1844 if (!qp || !s)
1845 goto error;
1846
1847 qp = isl_qpolynomial_cow(qp);
1848 if (!qp)
1849 goto error;
1850
1851 total = isl_dim_total(qp->dim);
1852 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1853 if (!qp->upoly)
1854 goto error;
1855
1856 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1857 if (!reordering)
1858 goto error;
1859 for (i = 0; i < total + div; ++i)
1860 reordering[i] = i;
1861 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1862 reordering[i] = i - 1;
1863 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1864 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1865 qp->upoly = reorder(qp->upoly, reordering);
1866 free(reordering);
1867
1868 if (!qp->upoly || !qp->div)
1869 goto error;
1870
1871 isl_upoly_free(s);
1872 return qp;
1873 error:
1874 isl_qpolynomial_free(qp);
1875 isl_upoly_free(s);
1876 return NULL;
1877 }
1878
1879 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1880 * divisions because d is equal to 1 by their definition, i.e., e.
1881 */
1882 static __isl_give isl_qpolynomial *substitute_non_divs(
1883 __isl_take isl_qpolynomial *qp)
1884 {
1885 int i, j;
1886 int total;
1887 struct isl_upoly *s;
1888
1889 if (!qp)
1890 return NULL;
1891
1892 total = isl_dim_total(qp->dim);
1893 for (i = 0; qp && i < qp->div->n_row; ++i) {
1894 if (!isl_int_is_one(qp->div->row[i][0]))
1895 continue;
1896 for (j = i + 1; j < qp->div->n_row; ++j) {
1897 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1898 continue;
1899 isl_seq_combine(qp->div->row[j] + 1,
1900 qp->div->ctx->one, qp->div->row[j] + 1,
1901 qp->div->row[j][2 + total + i],
1902 qp->div->row[i] + 1, 1 + total + i);
1903 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1904 normalize_div(qp, j);
1905 }
1906 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1907 qp->div->row[i][0], qp->div->n_col - 1);
1908 qp = substitute_div(qp, i, s);
1909 --i;
1910 }
1911
1912 return qp;
1913 }
1914
1915 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1916 * with d the denominator. When replacing the coefficient e of x by
1917 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1918 * inside the division, so we need to add floor(e/d) * x outside.
1919 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1920 * to adjust the coefficient of x in each later div that depends on the
1921 * current div "div" and also in the affine expression "aff"
1922 * (if it too depends on "div").
1923 */
1924 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1925 __isl_keep isl_vec *aff)
1926 {
1927 int i, j;
1928 isl_int v;
1929 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1930
1931 isl_int_init(v);
1932 for (i = 0; i < 1 + total + div; ++i) {
1933 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1934 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1935 continue;
1936 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1937 isl_int_fdiv_r(qp->div->row[div][1 + i],
1938 qp->div->row[div][1 + i], qp->div->row[div][0]);
1939 if (!isl_int_is_zero(aff->el[1 + total + div]))
1940 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1941 for (j = div + 1; j < qp->div->n_row; ++j) {
1942 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1943 continue;
1944 isl_int_addmul(qp->div->row[j][1 + i],
1945 v, qp->div->row[j][2 + total + div]);
1946 }
1947 }
1948 isl_int_clear(v);
1949 }
1950
1951 /* Check if the last non-zero coefficient is bigger that half of the
1952 * denominator. If so, we will invert the div to further reduce the number
1953 * of distinct divs that may appear.
1954 * If the last non-zero coefficient is exactly half the denominator,
1955 * then we continue looking for earlier coefficients that are bigger
1956 * than half the denominator.
1957 */
1958 static int needs_invert(__isl_keep isl_mat *div, int row)
1959 {
1960 int i;
1961 int cmp;
1962
1963 for (i = div->n_col - 1; i >= 1; --i) {
1964 if (isl_int_is_zero(div->row[row][i]))
1965 continue;
1966 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1967 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1968 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1969 if (cmp)
1970 return cmp > 0;
1971 if (i == 1)
1972 return 1;
1973 }
1974
1975 return 0;
1976 }
1977
1978 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1979 * We only invert the coefficients of e (and the coefficient of q in
1980 * later divs and in "aff"). After calling this function, the
1981 * coefficients of e should be reduced again.
1982 */
1983 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1984 __isl_keep isl_vec *aff)
1985 {
1986 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1987
1988 isl_seq_neg(qp->div->row[div] + 1,
1989 qp->div->row[div] + 1, qp->div->n_col - 1);
1990 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
1991 isl_int_add(qp->div->row[div][1],
1992 qp->div->row[div][1], qp->div->row[div][0]);
1993 if (!isl_int_is_zero(aff->el[1 + total + div]))
1994 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
1995 isl_mat_col_mul(qp->div, 2 + total + div,
1996 qp->div->ctx->negone, 2 + total + div);
1997 }
1998
1999 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2000 * in the interval [0, d-1], with d the denominator and such that the
2001 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2002 *
2003 * After the reduction, some divs may have become redundant or identical,
2004 * so we call substitute_non_divs and sort_divs. If these functions
2005 * eliminate divs or merge two or more divs into one, the coefficients
2006 * of the enclosing divs may have to be reduced again, so we call
2007 * ourselves recursively if the number of divs decreases.
2008 */
2009 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2010 {
2011 int i;
2012 isl_vec *aff = NULL;
2013 struct isl_upoly *s;
2014 unsigned n_div;
2015
2016 if (!qp)
2017 return NULL;
2018
2019 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2020 aff = isl_vec_clr(aff);
2021 if (!aff)
2022 goto error;
2023
2024 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2025
2026 for (i = 0; i < qp->div->n_row; ++i) {
2027 normalize_div(qp, i);
2028 reduce_div(qp, i, aff);
2029 if (needs_invert(qp->div, i)) {
2030 invert_div(qp, i, aff);
2031 reduce_div(qp, i, aff);
2032 }
2033 }
2034
2035 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2036 qp->div->ctx->one, aff->size);
2037 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2038 isl_upoly_free(s);
2039 if (!qp->upoly)
2040 goto error;
2041
2042 isl_vec_free(aff);
2043
2044 n_div = qp->div->n_row;
2045 qp = substitute_non_divs(qp);
2046 qp = sort_divs(qp);
2047 if (qp && qp->div->n_row < n_div)
2048 return reduce_divs(qp);
2049
2050 return qp;
2051 error:
2052 isl_qpolynomial_free(qp);
2053 isl_vec_free(aff);
2054 return NULL;
2055 }
2056
2057 /* Assumes each div only depends on earlier divs.
2058 */
2059 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2060 int power)
2061 {
2062 struct isl_qpolynomial *qp = NULL;
2063 struct isl_upoly_rec *rec;
2064 struct isl_upoly_cst *cst;
2065 int i, d;
2066 int pos;
2067
2068 if (!div)
2069 return NULL;
2070
2071 d = div->line - div->bmap->div;
2072
2073 pos = isl_dim_total(div->bmap->dim) + d;
2074 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2075 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2076 div->bmap->n_div, &rec->up);
2077 if (!qp)
2078 goto error;
2079
2080 for (i = 0; i < div->bmap->n_div; ++i)
2081 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2082
2083 for (i = 0; i < 1 + power; ++i) {
2084 rec->p[i] = isl_upoly_zero(div->ctx);
2085 if (!rec->p[i])
2086 goto error;
2087 rec->n++;
2088 }
2089 cst = isl_upoly_as_cst(rec->p[power]);
2090 isl_int_set_si(cst->n, 1);
2091
2092 isl_div_free(div);
2093
2094 qp = reduce_divs(qp);
2095
2096 return qp;
2097 error:
2098 isl_qpolynomial_free(qp);
2099 isl_div_free(div);
2100 return NULL;
2101 }
2102
2103 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2104 {
2105 return isl_qpolynomial_div_pow(div, 1);
2106 }
2107
2108 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2109 const isl_int n, const isl_int d)
2110 {
2111 struct isl_qpolynomial *qp;
2112 struct isl_upoly_cst *cst;
2113
2114 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2115 if (!qp)
2116 return NULL;
2117
2118 cst = isl_upoly_as_cst(qp->upoly);
2119 isl_int_set(cst->n, n);
2120 isl_int_set(cst->d, d);
2121
2122 return qp;
2123 }
2124
2125 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2126 {
2127 struct isl_upoly_rec *rec;
2128 int i;
2129
2130 if (!up)
2131 return -1;
2132
2133 if (isl_upoly_is_cst(up))
2134 return 0;
2135
2136 if (up->var < d)
2137 active[up->var] = 1;
2138
2139 rec = isl_upoly_as_rec(up);
2140 for (i = 0; i < rec->n; ++i)
2141 if (up_set_active(rec->p[i], active, d) < 0)
2142 return -1;
2143
2144 return 0;
2145 }
2146
2147 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2148 {
2149 int i, j;
2150 int d = isl_dim_total(qp->dim);
2151
2152 if (!qp || !active)
2153 return -1;
2154
2155 for (i = 0; i < d; ++i)
2156 for (j = 0; j < qp->div->n_row; ++j) {
2157 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2158 continue;
2159 active[i] = 1;
2160 break;
2161 }
2162
2163 return up_set_active(qp->upoly, active, d);
2164 }
2165
2166 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2167 enum isl_dim_type type, unsigned first, unsigned n)
2168 {
2169 int i;
2170 int *active = NULL;
2171 int involves = 0;
2172
2173 if (!qp)
2174 return -1;
2175 if (n == 0)
2176 return 0;
2177
2178 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2179 return -1);
2180 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2181 type == isl_dim_set, return -1);
2182
2183 active = isl_calloc_array(qp->dim->ctx, int, isl_dim_total(qp->dim));
2184 if (set_active(qp, active) < 0)
2185 goto error;
2186
2187 if (type == isl_dim_set)
2188 first += isl_dim_size(qp->dim, isl_dim_param);
2189 for (i = 0; i < n; ++i)
2190 if (active[first + i]) {
2191 involves = 1;
2192 break;
2193 }
2194
2195 free(active);
2196
2197 return involves;
2198 error:
2199 free(active);
2200 return -1;
2201 }
2202
2203 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2204 * of the divs that do appear in the quasi-polynomial.
2205 */
2206 static __isl_give isl_qpolynomial *remove_redundant_divs(
2207 __isl_take isl_qpolynomial *qp)
2208 {
2209 int i, j;
2210 int d;
2211 int len;
2212 int skip;
2213 int *active = NULL;
2214 int *reordering = NULL;
2215 int redundant = 0;
2216 int n_div;
2217 isl_ctx *ctx;
2218
2219 if (!qp)
2220 return NULL;
2221 if (qp->div->n_row == 0)
2222 return qp;
2223
2224 d = isl_dim_total(qp->dim);
2225 len = qp->div->n_col - 2;
2226 ctx = isl_qpolynomial_get_ctx(qp);
2227 active = isl_calloc_array(ctx, int, len);
2228 if (!active)
2229 goto error;
2230
2231 if (up_set_active(qp->upoly, active, len) < 0)
2232 goto error;
2233
2234 for (i = qp->div->n_row - 1; i >= 0; --i) {
2235 if (!active[d + i]) {
2236 redundant = 1;
2237 continue;
2238 }
2239 for (j = 0; j < i; ++j) {
2240 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2241 continue;
2242 active[d + j] = 1;
2243 break;
2244 }
2245 }
2246
2247 if (!redundant) {
2248 free(active);
2249 return qp;
2250 }
2251
2252 reordering = isl_alloc_array(qp->div->ctx, int, len);
2253 if (!reordering)
2254 goto error;
2255
2256 for (i = 0; i < d; ++i)
2257 reordering[i] = i;
2258
2259 skip = 0;
2260 n_div = qp->div->n_row;
2261 for (i = 0; i < n_div; ++i) {
2262 if (!active[d + i]) {
2263 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2264 qp->div = isl_mat_drop_cols(qp->div,
2265 2 + d + i - skip, 1);
2266 skip++;
2267 }
2268 reordering[d + i] = d + i - skip;
2269 }
2270
2271 qp->upoly = reorder(qp->upoly, reordering);
2272
2273 if (!qp->upoly || !qp->div)
2274 goto error;
2275
2276 free(active);
2277 free(reordering);
2278
2279 return qp;
2280 error:
2281 free(active);
2282 free(reordering);
2283 isl_qpolynomial_free(qp);
2284 return NULL;
2285 }
2286
2287 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2288 unsigned first, unsigned n)
2289 {
2290 int i;
2291 struct isl_upoly_rec *rec;
2292
2293 if (!up)
2294 return NULL;
2295 if (n == 0 || up->var < 0 || up->var < first)
2296 return up;
2297 if (up->var < first + n) {
2298 up = replace_by_constant_term(up);
2299 return isl_upoly_drop(up, first, n);
2300 }
2301 up = isl_upoly_cow(up);
2302 if (!up)
2303 return NULL;
2304 up->var -= n;
2305 rec = isl_upoly_as_rec(up);
2306 if (!rec)
2307 goto error;
2308
2309 for (i = 0; i < rec->n; ++i) {
2310 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2311 if (!rec->p[i])
2312 goto error;
2313 }
2314
2315 return up;
2316 error:
2317 isl_upoly_free(up);
2318 return NULL;
2319 }
2320
2321 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2322 __isl_take isl_qpolynomial *qp,
2323 enum isl_dim_type type, unsigned pos, const char *s)
2324 {
2325 qp = isl_qpolynomial_cow(qp);
2326 if (!qp)
2327 return NULL;
2328 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2329 if (!qp->dim)
2330 goto error;
2331 return qp;
2332 error:
2333 isl_qpolynomial_free(qp);
2334 return NULL;
2335 }
2336
2337 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2338 __isl_take isl_qpolynomial *qp,
2339 enum isl_dim_type type, unsigned first, unsigned n)
2340 {
2341 if (!qp)
2342 return NULL;
2343 if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
2344 return qp;
2345
2346 qp = isl_qpolynomial_cow(qp);
2347 if (!qp)
2348 return NULL;
2349
2350 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2351 goto error);
2352 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2353 type == isl_dim_set, goto error);
2354
2355 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2356 if (!qp->dim)
2357 goto error;
2358
2359 if (type == isl_dim_set)
2360 first += isl_dim_size(qp->dim, isl_dim_param);
2361
2362 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2363 if (!qp->div)
2364 goto error;
2365
2366 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2367 if (!qp->upoly)
2368 goto error;
2369
2370 return qp;
2371 error:
2372 isl_qpolynomial_free(qp);
2373 return NULL;
2374 }
2375
2376 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2377 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2378 {
2379 int i, j, k;
2380 isl_int denom;
2381 unsigned total;
2382 unsigned n_div;
2383 struct isl_upoly *up;
2384
2385 if (!eq)
2386 goto error;
2387 if (eq->n_eq == 0) {
2388 isl_basic_set_free(eq);
2389 return qp;
2390 }
2391
2392 qp = isl_qpolynomial_cow(qp);
2393 if (!qp)
2394 goto error;
2395 qp->div = isl_mat_cow(qp->div);
2396 if (!qp->div)
2397 goto error;
2398
2399 total = 1 + isl_dim_total(eq->dim);
2400 n_div = eq->n_div;
2401 isl_int_init(denom);
2402 for (i = 0; i < eq->n_eq; ++i) {
2403 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2404 if (j < 0 || j == 0 || j >= total)
2405 continue;
2406
2407 for (k = 0; k < qp->div->n_row; ++k) {
2408 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2409 continue;
2410 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2411 &qp->div->row[k][0]);
2412 normalize_div(qp, k);
2413 }
2414
2415 if (isl_int_is_pos(eq->eq[i][j]))
2416 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2417 isl_int_abs(denom, eq->eq[i][j]);
2418 isl_int_set_si(eq->eq[i][j], 0);
2419
2420 up = isl_upoly_from_affine(qp->dim->ctx,
2421 eq->eq[i], denom, total);
2422 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2423 isl_upoly_free(up);
2424 }
2425 isl_int_clear(denom);
2426
2427 if (!qp->upoly)
2428 goto error;
2429
2430 isl_basic_set_free(eq);
2431
2432 qp = substitute_non_divs(qp);
2433 qp = sort_divs(qp);
2434
2435 return qp;
2436 error:
2437 isl_basic_set_free(eq);
2438 isl_qpolynomial_free(qp);
2439 return NULL;
2440 }
2441
2442 static __isl_give isl_basic_set *add_div_constraints(
2443 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2444 {
2445 int i;
2446 unsigned total;
2447
2448 if (!bset || !div)
2449 goto error;
2450
2451 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2452 if (!bset)
2453 goto error;
2454 total = isl_basic_set_total_dim(bset);
2455 for (i = 0; i < div->n_row; ++i)
2456 if (isl_basic_set_add_div_constraints_var(bset,
2457 total - div->n_row + i, div->row[i]) < 0)
2458 goto error;
2459
2460 isl_mat_free(div);
2461 return bset;
2462 error:
2463 isl_mat_free(div);
2464 isl_basic_set_free(bset);
2465 return NULL;
2466 }
2467
2468 /* Look for equalities among the variables shared by context and qp
2469 * and the integer divisions of qp, if any.
2470 * The equalities are then used to eliminate variables and/or integer
2471 * divisions from qp.
2472 */
2473 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2474 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2475 {
2476 isl_basic_set *aff;
2477
2478 if (!qp)
2479 goto error;
2480 if (qp->div->n_row > 0) {
2481 isl_basic_set *bset;
2482 context = isl_set_add_dims(context, isl_dim_set,
2483 qp->div->n_row);
2484 bset = isl_basic_set_universe(isl_set_get_dim(context));
2485 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2486 context = isl_set_intersect(context,
2487 isl_set_from_basic_set(bset));
2488 }
2489
2490 aff = isl_set_affine_hull(context);
2491 return isl_qpolynomial_substitute_equalities(qp, aff);
2492 error:
2493 isl_qpolynomial_free(qp);
2494 isl_set_free(context);
2495 return NULL;
2496 }
2497
2498 #undef PW
2499 #define PW isl_pw_qpolynomial
2500 #undef EL
2501 #define EL isl_qpolynomial
2502 #undef IS_ZERO
2503 #define IS_ZERO is_zero
2504 #undef FIELD
2505 #define FIELD qp
2506
2507 #include <isl_pw_templ.c>
2508
2509 #undef UNION
2510 #define UNION isl_union_pw_qpolynomial
2511 #undef PART
2512 #define PART isl_pw_qpolynomial
2513 #undef PARTS
2514 #define PARTS pw_qpolynomial
2515
2516 #include <isl_union_templ.c>
2517
2518 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2519 {
2520 if (!pwqp)
2521 return -1;
2522
2523 if (pwqp->n != -1)
2524 return 0;
2525
2526 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2527 return 0;
2528
2529 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2530 }
2531
2532 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2533 __isl_take isl_pw_qpolynomial *pwqp1,
2534 __isl_take isl_pw_qpolynomial *pwqp2)
2535 {
2536 int i, j, n;
2537 struct isl_pw_qpolynomial *res;
2538
2539 if (!pwqp1 || !pwqp2)
2540 goto error;
2541
2542 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2543 goto error);
2544
2545 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2546 isl_pw_qpolynomial_free(pwqp2);
2547 return pwqp1;
2548 }
2549
2550 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2551 isl_pw_qpolynomial_free(pwqp1);
2552 return pwqp2;
2553 }
2554
2555 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2556 isl_pw_qpolynomial_free(pwqp1);
2557 return pwqp2;
2558 }
2559
2560 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2561 isl_pw_qpolynomial_free(pwqp2);
2562 return pwqp1;
2563 }
2564
2565 n = pwqp1->n * pwqp2->n;
2566 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2567
2568 for (i = 0; i < pwqp1->n; ++i) {
2569 for (j = 0; j < pwqp2->n; ++j) {
2570 struct isl_set *common;
2571 struct isl_qpolynomial *prod;
2572 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2573 isl_set_copy(pwqp2->p[j].set));
2574 if (isl_set_plain_is_empty(common)) {
2575 isl_set_free(common);
2576 continue;
2577 }
2578
2579 prod = isl_qpolynomial_mul(
2580 isl_qpolynomial_copy(pwqp1->p[i].qp),
2581 isl_qpolynomial_copy(pwqp2->p[j].qp));
2582
2583 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2584 }
2585 }
2586
2587 isl_pw_qpolynomial_free(pwqp1);
2588 isl_pw_qpolynomial_free(pwqp2);
2589
2590 return res;
2591 error:
2592 isl_pw_qpolynomial_free(pwqp1);
2593 isl_pw_qpolynomial_free(pwqp2);
2594 return NULL;
2595 }
2596
2597 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2598 __isl_take isl_pw_qpolynomial *pwqp)
2599 {
2600 int i;
2601
2602 if (!pwqp)
2603 return NULL;
2604
2605 if (isl_pw_qpolynomial_is_zero(pwqp))
2606 return pwqp;
2607
2608 pwqp = isl_pw_qpolynomial_cow(pwqp);
2609 if (!pwqp)
2610 return NULL;
2611
2612 for (i = 0; i < pwqp->n; ++i) {
2613 pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
2614 if (!pwqp->p[i].qp)
2615 goto error;
2616 }
2617
2618 return pwqp;
2619 error:
2620 isl_pw_qpolynomial_free(pwqp);
2621 return NULL;
2622 }
2623
2624 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2625 __isl_take isl_pw_qpolynomial *pwqp1,
2626 __isl_take isl_pw_qpolynomial *pwqp2)
2627 {
2628 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2629 }
2630
2631 __isl_give struct isl_upoly *isl_upoly_eval(
2632 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2633 {
2634 int i;
2635 struct isl_upoly_rec *rec;
2636 struct isl_upoly *res;
2637 struct isl_upoly *base;
2638
2639 if (isl_upoly_is_cst(up)) {
2640 isl_vec_free(vec);
2641 return up;
2642 }
2643
2644 rec = isl_upoly_as_rec(up);
2645 if (!rec)
2646 goto error;
2647
2648 isl_assert(up->ctx, rec->n >= 1, goto error);
2649
2650 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2651
2652 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2653 isl_vec_copy(vec));
2654
2655 for (i = rec->n - 2; i >= 0; --i) {
2656 res = isl_upoly_mul(res, isl_upoly_copy(base));
2657 res = isl_upoly_sum(res,
2658 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2659 isl_vec_copy(vec)));
2660 }
2661
2662 isl_upoly_free(base);
2663 isl_upoly_free(up);
2664 isl_vec_free(vec);
2665 return res;
2666 error:
2667 isl_upoly_free(up);
2668 isl_vec_free(vec);
2669 return NULL;
2670 }
2671
2672 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2673 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2674 {
2675 isl_vec *ext;
2676 struct isl_upoly *up;
2677 isl_dim *dim;
2678
2679 if (!qp || !pnt)
2680 goto error;
2681 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2682
2683 if (qp->div->n_row == 0)
2684 ext = isl_vec_copy(pnt->vec);
2685 else {
2686 int i;
2687 unsigned dim = isl_dim_total(qp->dim);
2688 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2689 if (!ext)
2690 goto error;
2691
2692 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2693 for (i = 0; i < qp->div->n_row; ++i) {
2694 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2695 1 + dim + i, &ext->el[1+dim+i]);
2696 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2697 qp->div->row[i][0]);
2698 }
2699 }
2700
2701 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2702 if (!up)
2703 goto error;
2704
2705 dim = isl_dim_copy(qp->dim);
2706 isl_qpolynomial_free(qp);
2707 isl_point_free(pnt);
2708
2709 return isl_qpolynomial_alloc(dim, 0, up);
2710 error:
2711 isl_qpolynomial_free(qp);
2712 isl_point_free(pnt);
2713 return NULL;
2714 }
2715
2716 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2717 __isl_keep struct isl_upoly_cst *cst2)
2718 {
2719 int cmp;
2720 isl_int t;
2721 isl_int_init(t);
2722 isl_int_mul(t, cst1->n, cst2->d);
2723 isl_int_submul(t, cst2->n, cst1->d);
2724 cmp = isl_int_sgn(t);
2725 isl_int_clear(t);
2726 return cmp;
2727 }
2728
2729 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2730 __isl_keep isl_qpolynomial *qp2)
2731 {
2732 struct isl_upoly_cst *cst1, *cst2;
2733
2734 if (!qp1 || !qp2)
2735 return -1;
2736 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2737 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2738 if (isl_qpolynomial_is_nan(qp1))
2739 return -1;
2740 if (isl_qpolynomial_is_nan(qp2))
2741 return -1;
2742 cst1 = isl_upoly_as_cst(qp1->upoly);
2743 cst2 = isl_upoly_as_cst(qp2->upoly);
2744
2745 return isl_upoly_cmp(cst1, cst2) <= 0;
2746 }
2747
2748 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2749 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2750 {
2751 struct isl_upoly_cst *cst1, *cst2;
2752 int cmp;
2753
2754 if (!qp1 || !qp2)
2755 goto error;
2756 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2757 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2758 cst1 = isl_upoly_as_cst(qp1->upoly);
2759 cst2 = isl_upoly_as_cst(qp2->upoly);
2760 cmp = isl_upoly_cmp(cst1, cst2);
2761
2762 if (cmp <= 0) {
2763 isl_qpolynomial_free(qp2);
2764 } else {
2765 isl_qpolynomial_free(qp1);
2766 qp1 = qp2;
2767 }
2768 return qp1;
2769 error:
2770 isl_qpolynomial_free(qp1);
2771 isl_qpolynomial_free(qp2);
2772 return NULL;
2773 }
2774
2775 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2776 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2777 {
2778 struct isl_upoly_cst *cst1, *cst2;
2779 int cmp;
2780
2781 if (!qp1 || !qp2)
2782 goto error;
2783 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2784 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2785 cst1 = isl_upoly_as_cst(qp1->upoly);
2786 cst2 = isl_upoly_as_cst(qp2->upoly);
2787 cmp = isl_upoly_cmp(cst1, cst2);
2788
2789 if (cmp >= 0) {
2790 isl_qpolynomial_free(qp2);
2791 } else {
2792 isl_qpolynomial_free(qp1);
2793 qp1 = qp2;
2794 }
2795 return qp1;
2796 error:
2797 isl_qpolynomial_free(qp1);
2798 isl_qpolynomial_free(qp2);
2799 return NULL;
2800 }
2801
2802 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2803 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2804 unsigned first, unsigned n)
2805 {
2806 unsigned total;
2807 unsigned g_pos;
2808 int *exp;
2809
2810 if (n == 0)
2811 return qp;
2812
2813 qp = isl_qpolynomial_cow(qp);
2814 if (!qp)
2815 return NULL;
2816
2817 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2818 goto error);
2819
2820 g_pos = pos(qp->dim, type) + first;
2821
2822 qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
2823 if (!qp->div)
2824 goto error;
2825
2826 total = qp->div->n_col - 2;
2827 if (total > g_pos) {
2828 int i;
2829 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2830 if (!exp)
2831 goto error;
2832 for (i = 0; i < total - g_pos; ++i)
2833 exp[i] = i + n;
2834 qp->upoly = expand(qp->upoly, exp, g_pos);
2835 free(exp);
2836 if (!qp->upoly)
2837 goto error;
2838 }
2839
2840 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2841 if (!qp->dim)
2842 goto error;
2843
2844 return qp;
2845 error:
2846 isl_qpolynomial_free(qp);
2847 return NULL;
2848 }
2849
2850 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2851 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2852 {
2853 unsigned pos;
2854
2855 pos = isl_qpolynomial_dim(qp, type);
2856
2857 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2858 }
2859
2860 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2861 __isl_take isl_pw_qpolynomial *pwqp,
2862 enum isl_dim_type type, unsigned n)
2863 {
2864 unsigned pos;
2865
2866 pos = isl_pw_qpolynomial_dim(pwqp, type);
2867
2868 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2869 }
2870
2871 static int *reordering_move(isl_ctx *ctx,
2872 unsigned len, unsigned dst, unsigned src, unsigned n)
2873 {
2874 int i;
2875 int *reordering;
2876
2877 reordering = isl_alloc_array(ctx, int, len);
2878 if (!reordering)
2879 return NULL;
2880
2881 if (dst <= src) {
2882 for (i = 0; i < dst; ++i)
2883 reordering[i] = i;
2884 for (i = 0; i < n; ++i)
2885 reordering[src + i] = dst + i;
2886 for (i = 0; i < src - dst; ++i)
2887 reordering[dst + i] = dst + n + i;
2888 for (i = 0; i < len - src - n; ++i)
2889 reordering[src + n + i] = src + n + i;
2890 } else {
2891 for (i = 0; i < src; ++i)
2892 reordering[i] = i;
2893 for (i = 0; i < n; ++i)
2894 reordering[src + i] = dst + i;
2895 for (i = 0; i < dst - src; ++i)
2896 reordering[src + n + i] = src + i;
2897 for (i = 0; i < len - dst - n; ++i)
2898 reordering[dst + n + i] = dst + n + i;
2899 }
2900
2901 return reordering;
2902 }
2903
2904 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2905 __isl_take isl_qpolynomial *qp,
2906 enum isl_dim_type dst_type, unsigned dst_pos,
2907 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2908 {
2909 unsigned g_dst_pos;
2910 unsigned g_src_pos;
2911 int *reordering;
2912
2913 qp = isl_qpolynomial_cow(qp);
2914 if (!qp)
2915 return NULL;
2916
2917 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2918 goto error);
2919
2920 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2921 g_src_pos = pos(qp->dim, src_type) + src_pos;
2922 if (dst_type > src_type)
2923 g_dst_pos -= n;
2924
2925 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2926 if (!qp->div)
2927 goto error;
2928 qp = sort_divs(qp);
2929 if (!qp)
2930 goto error;
2931
2932 reordering = reordering_move(qp->dim->ctx,
2933 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2934 if (!reordering)
2935 goto error;
2936
2937 qp->upoly = reorder(qp->upoly, reordering);
2938 free(reordering);
2939 if (!qp->upoly)
2940 goto error;
2941
2942 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2943 if (!qp->dim)
2944 goto error;
2945
2946 return qp;
2947 error:
2948 isl_qpolynomial_free(qp);
2949 return NULL;
2950 }
2951
2952 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2953 isl_int *f, isl_int denom)
2954 {
2955 struct isl_upoly *up;
2956
2957 if (!dim)
2958 return NULL;
2959
2960 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2961
2962 return isl_qpolynomial_alloc(dim, 0, up);
2963 }
2964
2965 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
2966 {
2967 isl_ctx *ctx;
2968 struct isl_upoly *up;
2969 isl_qpolynomial *qp;
2970
2971 if (!aff)
2972 return NULL;
2973
2974 ctx = isl_aff_get_ctx(aff);
2975 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
2976 aff->v->size - 1);
2977
2978 qp = isl_qpolynomial_alloc(isl_aff_get_dim(aff),
2979 aff->ls->div->n_row, up);
2980 if (!qp)
2981 goto error;
2982
2983 isl_mat_free(qp->div);
2984 qp->div = isl_mat_copy(aff->ls->div);
2985 qp->div = isl_mat_cow(qp->div);
2986 if (!qp->div)
2987 goto error;
2988
2989 isl_aff_free(aff);
2990 qp = reduce_divs(qp);
2991 qp = remove_redundant_divs(qp);
2992 return qp;
2993 error:
2994 isl_aff_free(aff);
2995 return NULL;
2996 }
2997
2998 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2999 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3000 {
3001 isl_int denom;
3002 isl_dim *dim;
3003 struct isl_upoly *up;
3004 isl_qpolynomial *qp;
3005 int sgn;
3006
3007 if (!c)
3008 return NULL;
3009
3010 isl_int_init(denom);
3011
3012 isl_constraint_get_coefficient(c, type, pos, &denom);
3013 isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
3014 sgn = isl_int_sgn(denom);
3015 isl_int_abs(denom, denom);
3016 up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
3017 1 + isl_constraint_dim(c, isl_dim_all));
3018 if (sgn < 0)
3019 isl_int_neg(denom, denom);
3020 isl_constraint_set_coefficient(c, type, pos, denom);
3021
3022 dim = isl_dim_copy(c->bmap->dim);
3023
3024 isl_int_clear(denom);
3025 isl_constraint_free(c);
3026
3027 qp = isl_qpolynomial_alloc(dim, 0, up);
3028 if (sgn > 0)
3029 qp = isl_qpolynomial_neg(qp);
3030 return qp;
3031 }
3032
3033 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3034 * in "qp" by subs[i].
3035 */
3036 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3037 __isl_take isl_qpolynomial *qp,
3038 enum isl_dim_type type, unsigned first, unsigned n,
3039 __isl_keep isl_qpolynomial **subs)
3040 {
3041 int i;
3042 struct isl_upoly **ups;
3043
3044 if (n == 0)
3045 return qp;
3046
3047 qp = isl_qpolynomial_cow(qp);
3048 if (!qp)
3049 return NULL;
3050 for (i = 0; i < n; ++i)
3051 if (!subs[i])
3052 goto error;
3053
3054 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
3055 goto error);
3056
3057 for (i = 0; i < n; ++i)
3058 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
3059 goto error);
3060
3061 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3062 for (i = 0; i < n; ++i)
3063 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3064
3065 first += pos(qp->dim, type);
3066
3067 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3068 if (!ups)
3069 goto error;
3070 for (i = 0; i < n; ++i)
3071 ups[i] = subs[i]->upoly;
3072
3073 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3074
3075 free(ups);
3076
3077 if (!qp->upoly)
3078 goto error;
3079
3080 return qp;
3081 error:
3082 isl_qpolynomial_free(qp);
3083 return NULL;
3084 }
3085
3086 /* Extend "bset" with extra set dimensions for each integer division
3087 * in "qp" and then call "fn" with the extended bset and the polynomial
3088 * that results from replacing each of the integer divisions by the
3089 * corresponding extra set dimension.
3090 */
3091 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3092 __isl_keep isl_basic_set *bset,
3093 int (*fn)(__isl_take isl_basic_set *bset,
3094 __isl_take isl_qpolynomial *poly, void *user), void *user)
3095 {
3096 isl_dim *dim;
3097 isl_mat *div;
3098 isl_qpolynomial *poly;
3099
3100 if (!qp || !bset)
3101 goto error;
3102 if (qp->div->n_row == 0)
3103 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3104 user);
3105
3106 div = isl_mat_copy(qp->div);
3107 dim = isl_dim_copy(qp->dim);
3108 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3109 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3110 bset = isl_basic_set_copy(bset);
3111 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3112 bset = add_div_constraints(bset, div);
3113
3114 return fn(bset, poly, user);
3115 error:
3116 return -1;
3117 }
3118
3119 /* Return total degree in variables first (inclusive) up to last (exclusive).
3120 */
3121 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3122 {
3123 int deg = -1;
3124 int i;
3125 struct isl_upoly_rec *rec;
3126
3127 if (!up)
3128 return -2;
3129 if (isl_upoly_is_zero(up))
3130 return -1;
3131 if (isl_upoly_is_cst(up) || up->var < first)
3132 return 0;
3133
3134 rec = isl_upoly_as_rec(up);
3135 if (!rec)
3136 return -2;
3137
3138 for (i = 0; i < rec->n; ++i) {
3139 int d;
3140
3141 if (isl_upoly_is_zero(rec->p[i]))
3142 continue;
3143 d = isl_upoly_degree(rec->p[i], first, last);
3144 if (up->var < last)
3145 d += i;
3146 if (d > deg)
3147 deg = d;
3148 }
3149
3150 return deg;
3151 }
3152
3153 /* Return total degree in set variables.
3154 */
3155 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3156 {
3157 unsigned ovar;
3158 unsigned nvar;
3159
3160 if (!poly)
3161 return -2;
3162
3163 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3164 nvar = isl_dim_size(poly->dim, isl_dim_set);
3165 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3166 }
3167
3168 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3169 unsigned pos, int deg)
3170 {
3171 int i;
3172 struct isl_upoly_rec *rec;
3173
3174 if (!up)
3175 return NULL;
3176
3177 if (isl_upoly_is_cst(up) || up->var < pos) {
3178 if (deg == 0)
3179 return isl_upoly_copy(up);
3180 else
3181 return isl_upoly_zero(up->ctx);
3182 }
3183
3184 rec = isl_upoly_as_rec(up);
3185 if (!rec)
3186 return NULL;
3187
3188 if (up->var == pos) {
3189 if (deg < rec->n)
3190 return isl_upoly_copy(rec->p[deg]);
3191 else
3192 return isl_upoly_zero(up->ctx);
3193 }
3194
3195 up = isl_upoly_copy(up);
3196 up = isl_upoly_cow(up);
3197 rec = isl_upoly_as_rec(up);
3198 if (!rec)
3199 goto error;
3200
3201 for (i = 0; i < rec->n; ++i) {
3202 struct isl_upoly *t;
3203 t = isl_upoly_coeff(rec->p[i], pos, deg);
3204 if (!t)
3205 goto error;
3206 isl_upoly_free(rec->p[i]);
3207 rec->p[i] = t;
3208 }
3209
3210 return up;
3211 error:
3212 isl_upoly_free(up);
3213 return NULL;
3214 }
3215
3216 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3217 */
3218 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3219 __isl_keep isl_qpolynomial *qp,
3220 enum isl_dim_type type, unsigned t_pos, int deg)
3221 {
3222 unsigned g_pos;
3223 struct isl_upoly *up;
3224 isl_qpolynomial *c;
3225
3226 if (!qp)
3227 return NULL;
3228
3229 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3230 return NULL);
3231
3232 g_pos = pos(qp->dim, type) + t_pos;
3233 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3234
3235 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3236 if (!c)
3237 return NULL;
3238 isl_mat_free(c->div);
3239 c->div = isl_mat_copy(qp->div);
3240 if (!c->div)
3241 goto error;
3242 return c;
3243 error:
3244 isl_qpolynomial_free(c);
3245 return NULL;
3246 }
3247
3248 /* Homogenize the polynomial in the variables first (inclusive) up to
3249 * last (exclusive) by inserting powers of variable first.
3250 * Variable first is assumed not to appear in the input.
3251 */
3252 __isl_give struct isl_upoly *isl_upoly_homogenize(
3253 __isl_take struct isl_upoly *up, int deg, int target,
3254 int first, int last)
3255 {
3256 int i;
3257 struct isl_upoly_rec *rec;
3258
3259 if (!up)
3260 return NULL;
3261 if (isl_upoly_is_zero(up))
3262 return up;
3263 if (deg == target)
3264 return up;
3265 if (isl_upoly_is_cst(up) || up->var < first) {
3266 struct isl_upoly *hom;
3267
3268 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3269 if (!hom)
3270 goto error;
3271 rec = isl_upoly_as_rec(hom);
3272 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3273
3274 return hom;
3275 }
3276
3277 up = isl_upoly_cow(up);
3278 rec = isl_upoly_as_rec(up);
3279 if (!rec)
3280 goto error;
3281
3282 for (i = 0; i < rec->n; ++i) {
3283 if (isl_upoly_is_zero(rec->p[i]))
3284 continue;
3285 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3286 up->var < last ? deg + i : i, target,
3287 first, last);
3288 if (!rec->p[i])
3289 goto error;
3290 }
3291
3292 return up;
3293 error:
3294 isl_upoly_free(up);
3295 return NULL;
3296 }
3297
3298 /* Homogenize the polynomial in the set variables by introducing
3299 * powers of an extra set variable at position 0.
3300 */
3301 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3302 __isl_take isl_qpolynomial *poly)
3303 {
3304 unsigned ovar;
3305 unsigned nvar;
3306 int deg = isl_qpolynomial_degree(poly);
3307
3308 if (deg < -1)
3309 goto error;
3310
3311 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3312 poly = isl_qpolynomial_cow(poly);
3313 if (!poly)
3314 goto error;
3315
3316 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3317 nvar = isl_dim_size(poly->dim, isl_dim_set);
3318 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3319 ovar, ovar + nvar);
3320 if (!poly->upoly)
3321 goto error;
3322
3323 return poly;
3324 error:
3325 isl_qpolynomial_free(poly);
3326 return NULL;
3327 }
3328
3329 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3330 __isl_take isl_mat *div)
3331 {
3332 isl_term *term;
3333 int n;
3334
3335 if (!dim || !div)
3336 goto error;
3337
3338 n = isl_dim_total(dim) + div->n_row;
3339
3340 term = isl_calloc(dim->ctx, struct isl_term,
3341 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3342 if (!term)
3343 goto error;
3344
3345 term->ref = 1;
3346 term->dim = dim;
3347 term->div = div;
3348 isl_int_init(term->n);
3349 isl_int_init(term->d);
3350
3351 return term;
3352 error:
3353 isl_dim_free(dim);
3354 isl_mat_free(div);
3355 return NULL;
3356 }
3357
3358 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3359 {
3360 if (!term)
3361 return NULL;
3362
3363 term->ref++;
3364 return term;
3365 }
3366
3367 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3368 {
3369 int i;
3370 isl_term *dup;
3371 unsigned total;
3372
3373 if (term)
3374 return NULL;
3375
3376 total = isl_dim_total(term->dim) + term->div->n_row;
3377
3378 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3379 if (!dup)
3380 return NULL;
3381
3382 isl_int_set(dup->n, term->n);
3383 isl_int_set(dup->d, term->d);
3384
3385 for (i = 0; i < total; ++i)
3386 dup->pow[i] = term->pow[i];
3387
3388 return dup;
3389 }
3390
3391 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3392 {
3393 if (!term)
3394 return NULL;
3395
3396 if (term->ref == 1)
3397 return term;
3398 term->ref--;
3399 return isl_term_dup(term);
3400 }
3401
3402 void isl_term_free(__isl_take isl_term *term)
3403 {
3404 if (!term)
3405 return;
3406
3407 if (--term->ref > 0)
3408 return;
3409
3410 isl_dim_free(term->dim);
3411 isl_mat_free(term->div);
3412 isl_int_clear(term->n);
3413 isl_int_clear(term->d);
3414 free(term);
3415 }
3416
3417 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3418 {
3419 if (!term)
3420 return 0;
3421
3422 switch (type) {
3423 case isl_dim_param:
3424 case isl_dim_in:
3425 case isl_dim_out: return isl_dim_size(term->dim, type);
3426 case isl_dim_div: return term->div->n_row;
3427 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3428 default: return 0;
3429 }
3430 }
3431
3432 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3433 {
3434 return term ? term->dim->ctx : NULL;
3435 }
3436
3437 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3438 {
3439 if (!term)
3440 return;
3441 isl_int_set(*n, term->n);
3442 }
3443
3444 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3445 {
3446 if (!term)
3447 return;
3448 isl_int_set(*d, term->d);
3449 }
3450
3451 int isl_term_get_exp(__isl_keep isl_term *term,
3452 enum isl_dim_type type, unsigned pos)
3453 {
3454 if (!term)
3455 return -1;
3456
3457 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3458
3459 if (type >= isl_dim_set)
3460 pos += isl_dim_size(term->dim, isl_dim_param);
3461 if (type >= isl_dim_div)
3462 pos += isl_dim_size(term->dim, isl_dim_set);
3463
3464 return term->pow[pos];
3465 }
3466
3467 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3468 {
3469 isl_basic_map *bmap;
3470 unsigned total;
3471 int k;
3472
3473 if (!term)
3474 return NULL;
3475
3476 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3477 return NULL);
3478
3479 total = term->div->n_col - term->div->n_row - 2;
3480 /* No nested divs for now */
3481 isl_assert(term->dim->ctx,
3482 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3483 term->div->n_row) == -1,
3484 return NULL);
3485
3486 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3487 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3488 goto error;
3489
3490 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3491
3492 return isl_basic_map_div(bmap, k);
3493 error:
3494 isl_basic_map_free(bmap);
3495 return NULL;
3496 }
3497
3498 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3499 int (*fn)(__isl_take isl_term *term, void *user),
3500 __isl_take isl_term *term, void *user)
3501 {
3502 int i;
3503 struct isl_upoly_rec *rec;
3504
3505 if (!up || !term)
3506 goto error;
3507
3508 if (isl_upoly_is_zero(up))
3509 return term;
3510
3511 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3512 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3513 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3514
3515 if (isl_upoly_is_cst(up)) {
3516 struct isl_upoly_cst *cst;
3517 cst = isl_upoly_as_cst(up);
3518 if (!cst)
3519 goto error;
3520 term = isl_term_cow(term);
3521 if (!term)
3522 goto error;
3523 isl_int_set(term->n, cst->n);
3524 isl_int_set(term->d, cst->d);
3525 if (fn(isl_term_copy(term), user) < 0)
3526 goto error;
3527 return term;
3528 }
3529
3530 rec = isl_upoly_as_rec(up);
3531 if (!rec)
3532 goto error;
3533
3534 for (i = 0; i < rec->n; ++i) {
3535 term = isl_term_cow(term);
3536 if (!term)
3537 goto error;
3538 term->pow[up->var] = i;
3539 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3540 if (!term)
3541 goto error;
3542 }
3543 term->pow[up->var] = 0;
3544
3545 return term;
3546 error:
3547 isl_term_free(term);
3548 return NULL;
3549 }
3550
3551 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3552 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3553 {
3554 isl_term *term;
3555
3556 if (!qp)
3557 return -1;
3558
3559 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3560 if (!term)
3561 return -1;
3562
3563 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3564
3565 isl_term_free(term);
3566
3567 return term ? 0 : -1;
3568 }
3569
3570 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3571 {
3572 struct isl_upoly *up;
3573 isl_qpolynomial *qp;
3574 int i, n;
3575
3576 if (!term)
3577 return NULL;
3578
3579 n = isl_dim_total(term->dim) + term->div->n_row;
3580
3581 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3582 for (i = 0; i < n; ++i) {
3583 if (!term->pow[i])
3584 continue;
3585 up = isl_upoly_mul(up,
3586 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3587 }
3588
3589 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3590 if (!qp)
3591 goto error;
3592 isl_mat_free(qp->div);
3593 qp->div = isl_mat_copy(term->div);
3594 if (!qp->div)
3595 goto error;
3596
3597 isl_term_free(term);
3598 return qp;
3599 error:
3600 isl_qpolynomial_free(qp);
3601 isl_term_free(term);
3602 return NULL;
3603 }
3604
3605 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3606 __isl_take isl_dim *dim)
3607 {
3608 int i;
3609 int extra;
3610 unsigned total;
3611
3612 if (!qp || !dim)
3613 goto error;
3614
3615 if (isl_dim_equal(qp->dim, dim)) {
3616 isl_dim_free(dim);
3617 return qp;
3618 }
3619
3620 qp = isl_qpolynomial_cow(qp);
3621 if (!qp)
3622 goto error;
3623
3624 extra = isl_dim_size(dim, isl_dim_set) -
3625 isl_dim_size(qp->dim, isl_dim_set);
3626 total = isl_dim_total(qp->dim);
3627 if (qp->div->n_row) {
3628 int *exp;
3629
3630 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3631 if (!exp)
3632 goto error;
3633 for (i = 0; i < qp->div->n_row; ++i)
3634 exp[i] = extra + i;
3635 qp->upoly = expand(qp->upoly, exp, total);
3636 free(exp);
3637 if (!qp->upoly)
3638 goto error;
3639 }
3640 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3641 if (!qp->div)
3642 goto error;
3643 for (i = 0; i < qp->div->n_row; ++i)
3644 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3645
3646 isl_dim_free(qp->dim);
3647 qp->dim = dim;
3648
3649 return qp;
3650 error:
3651 isl_dim_free(dim);
3652 isl_qpolynomial_free(qp);
3653 return NULL;
3654 }
3655
3656 /* For each parameter or variable that does not appear in qp,
3657 * first eliminate the variable from all constraints and then set it to zero.
3658 */
3659 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3660 __isl_keep isl_qpolynomial *qp)
3661 {
3662 int *active = NULL;
3663 int i;
3664 int d;
3665 unsigned nparam;
3666 unsigned nvar;
3667
3668 if (!set || !qp)
3669 goto error;
3670
3671 d = isl_dim_total(set->dim);
3672 active = isl_calloc_array(set->ctx, int, d);
3673 if (set_active(qp, active) < 0)
3674 goto error;
3675
3676 for (i = 0; i < d; ++i)
3677 if (!active[i])
3678 break;
3679
3680 if (i == d) {
3681 free(active);
3682 return set;
3683 }
3684
3685 nparam = isl_dim_size(set->dim, isl_dim_param);
3686 nvar = isl_dim_size(set->dim, isl_dim_set);
3687 for (i = 0; i < nparam; ++i) {
3688 if (active[i])
3689 continue;
3690 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3691 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3692 }
3693 for (i = 0; i < nvar; ++i) {
3694 if (active[nparam + i])
3695 continue;
3696 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3697 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3698 }
3699
3700 free(active);
3701
3702 return set;
3703 error:
3704 free(active);
3705 isl_set_free(set);
3706 return NULL;
3707 }
3708
3709 struct isl_opt_data {
3710 isl_qpolynomial *qp;
3711 int first;
3712 isl_qpolynomial *opt;
3713 int max;
3714 };
3715
3716 static int opt_fn(__isl_take isl_point *pnt, void *user)
3717 {
3718 struct isl_opt_data *data = (struct isl_opt_data *)user;
3719 isl_qpolynomial *val;
3720
3721 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3722 if (data->first) {
3723 data->first = 0;
3724 data->opt = val;
3725 } else if (data->max) {
3726 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3727 } else {
3728 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3729 }
3730
3731 return 0;
3732 }
3733
3734 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3735 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3736 {
3737 struct isl_opt_data data = { NULL, 1, NULL, max };
3738
3739 if (!set || !qp)
3740 goto error;
3741
3742 if (isl_upoly_is_cst(qp->upoly)) {
3743 isl_set_free(set);
3744 return qp;
3745 }
3746
3747 set = fix_inactive(set, qp);
3748
3749 data.qp = qp;
3750 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3751 goto error;
3752
3753 if (data.first)
3754 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3755
3756 isl_set_free(set);
3757 isl_qpolynomial_free(qp);
3758 return data.opt;
3759 error:
3760 isl_set_free(set);
3761 isl_qpolynomial_free(qp);
3762 isl_qpolynomial_free(data.opt);
3763 return NULL;
3764 }
3765
3766 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3767 __isl_take isl_morph *morph)
3768 {
3769 int i;
3770 int n_sub;
3771 isl_ctx *ctx;
3772 struct isl_upoly **subs;
3773 isl_mat *mat;
3774
3775 qp = isl_qpolynomial_cow(qp);
3776 if (!qp || !morph)
3777 goto error;
3778
3779 ctx = qp->dim->ctx;
3780 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3781
3782 n_sub = morph->inv->n_row - 1;
3783 if (morph->inv->n_row != morph->inv->n_col)
3784 n_sub += qp->div->n_row;
3785 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3786 if (!subs)
3787 goto error;
3788
3789 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3790 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3791 morph->inv->row[0][0], morph->inv->n_col);
3792 if (morph->inv->n_row != morph->inv->n_col)
3793 for (i = 0; i < qp->div->n_row; ++i)
3794 subs[morph->inv->n_row - 1 + i] =
3795 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3796
3797 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3798
3799 for (i = 0; i < n_sub; ++i)
3800 isl_upoly_free(subs[i]);
3801 free(subs);
3802
3803 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3804 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3805 qp->div = isl_mat_product(qp->div, mat);
3806 isl_dim_free(qp->dim);
3807 qp->dim = isl_dim_copy(morph->ran->dim);
3808
3809 if (!qp->upoly || !qp->div || !qp->dim)
3810 goto error;
3811
3812 isl_morph_free(morph);
3813
3814 return qp;
3815 error:
3816 isl_qpolynomial_free(qp);
3817 isl_morph_free(morph);
3818 return NULL;
3819 }
3820
3821 static int neg_entry(void **entry, void *user)
3822 {
3823 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3824
3825 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3826
3827 return *pwqp ? 0 : -1;
3828 }
3829
3830 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3831 __isl_take isl_union_pw_qpolynomial *upwqp)
3832 {
3833 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3834 if (!upwqp)
3835 return NULL;
3836
3837 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3838 &neg_entry, NULL) < 0)
3839 goto error;
3840
3841 return upwqp;
3842 error:
3843 isl_union_pw_qpolynomial_free(upwqp);
3844 return NULL;
3845 }
3846
3847 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3848 __isl_take isl_union_pw_qpolynomial *upwqp1,
3849 __isl_take isl_union_pw_qpolynomial *upwqp2)
3850 {
3851 return isl_union_pw_qpolynomial_add(upwqp1,
3852 isl_union_pw_qpolynomial_neg(upwqp2));
3853 }
3854
3855 static int mul_entry(void **entry, void *user)
3856 {
3857 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3858 uint32_t hash;
3859 struct isl_hash_table_entry *entry2;
3860 isl_pw_qpolynomial *pwpq = *entry;
3861 int empty;
3862
3863 hash = isl_dim_get_hash(pwpq->dim);
3864 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3865 hash, &has_dim, pwpq->dim, 0);
3866 if (!entry2)
3867 return 0;
3868
3869 pwpq = isl_pw_qpolynomial_copy(pwpq);
3870 pwpq = isl_pw_qpolynomial_mul(pwpq,
3871 isl_pw_qpolynomial_copy(entry2->data));
3872
3873 empty = isl_pw_qpolynomial_is_zero(pwpq);
3874 if (empty < 0) {
3875 isl_pw_qpolynomial_free(pwpq);
3876 return -1;
3877 }
3878 if (empty) {
3879 isl_pw_qpolynomial_free(pwpq);
3880 return 0;
3881 }
3882
3883 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3884
3885 return 0;
3886 }
3887
3888 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3889 __isl_take isl_union_pw_qpolynomial *upwqp1,
3890 __isl_take isl_union_pw_qpolynomial *upwqp2)
3891 {
3892 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3893 }
3894
3895 /* Reorder the columns of the given div definitions according to the
3896 * given reordering.
3897 */
3898 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3899 __isl_take isl_reordering *r)
3900 {
3901 int i, j;
3902 isl_mat *mat;
3903 int extra;
3904
3905 if (!div || !r)
3906 goto error;
3907
3908 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3909 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3910 if (!mat)
3911 goto error;
3912
3913 for (i = 0; i < div->n_row; ++i) {
3914 isl_seq_cpy(mat->row[i], div->row[i], 2);
3915 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3916 for (j = 0; j < r->len; ++j)
3917 isl_int_set(mat->row[i][2 + r->pos[j]],
3918 div->row[i][2 + j]);
3919 }
3920
3921 isl_reordering_free(r);
3922 isl_mat_free(div);
3923 return mat;
3924 error:
3925 isl_reordering_free(r);
3926 isl_mat_free(div);
3927 return NULL;
3928 }
3929
3930 /* Reorder the dimension of "qp" according to the given reordering.
3931 */
3932 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3933 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3934 {
3935 qp = isl_qpolynomial_cow(qp);
3936 if (!qp)
3937 goto error;
3938
3939 r = isl_reordering_extend(r, qp->div->n_row);
3940 if (!r)
3941 goto error;
3942
3943 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3944 if (!qp->div)
3945 goto error;
3946
3947 qp->upoly = reorder(qp->upoly, r->pos);
3948 if (!qp->upoly)
3949 goto error;
3950
3951 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3952
3953 isl_reordering_free(r);
3954 return qp;
3955 error:
3956 isl_qpolynomial_free(qp);
3957 isl_reordering_free(r);
3958 return NULL;
3959 }
3960
3961 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3962 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3963 {
3964 if (!qp || !model)
3965 goto error;
3966
3967 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
3968 isl_reordering *exp;
3969
3970 model = isl_dim_drop(model, isl_dim_in,
3971 0, isl_dim_size(model, isl_dim_in));
3972 model = isl_dim_drop(model, isl_dim_out,
3973 0, isl_dim_size(model, isl_dim_out));
3974 exp = isl_parameter_alignment_reordering(qp->dim, model);
3975 exp = isl_reordering_extend_dim(exp,
3976 isl_qpolynomial_get_dim(qp));
3977 qp = isl_qpolynomial_realign(qp, exp);
3978 }
3979
3980 isl_dim_free(model);
3981 return qp;
3982 error:
3983 isl_dim_free(model);
3984 isl_qpolynomial_free(qp);
3985 return NULL;
3986 }
3987
3988 struct isl_split_periods_data {
3989 int max_periods;
3990 isl_pw_qpolynomial *res;
3991 };
3992
3993 /* Create a slice where the integer division "div" has the fixed value "v".
3994 * In particular, if "div" refers to floor(f/m), then create a slice
3995 *
3996 * m v <= f <= m v + (m - 1)
3997 *
3998 * or
3999 *
4000 * f - m v >= 0
4001 * -f + m v + (m - 1) >= 0
4002 */
4003 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
4004 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4005 {
4006 int total;
4007 isl_basic_set *bset = NULL;
4008 int k;
4009
4010 if (!dim || !qp)
4011 goto error;
4012
4013 total = isl_dim_total(dim);
4014 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
4015
4016 k = isl_basic_set_alloc_inequality(bset);
4017 if (k < 0)
4018 goto error;
4019 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4020 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4021
4022 k = isl_basic_set_alloc_inequality(bset);
4023 if (k < 0)
4024 goto error;
4025 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4026 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4027 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4028 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4029
4030 isl_dim_free(dim);
4031 return isl_set_from_basic_set(bset);
4032 error:
4033 isl_basic_set_free(bset);
4034 isl_dim_free(dim);
4035 return NULL;
4036 }
4037
4038 static int split_periods(__isl_take isl_set *set,
4039 __isl_take isl_qpolynomial *qp, void *user);
4040
4041 /* Create a slice of the domain "set" such that integer division "div"
4042 * has the fixed value "v" and add the results to data->res,
4043 * replacing the integer division by "v" in "qp".
4044 */
4045 static int set_div(__isl_take isl_set *set,
4046 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4047 struct isl_split_periods_data *data)
4048 {
4049 int i;
4050 int total;
4051 isl_set *slice;
4052 struct isl_upoly *cst;
4053
4054 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
4055 set = isl_set_intersect(set, slice);
4056
4057 if (!qp)
4058 goto error;
4059
4060 total = isl_dim_total(qp->dim);
4061
4062 for (i = div + 1; i < qp->div->n_row; ++i) {
4063 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4064 continue;
4065 isl_int_addmul(qp->div->row[i][1],
4066 qp->div->row[i][2 + total + div], v);
4067 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4068 }
4069
4070 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4071 qp = substitute_div(qp, div, cst);
4072
4073 return split_periods(set, qp, data);
4074 error:
4075 isl_set_free(set);
4076 isl_qpolynomial_free(qp);
4077 return -1;
4078 }
4079
4080 /* Split the domain "set" such that integer division "div"
4081 * has a fixed value (ranging from "min" to "max") on each slice
4082 * and add the results to data->res.
4083 */
4084 static int split_div(__isl_take isl_set *set,
4085 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4086 struct isl_split_periods_data *data)
4087 {
4088 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4089 isl_set *set_i = isl_set_copy(set);
4090 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4091
4092 if (set_div(set_i, qp_i, div, min, data) < 0)
4093 goto error;
4094 }
4095 isl_set_free(set);
4096 isl_qpolynomial_free(qp);
4097 return 0;
4098 error:
4099 isl_set_free(set);
4100 isl_qpolynomial_free(qp);
4101 return -1;
4102 }
4103
4104 /* If "qp" refers to any integer division
4105 * that can only attain "max_periods" distinct values on "set"
4106 * then split the domain along those distinct values.
4107 * Add the results (or the original if no splitting occurs)
4108 * to data->res.
4109 */
4110 static int split_periods(__isl_take isl_set *set,
4111 __isl_take isl_qpolynomial *qp, void *user)
4112 {
4113 int i;
4114 isl_pw_qpolynomial *pwqp;
4115 struct isl_split_periods_data *data;
4116 isl_int min, max;
4117 int total;
4118 int r = 0;
4119
4120 data = (struct isl_split_periods_data *)user;
4121
4122 if (!set || !qp)
4123 goto error;
4124
4125 if (qp->div->n_row == 0) {
4126 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4127 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4128 return 0;
4129 }
4130
4131 isl_int_init(min);
4132 isl_int_init(max);
4133 total = isl_dim_total(qp->dim);
4134 for (i = 0; i < qp->div->n_row; ++i) {
4135 enum isl_lp_result lp_res;
4136
4137 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4138 qp->div->n_row) != -1)
4139 continue;
4140
4141 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4142 set->ctx->one, &min, NULL, NULL);
4143 if (lp_res == isl_lp_error)
4144 goto error2;
4145 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4146 continue;
4147 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4148
4149 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4150 set->ctx->one, &max, NULL, NULL);
4151 if (lp_res == isl_lp_error)
4152 goto error2;
4153 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4154 continue;
4155 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4156
4157 isl_int_sub(max, max, min);
4158 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4159 isl_int_add(max, max, min);
4160 break;
4161 }
4162 }
4163
4164 if (i < qp->div->n_row) {
4165 r = split_div(set, qp, i, min, max, data);
4166 } else {
4167 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4168 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4169 }
4170
4171 isl_int_clear(max);
4172 isl_int_clear(min);
4173
4174 return r;
4175 error2:
4176 isl_int_clear(max);
4177 isl_int_clear(min);
4178 error:
4179 isl_set_free(set);
4180 isl_qpolynomial_free(qp);
4181 return -1;
4182 }
4183
4184 /* If any quasi-polynomial in pwqp refers to any integer division
4185 * that can only attain "max_periods" distinct values on its domain
4186 * then split the domain along those distinct values.
4187 */
4188 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4189 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4190 {
4191 struct isl_split_periods_data data;
4192
4193 data.max_periods = max_periods;
4194 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4195
4196 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4197 goto error;
4198
4199 isl_pw_qpolynomial_free(pwqp);
4200
4201 return data.res;
4202 error:
4203 isl_pw_qpolynomial_free(data.res);
4204 isl_pw_qpolynomial_free(pwqp);
4205 return NULL;
4206 }
4207
4208 /* Construct a piecewise quasipolynomial that is constant on the given
4209 * domain. In particular, it is
4210 * 0 if cst == 0
4211 * 1 if cst == 1
4212 * infinity if cst == -1
4213 */
4214 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4215 __isl_take isl_basic_set *bset, int cst)
4216 {
4217 isl_dim *dim;
4218 isl_qpolynomial *qp;
4219
4220 if (!bset)
4221 return NULL;
4222
4223 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4224 dim = isl_basic_set_get_dim(bset);
4225 if (cst < 0)
4226 qp = isl_qpolynomial_infty(dim);
4227 else if (cst == 0)
4228 qp = isl_qpolynomial_zero(dim);
4229 else
4230 qp = isl_qpolynomial_one(dim);
4231 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4232 }
4233
4234 /* Factor bset, call fn on each of the factors and return the product.
4235 *
4236 * If no factors can be found, simply call fn on the input.
4237 * Otherwise, construct the factors based on the factorizer,
4238 * call fn on each factor and compute the product.
4239 */
4240 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4241 __isl_take isl_basic_set *bset,
4242 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4243 {
4244 int i, n;
4245 isl_dim *dim;
4246 isl_set *set;
4247 isl_factorizer *f;
4248 isl_qpolynomial *qp;
4249 isl_pw_qpolynomial *pwqp;
4250 unsigned nparam;
4251 unsigned nvar;
4252
4253 f = isl_basic_set_factorizer(bset);
4254 if (!f)
4255 goto error;
4256 if (f->n_group == 0) {
4257 isl_factorizer_free(f);
4258 return fn(bset);
4259 }
4260
4261 nparam = isl_basic_set_dim(bset, isl_dim_param);
4262 nvar = isl_basic_set_dim(bset, isl_dim_set);
4263
4264 dim = isl_basic_set_get_dim(bset);
4265 dim = isl_dim_domain(dim);
4266 set = isl_set_universe(isl_dim_copy(dim));
4267 qp = isl_qpolynomial_one(dim);
4268 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4269
4270 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4271
4272 for (i = 0, n = 0; i < f->n_group; ++i) {
4273 isl_basic_set *bset_i;
4274 isl_pw_qpolynomial *pwqp_i;
4275
4276 bset_i = isl_basic_set_copy(bset);
4277 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4278 nparam + n + f->len[i], nvar - n - f->len[i]);
4279 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4280 nparam, n);
4281 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4282 n + f->len[i], nvar - n - f->len[i]);
4283 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4284
4285 pwqp_i = fn(bset_i);
4286 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4287
4288 n += f->len[i];
4289 }
4290
4291 isl_basic_set_free(bset);
4292 isl_factorizer_free(f);
4293
4294 return pwqp;
4295 error:
4296 isl_basic_set_free(bset);
4297 return NULL;
4298 }
4299
4300 /* Factor bset, call fn on each of the factors and return the product.
4301 * The function is assumed to evaluate to zero on empty domains,
4302 * to one on zero-dimensional domains and to infinity on unbounded domains
4303 * and will not be called explicitly on zero-dimensional or unbounded domains.
4304 *
4305 * We first check for some special cases and remove all equalities.
4306 * Then we hand over control to compressed_multiplicative_call.
4307 */
4308 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4309 __isl_take isl_basic_set *bset,
4310 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4311 {
4312 int bounded;
4313 isl_morph *morph;
4314 isl_pw_qpolynomial *pwqp;
4315 unsigned orig_nvar, final_nvar;
4316
4317 if (!bset)
4318 return NULL;
4319
4320 if (isl_basic_set_plain_is_empty(bset))
4321 return constant_on_domain(bset, 0);
4322
4323 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4324
4325 if (orig_nvar == 0)
4326 return constant_on_domain(bset, 1);
4327
4328 bounded = isl_basic_set_is_bounded(bset);
4329 if (bounded < 0)
4330 goto error;
4331 if (!bounded)
4332 return constant_on_domain(bset, -1);
4333
4334 if (bset->n_eq == 0)
4335 return compressed_multiplicative_call(bset, fn);
4336
4337 morph = isl_basic_set_full_compression(bset);
4338 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4339
4340 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4341
4342 pwqp = compressed_multiplicative_call(bset, fn);
4343
4344 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4345 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4346 morph = isl_morph_inverse(morph);
4347
4348 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4349
4350 return pwqp;
4351 error:
4352 isl_basic_set_free(bset);
4353 return NULL;
4354 }
4355
4356 /* Drop all floors in "qp", turning each integer division [a/m] into
4357 * a rational division a/m. If "down" is set, then the integer division
4358 * is replaces by (a-(m-1))/m instead.
4359 */
4360 static __isl_give isl_qpolynomial *qp_drop_floors(
4361 __isl_take isl_qpolynomial *qp, int down)
4362 {
4363 int i;
4364 struct isl_upoly *s;
4365
4366 if (!qp)
4367 return NULL;
4368 if (qp->div->n_row == 0)
4369 return qp;
4370
4371 qp = isl_qpolynomial_cow(qp);
4372 if (!qp)
4373 return NULL;
4374
4375 for (i = qp->div->n_row - 1; i >= 0; --i) {
4376 if (down) {
4377 isl_int_sub(qp->div->row[i][1],
4378 qp->div->row[i][1], qp->div->row[i][0]);
4379 isl_int_add_ui(qp->div->row[i][1],
4380 qp->div->row[i][1], 1);
4381 }
4382 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4383 qp->div->row[i][0], qp->div->n_col - 1);
4384 qp = substitute_div(qp, i, s);
4385 if (!qp)
4386 return NULL;
4387 }
4388
4389 return qp;
4390 }
4391
4392 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4393 * a rational division a/m.
4394 */
4395 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4396 __isl_take isl_pw_qpolynomial *pwqp)
4397 {
4398 int i;
4399
4400 if (!pwqp)
4401 return NULL;
4402
4403 if (isl_pw_qpolynomial_is_zero(pwqp))
4404 return pwqp;
4405
4406 pwqp = isl_pw_qpolynomial_cow(pwqp);
4407 if (!pwqp)
4408 return NULL;
4409
4410 for (i = 0; i < pwqp->n; ++i) {
4411 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4412 if (!pwqp->p[i].qp)
4413 goto error;
4414 }
4415
4416 return pwqp;
4417 error:
4418 isl_pw_qpolynomial_free(pwqp);
4419 return NULL;
4420 }
4421
4422 /* Adjust all the integer divisions in "qp" such that they are at least
4423 * one over the given orthant (identified by "signs"). This ensures
4424 * that they will still be non-negative even after subtracting (m-1)/m.
4425 *
4426 * In particular, f is replaced by f' + v, changing f = [a/m]
4427 * to f' = [(a - m v)/m].
4428 * If the constant term k in a is smaller than m,
4429 * the constant term of v is set to floor(k/m) - 1.
4430 * For any other term, if the coefficient c and the variable x have
4431 * the same sign, then no changes are needed.
4432 * Otherwise, if the variable is positive (and c is negative),
4433 * then the coefficient of x in v is set to floor(c/m).
4434 * If the variable is negative (and c is positive),
4435 * then the coefficient of x in v is set to ceil(c/m).
4436 */
4437 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4438 int *signs)
4439 {
4440 int i, j;
4441 int total;
4442 isl_vec *v = NULL;
4443 struct isl_upoly *s;
4444
4445 qp = isl_qpolynomial_cow(qp);
4446 if (!qp)
4447 return NULL;
4448 qp->div = isl_mat_cow(qp->div);
4449 if (!qp->div)
4450 goto error;
4451
4452 total = isl_dim_total(qp->dim);
4453 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4454
4455 for (i = 0; i < qp->div->n_row; ++i) {
4456 isl_int *row = qp->div->row[i];
4457 v = isl_vec_clr(v);
4458 if (!v)
4459 goto error;
4460 if (isl_int_lt(row[1], row[0])) {
4461 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4462 isl_int_sub_ui(v->el[0], v->el[0], 1);
4463 isl_int_submul(row[1], row[0], v->el[0]);
4464 }
4465 for (j = 0; j < total; ++j) {
4466 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4467 continue;
4468 if (signs[j] < 0)
4469 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4470 else
4471 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4472 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4473 }
4474 for (j = 0; j < i; ++j) {
4475 if (isl_int_sgn(row[2 + total + j]) >= 0)
4476 continue;
4477 isl_int_fdiv_q(v->el[1 + total + j],
4478 row[2 + total + j], row[0]);
4479 isl_int_submul(row[2 + total + j],
4480 row[0], v->el[1 + total + j]);
4481 }
4482 for (j = i + 1; j < qp->div->n_row; ++j) {
4483 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4484 continue;
4485 isl_seq_combine(qp->div->row[j] + 1,
4486 qp->div->ctx->one, qp->div->row[j] + 1,
4487 qp->div->row[j][2 + total + i], v->el, v->size);
4488 }
4489 isl_int_set_si(v->el[1 + total + i], 1);
4490 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4491 qp->div->ctx->one, v->size);
4492 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4493 isl_upoly_free(s);
4494 if (!qp->upoly)
4495 goto error;
4496 }
4497
4498 isl_vec_free(v);
4499 return qp;
4500 error:
4501 isl_vec_free(v);
4502 isl_qpolynomial_free(qp);
4503 return NULL;
4504 }
4505
4506 struct isl_to_poly_data {
4507 int sign;
4508 isl_pw_qpolynomial *res;
4509 isl_qpolynomial *qp;
4510 };
4511
4512 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4513 * We first make all integer divisions positive and then split the
4514 * quasipolynomials into terms with sign data->sign (the direction
4515 * of the requested approximation) and terms with the opposite sign.
4516 * In the first set of terms, each integer division [a/m] is
4517 * overapproximated by a/m, while in the second it is underapproximated
4518 * by (a-(m-1))/m.
4519 */
4520 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4521 void *user)
4522 {
4523 struct isl_to_poly_data *data = user;
4524 isl_pw_qpolynomial *t;
4525 isl_qpolynomial *qp, *up, *down;
4526
4527 qp = isl_qpolynomial_copy(data->qp);
4528 qp = make_divs_pos(qp, signs);
4529
4530 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4531 up = qp_drop_floors(up, 0);
4532 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4533 down = qp_drop_floors(down, 1);
4534
4535 isl_qpolynomial_free(qp);
4536 qp = isl_qpolynomial_add(up, down);
4537
4538 t = isl_pw_qpolynomial_alloc(orthant, qp);
4539 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4540
4541 return 0;
4542 }
4543
4544 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4545 * the polynomial will be an overapproximation. If "sign" is negative,
4546 * it will be an underapproximation. If "sign" is zero, the approximation
4547 * will lie somewhere in between.
4548 *
4549 * In particular, is sign == 0, we simply drop the floors, turning
4550 * the integer divisions into rational divisions.
4551 * Otherwise, we split the domains into orthants, make all integer divisions
4552 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4553 * depending on the requested sign and the sign of the term in which
4554 * the integer division appears.
4555 */
4556 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4557 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4558 {
4559 int i;
4560 struct isl_to_poly_data data;
4561
4562 if (sign == 0)
4563 return pwqp_drop_floors(pwqp);
4564
4565 if (!pwqp)
4566 return NULL;
4567
4568 data.sign = sign;
4569 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4570
4571 for (i = 0; i < pwqp->n; ++i) {
4572 if (pwqp->p[i].qp->div->n_row == 0) {
4573 isl_pw_qpolynomial *t;
4574 t = isl_pw_qpolynomial_alloc(
4575 isl_set_copy(pwqp->p[i].set),
4576 isl_qpolynomial_copy(pwqp->p[i].qp));
4577 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4578 continue;
4579 }
4580 data.qp = pwqp->p[i].qp;
4581 if (isl_set_foreach_orthant(pwqp->p[i].set,
4582 &to_polynomial_on_orthant, &data) < 0)
4583 goto error;
4584 }
4585
4586 isl_pw_qpolynomial_free(pwqp);
4587
4588 return data.res;
4589 error:
4590 isl_pw_qpolynomial_free(pwqp);
4591 isl_pw_qpolynomial_free(data.res);
4592 return NULL;
4593 }
4594
4595 static int poly_entry(void **entry, void *user)
4596 {
4597 int *sign = user;
4598 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4599
4600 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4601
4602 return *pwqp ? 0 : -1;
4603 }
4604
4605 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4606 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4607 {
4608 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4609 if (!upwqp)
4610 return NULL;
4611
4612 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4613 &poly_entry, &sign) < 0)
4614 goto error;
4615
4616 return upwqp;
4617 error:
4618 isl_union_pw_qpolynomial_free(upwqp);
4619 return NULL;
4620 }
4621
4622 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4623 __isl_take isl_qpolynomial *qp)
4624 {
4625 int i, k;
4626 isl_dim *dim;
4627 isl_vec *aff = NULL;
4628 isl_basic_map *bmap = NULL;
4629 unsigned pos;
4630 unsigned n_div;
4631
4632 if (!qp)
4633 return NULL;
4634 if (!isl_upoly_is_affine(qp->upoly))
4635 isl_die(qp->dim->ctx, isl_error_invalid,
4636 "input quasi-polynomial not affine", goto error);
4637 aff = isl_qpolynomial_extract_affine(qp);
4638 if (!aff)
4639 goto error;
4640 dim = isl_qpolynomial_get_dim(qp);
4641 dim = isl_dim_from_domain(dim);
4642 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4643 dim = isl_dim_add(dim, isl_dim_out, 1);
4644 n_div = qp->div->n_row;
4645 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4646
4647 for (i = 0; i < n_div; ++i) {
4648 k = isl_basic_map_alloc_div(bmap);
4649 if (k < 0)
4650 goto error;
4651 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4652 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4653 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4654 goto error;
4655 }
4656 k = isl_basic_map_alloc_equality(bmap);
4657 if (k < 0)
4658 goto error;
4659 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4660 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4661 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4662
4663 isl_vec_free(aff);
4664 isl_qpolynomial_free(qp);
4665 bmap = isl_basic_map_finalize(bmap);
4666 return bmap;
4667 error:
4668 isl_vec_free(aff);
4669 isl_qpolynomial_free(qp);
4670 isl_basic_map_free(bmap);
4671 return NULL;
4672 }
Integer set library