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isl_stream_read_map: accept alternative [i][j] tuple syntax
[isl.git] / isl_polynomial.c
blob2b7f1d6b5e9833f20eb371516617eeb2c5237dbb
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_scale(
1422 __isl_take isl_qpolynomial *qp, isl_int v)
1423 {
1424 return isl_qpolynomial_mul_isl_int(qp, v);
1425 }
1426
1427 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1428 __isl_take isl_qpolynomial *qp2)
1429 {
1430 qp1 = isl_qpolynomial_cow(qp1);
1431
1432 if (!qp1 || !qp2)
1433 goto error;
1434
1435 if (qp1->div->n_row < qp2->div->n_row)
1436 return isl_qpolynomial_mul(qp2, qp1);
1437
1438 isl_assert(qp1->dim->ctx, isl_dim_equal(qp1->dim, qp2->dim), goto error);
1439 if (!compatible_divs(qp1->div, qp2->div))
1440 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1441
1442 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1443 if (!qp1->upoly)
1444 goto error;
1445
1446 isl_qpolynomial_free(qp2);
1447
1448 return qp1;
1449 error:
1450 isl_qpolynomial_free(qp1);
1451 isl_qpolynomial_free(qp2);
1452 return NULL;
1453 }
1454
1455 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1456 unsigned power)
1457 {
1458 qp = isl_qpolynomial_cow(qp);
1459
1460 if (!qp)
1461 return NULL;
1462
1463 qp->upoly = isl_upoly_pow(qp->upoly, power);
1464 if (!qp->upoly)
1465 goto error;
1466
1467 return qp;
1468 error:
1469 isl_qpolynomial_free(qp);
1470 return NULL;
1471 }
1472
1473 __isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
1474 {
1475 if (!dim)
1476 return NULL;
1477 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1478 }
1479
1480 __isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
1481 {
1482 if (!dim)
1483 return NULL;
1484 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1485 }
1486
1487 __isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
1488 {
1489 if (!dim)
1490 return NULL;
1491 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1492 }
1493
1494 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
1495 {
1496 if (!dim)
1497 return NULL;
1498 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1499 }
1500
1501 __isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
1502 {
1503 if (!dim)
1504 return NULL;
1505 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1506 }
1507
1508 __isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
1509 isl_int v)
1510 {
1511 struct isl_qpolynomial *qp;
1512 struct isl_upoly_cst *cst;
1513
1514 if (!dim)
1515 return NULL;
1516
1517 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1518 if (!qp)
1519 return NULL;
1520
1521 cst = isl_upoly_as_cst(qp->upoly);
1522 isl_int_set(cst->n, v);
1523
1524 return qp;
1525 }
1526
1527 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1528 isl_int *n, isl_int *d)
1529 {
1530 struct isl_upoly_cst *cst;
1531
1532 if (!qp)
1533 return -1;
1534
1535 if (!isl_upoly_is_cst(qp->upoly))
1536 return 0;
1537
1538 cst = isl_upoly_as_cst(qp->upoly);
1539 if (!cst)
1540 return -1;
1541
1542 if (n)
1543 isl_int_set(*n, cst->n);
1544 if (d)
1545 isl_int_set(*d, cst->d);
1546
1547 return 1;
1548 }
1549
1550 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1551 {
1552 int is_cst;
1553 struct isl_upoly_rec *rec;
1554
1555 if (!up)
1556 return -1;
1557
1558 if (up->var < 0)
1559 return 1;
1560
1561 rec = isl_upoly_as_rec(up);
1562 if (!rec)
1563 return -1;
1564
1565 if (rec->n > 2)
1566 return 0;
1567
1568 isl_assert(up->ctx, rec->n > 1, return -1);
1569
1570 is_cst = isl_upoly_is_cst(rec->p[1]);
1571 if (is_cst < 0)
1572 return -1;
1573 if (!is_cst)
1574 return 0;
1575
1576 return isl_upoly_is_affine(rec->p[0]);
1577 }
1578
1579 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1580 {
1581 if (!qp)
1582 return -1;
1583
1584 if (qp->div->n_row > 0)
1585 return 0;
1586
1587 return isl_upoly_is_affine(qp->upoly);
1588 }
1589
1590 static void update_coeff(__isl_keep isl_vec *aff,
1591 __isl_keep struct isl_upoly_cst *cst, int pos)
1592 {
1593 isl_int gcd;
1594 isl_int f;
1595
1596 if (isl_int_is_zero(cst->n))
1597 return;
1598
1599 isl_int_init(gcd);
1600 isl_int_init(f);
1601 isl_int_gcd(gcd, cst->d, aff->el[0]);
1602 isl_int_divexact(f, cst->d, gcd);
1603 isl_int_divexact(gcd, aff->el[0], gcd);
1604 isl_seq_scale(aff->el, aff->el, f, aff->size);
1605 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1606 isl_int_clear(gcd);
1607 isl_int_clear(f);
1608 }
1609
1610 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1611 __isl_keep isl_vec *aff)
1612 {
1613 struct isl_upoly_cst *cst;
1614 struct isl_upoly_rec *rec;
1615
1616 if (!up || !aff)
1617 return -1;
1618
1619 if (up->var < 0) {
1620 struct isl_upoly_cst *cst;
1621
1622 cst = isl_upoly_as_cst(up);
1623 if (!cst)
1624 return -1;
1625 update_coeff(aff, cst, 0);
1626 return 0;
1627 }
1628
1629 rec = isl_upoly_as_rec(up);
1630 if (!rec)
1631 return -1;
1632 isl_assert(up->ctx, rec->n == 2, return -1);
1633
1634 cst = isl_upoly_as_cst(rec->p[1]);
1635 if (!cst)
1636 return -1;
1637 update_coeff(aff, cst, 1 + up->var);
1638
1639 return isl_upoly_update_affine(rec->p[0], aff);
1640 }
1641
1642 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1643 __isl_keep isl_qpolynomial *qp)
1644 {
1645 isl_vec *aff;
1646 unsigned d;
1647
1648 if (!qp)
1649 return NULL;
1650
1651 d = isl_dim_total(qp->dim);
1652 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1653 if (!aff)
1654 return NULL;
1655
1656 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1657 isl_int_set_si(aff->el[0], 1);
1658
1659 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1660 goto error;
1661
1662 return aff;
1663 error:
1664 isl_vec_free(aff);
1665 return NULL;
1666 }
1667
1668 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1669 __isl_keep isl_qpolynomial *qp2)
1670 {
1671 int equal;
1672
1673 if (!qp1 || !qp2)
1674 return -1;
1675
1676 equal = isl_dim_equal(qp1->dim, qp2->dim);
1677 if (equal < 0 || !equal)
1678 return equal;
1679
1680 equal = isl_mat_is_equal(qp1->div, qp2->div);
1681 if (equal < 0 || !equal)
1682 return equal;
1683
1684 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1685 }
1686
1687 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1688 {
1689 int i;
1690 struct isl_upoly_rec *rec;
1691
1692 if (isl_upoly_is_cst(up)) {
1693 struct isl_upoly_cst *cst;
1694 cst = isl_upoly_as_cst(up);
1695 if (!cst)
1696 return;
1697 isl_int_lcm(*d, *d, cst->d);
1698 return;
1699 }
1700
1701 rec = isl_upoly_as_rec(up);
1702 if (!rec)
1703 return;
1704
1705 for (i = 0; i < rec->n; ++i)
1706 upoly_update_den(rec->p[i], d);
1707 }
1708
1709 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1710 {
1711 isl_int_set_si(*d, 1);
1712 if (!qp)
1713 return;
1714 upoly_update_den(qp->upoly, d);
1715 }
1716
1717 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
1718 int pos, int power)
1719 {
1720 struct isl_ctx *ctx;
1721
1722 if (!dim)
1723 return NULL;
1724
1725 ctx = dim->ctx;
1726
1727 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1728 }
1729
1730 __isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
1731 enum isl_dim_type type, unsigned pos)
1732 {
1733 if (!dim)
1734 return NULL;
1735
1736 isl_assert(dim->ctx, isl_dim_size(dim, isl_dim_in) == 0, goto error);
1737 isl_assert(dim->ctx, pos < isl_dim_size(dim, type), goto error);
1738
1739 if (type == isl_dim_set)
1740 pos += isl_dim_size(dim, isl_dim_param);
1741
1742 return isl_qpolynomial_var_pow(dim, pos, 1);
1743 error:
1744 isl_dim_free(dim);
1745 return NULL;
1746 }
1747
1748 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1749 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1750 {
1751 int i;
1752 struct isl_upoly_rec *rec;
1753 struct isl_upoly *base, *res;
1754
1755 if (!up)
1756 return NULL;
1757
1758 if (isl_upoly_is_cst(up))
1759 return up;
1760
1761 if (up->var < first)
1762 return up;
1763
1764 rec = isl_upoly_as_rec(up);
1765 if (!rec)
1766 goto error;
1767
1768 isl_assert(up->ctx, rec->n >= 1, goto error);
1769
1770 if (up->var >= first + n)
1771 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1772 else
1773 base = isl_upoly_copy(subs[up->var - first]);
1774
1775 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1776 for (i = rec->n - 2; i >= 0; --i) {
1777 struct isl_upoly *t;
1778 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1779 res = isl_upoly_mul(res, isl_upoly_copy(base));
1780 res = isl_upoly_sum(res, t);
1781 }
1782
1783 isl_upoly_free(base);
1784 isl_upoly_free(up);
1785
1786 return res;
1787 error:
1788 isl_upoly_free(up);
1789 return NULL;
1790 }
1791
1792 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1793 isl_int denom, unsigned len)
1794 {
1795 int i;
1796 struct isl_upoly *up;
1797
1798 isl_assert(ctx, len >= 1, return NULL);
1799
1800 up = isl_upoly_rat_cst(ctx, f[0], denom);
1801 for (i = 0; i < len - 1; ++i) {
1802 struct isl_upoly *t;
1803 struct isl_upoly *c;
1804
1805 if (isl_int_is_zero(f[1 + i]))
1806 continue;
1807
1808 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1809 t = isl_upoly_var_pow(ctx, i, 1);
1810 t = isl_upoly_mul(c, t);
1811 up = isl_upoly_sum(up, t);
1812 }
1813
1814 return up;
1815 }
1816
1817 /* Remove common factor of non-constant terms and denominator.
1818 */
1819 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1820 {
1821 isl_ctx *ctx = qp->div->ctx;
1822 unsigned total = qp->div->n_col - 2;
1823
1824 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1825 isl_int_gcd(ctx->normalize_gcd,
1826 ctx->normalize_gcd, qp->div->row[div][0]);
1827 if (isl_int_is_one(ctx->normalize_gcd))
1828 return;
1829
1830 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1831 ctx->normalize_gcd, total);
1832 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1833 ctx->normalize_gcd);
1834 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1835 ctx->normalize_gcd);
1836 }
1837
1838 /* Replace the integer division identified by "div" by the polynomial "s".
1839 * The integer division is assumed not to appear in the definition
1840 * of any other integer divisions.
1841 */
1842 static __isl_give isl_qpolynomial *substitute_div(
1843 __isl_take isl_qpolynomial *qp,
1844 int div, __isl_take struct isl_upoly *s)
1845 {
1846 int i;
1847 int total;
1848 int *reordering;
1849
1850 if (!qp || !s)
1851 goto error;
1852
1853 qp = isl_qpolynomial_cow(qp);
1854 if (!qp)
1855 goto error;
1856
1857 total = isl_dim_total(qp->dim);
1858 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1859 if (!qp->upoly)
1860 goto error;
1861
1862 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1863 if (!reordering)
1864 goto error;
1865 for (i = 0; i < total + div; ++i)
1866 reordering[i] = i;
1867 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1868 reordering[i] = i - 1;
1869 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1870 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1871 qp->upoly = reorder(qp->upoly, reordering);
1872 free(reordering);
1873
1874 if (!qp->upoly || !qp->div)
1875 goto error;
1876
1877 isl_upoly_free(s);
1878 return qp;
1879 error:
1880 isl_qpolynomial_free(qp);
1881 isl_upoly_free(s);
1882 return NULL;
1883 }
1884
1885 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1886 * divisions because d is equal to 1 by their definition, i.e., e.
1887 */
1888 static __isl_give isl_qpolynomial *substitute_non_divs(
1889 __isl_take isl_qpolynomial *qp)
1890 {
1891 int i, j;
1892 int total;
1893 struct isl_upoly *s;
1894
1895 if (!qp)
1896 return NULL;
1897
1898 total = isl_dim_total(qp->dim);
1899 for (i = 0; qp && i < qp->div->n_row; ++i) {
1900 if (!isl_int_is_one(qp->div->row[i][0]))
1901 continue;
1902 for (j = i + 1; j < qp->div->n_row; ++j) {
1903 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
1904 continue;
1905 isl_seq_combine(qp->div->row[j] + 1,
1906 qp->div->ctx->one, qp->div->row[j] + 1,
1907 qp->div->row[j][2 + total + i],
1908 qp->div->row[i] + 1, 1 + total + i);
1909 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
1910 normalize_div(qp, j);
1911 }
1912 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
1913 qp->div->row[i][0], qp->div->n_col - 1);
1914 qp = substitute_div(qp, i, s);
1915 --i;
1916 }
1917
1918 return qp;
1919 }
1920
1921 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
1922 * with d the denominator. When replacing the coefficient e of x by
1923 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
1924 * inside the division, so we need to add floor(e/d) * x outside.
1925 * That is, we replace q by q' + floor(e/d) * x and we therefore need
1926 * to adjust the coefficient of x in each later div that depends on the
1927 * current div "div" and also in the affine expression "aff"
1928 * (if it too depends on "div").
1929 */
1930 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
1931 __isl_keep isl_vec *aff)
1932 {
1933 int i, j;
1934 isl_int v;
1935 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1936
1937 isl_int_init(v);
1938 for (i = 0; i < 1 + total + div; ++i) {
1939 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
1940 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
1941 continue;
1942 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
1943 isl_int_fdiv_r(qp->div->row[div][1 + i],
1944 qp->div->row[div][1 + i], qp->div->row[div][0]);
1945 if (!isl_int_is_zero(aff->el[1 + total + div]))
1946 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
1947 for (j = div + 1; j < qp->div->n_row; ++j) {
1948 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
1949 continue;
1950 isl_int_addmul(qp->div->row[j][1 + i],
1951 v, qp->div->row[j][2 + total + div]);
1952 }
1953 }
1954 isl_int_clear(v);
1955 }
1956
1957 /* Check if the last non-zero coefficient is bigger that half of the
1958 * denominator. If so, we will invert the div to further reduce the number
1959 * of distinct divs that may appear.
1960 * If the last non-zero coefficient is exactly half the denominator,
1961 * then we continue looking for earlier coefficients that are bigger
1962 * than half the denominator.
1963 */
1964 static int needs_invert(__isl_keep isl_mat *div, int row)
1965 {
1966 int i;
1967 int cmp;
1968
1969 for (i = div->n_col - 1; i >= 1; --i) {
1970 if (isl_int_is_zero(div->row[row][i]))
1971 continue;
1972 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
1973 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
1974 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
1975 if (cmp)
1976 return cmp > 0;
1977 if (i == 1)
1978 return 1;
1979 }
1980
1981 return 0;
1982 }
1983
1984 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
1985 * We only invert the coefficients of e (and the coefficient of q in
1986 * later divs and in "aff"). After calling this function, the
1987 * coefficients of e should be reduced again.
1988 */
1989 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
1990 __isl_keep isl_vec *aff)
1991 {
1992 unsigned total = qp->div->n_col - qp->div->n_row - 2;
1993
1994 isl_seq_neg(qp->div->row[div] + 1,
1995 qp->div->row[div] + 1, qp->div->n_col - 1);
1996 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
1997 isl_int_add(qp->div->row[div][1],
1998 qp->div->row[div][1], qp->div->row[div][0]);
1999 if (!isl_int_is_zero(aff->el[1 + total + div]))
2000 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2001 isl_mat_col_mul(qp->div, 2 + total + div,
2002 qp->div->ctx->negone, 2 + total + div);
2003 }
2004
2005 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2006 * in the interval [0, d-1], with d the denominator and such that the
2007 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2008 *
2009 * After the reduction, some divs may have become redundant or identical,
2010 * so we call substitute_non_divs and sort_divs. If these functions
2011 * eliminate divs or merge two or more divs into one, the coefficients
2012 * of the enclosing divs may have to be reduced again, so we call
2013 * ourselves recursively if the number of divs decreases.
2014 */
2015 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2016 {
2017 int i;
2018 isl_vec *aff = NULL;
2019 struct isl_upoly *s;
2020 unsigned n_div;
2021
2022 if (!qp)
2023 return NULL;
2024
2025 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2026 aff = isl_vec_clr(aff);
2027 if (!aff)
2028 goto error;
2029
2030 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2031
2032 for (i = 0; i < qp->div->n_row; ++i) {
2033 normalize_div(qp, i);
2034 reduce_div(qp, i, aff);
2035 if (needs_invert(qp->div, i)) {
2036 invert_div(qp, i, aff);
2037 reduce_div(qp, i, aff);
2038 }
2039 }
2040
2041 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2042 qp->div->ctx->one, aff->size);
2043 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2044 isl_upoly_free(s);
2045 if (!qp->upoly)
2046 goto error;
2047
2048 isl_vec_free(aff);
2049
2050 n_div = qp->div->n_row;
2051 qp = substitute_non_divs(qp);
2052 qp = sort_divs(qp);
2053 if (qp && qp->div->n_row < n_div)
2054 return reduce_divs(qp);
2055
2056 return qp;
2057 error:
2058 isl_qpolynomial_free(qp);
2059 isl_vec_free(aff);
2060 return NULL;
2061 }
2062
2063 /* Assumes each div only depends on earlier divs.
2064 */
2065 __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
2066 int power)
2067 {
2068 struct isl_qpolynomial *qp = NULL;
2069 struct isl_upoly_rec *rec;
2070 struct isl_upoly_cst *cst;
2071 int i, d;
2072 int pos;
2073
2074 if (!div)
2075 return NULL;
2076
2077 d = div->line - div->bmap->div;
2078
2079 pos = isl_dim_total(div->bmap->dim) + d;
2080 rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
2081 qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
2082 div->bmap->n_div, &rec->up);
2083 if (!qp)
2084 goto error;
2085
2086 for (i = 0; i < div->bmap->n_div; ++i)
2087 isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
2088
2089 for (i = 0; i < 1 + power; ++i) {
2090 rec->p[i] = isl_upoly_zero(div->ctx);
2091 if (!rec->p[i])
2092 goto error;
2093 rec->n++;
2094 }
2095 cst = isl_upoly_as_cst(rec->p[power]);
2096 isl_int_set_si(cst->n, 1);
2097
2098 isl_div_free(div);
2099
2100 qp = reduce_divs(qp);
2101
2102 return qp;
2103 error:
2104 isl_qpolynomial_free(qp);
2105 isl_div_free(div);
2106 return NULL;
2107 }
2108
2109 __isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
2110 {
2111 return isl_qpolynomial_div_pow(div, 1);
2112 }
2113
2114 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
2115 const isl_int n, const isl_int d)
2116 {
2117 struct isl_qpolynomial *qp;
2118 struct isl_upoly_cst *cst;
2119
2120 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2121 if (!qp)
2122 return NULL;
2123
2124 cst = isl_upoly_as_cst(qp->upoly);
2125 isl_int_set(cst->n, n);
2126 isl_int_set(cst->d, d);
2127
2128 return qp;
2129 }
2130
2131 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2132 {
2133 struct isl_upoly_rec *rec;
2134 int i;
2135
2136 if (!up)
2137 return -1;
2138
2139 if (isl_upoly_is_cst(up))
2140 return 0;
2141
2142 if (up->var < d)
2143 active[up->var] = 1;
2144
2145 rec = isl_upoly_as_rec(up);
2146 for (i = 0; i < rec->n; ++i)
2147 if (up_set_active(rec->p[i], active, d) < 0)
2148 return -1;
2149
2150 return 0;
2151 }
2152
2153 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2154 {
2155 int i, j;
2156 int d = isl_dim_total(qp->dim);
2157
2158 if (!qp || !active)
2159 return -1;
2160
2161 for (i = 0; i < d; ++i)
2162 for (j = 0; j < qp->div->n_row; ++j) {
2163 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2164 continue;
2165 active[i] = 1;
2166 break;
2167 }
2168
2169 return up_set_active(qp->upoly, active, d);
2170 }
2171
2172 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2173 enum isl_dim_type type, unsigned first, unsigned n)
2174 {
2175 int i;
2176 int *active = NULL;
2177 int involves = 0;
2178
2179 if (!qp)
2180 return -1;
2181 if (n == 0)
2182 return 0;
2183
2184 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2185 return -1);
2186 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2187 type == isl_dim_set, return -1);
2188
2189 active = isl_calloc_array(qp->dim->ctx, int, isl_dim_total(qp->dim));
2190 if (set_active(qp, active) < 0)
2191 goto error;
2192
2193 if (type == isl_dim_set)
2194 first += isl_dim_size(qp->dim, isl_dim_param);
2195 for (i = 0; i < n; ++i)
2196 if (active[first + i]) {
2197 involves = 1;
2198 break;
2199 }
2200
2201 free(active);
2202
2203 return involves;
2204 error:
2205 free(active);
2206 return -1;
2207 }
2208
2209 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2210 * of the divs that do appear in the quasi-polynomial.
2211 */
2212 static __isl_give isl_qpolynomial *remove_redundant_divs(
2213 __isl_take isl_qpolynomial *qp)
2214 {
2215 int i, j;
2216 int d;
2217 int len;
2218 int skip;
2219 int *active = NULL;
2220 int *reordering = NULL;
2221 int redundant = 0;
2222 int n_div;
2223 isl_ctx *ctx;
2224
2225 if (!qp)
2226 return NULL;
2227 if (qp->div->n_row == 0)
2228 return qp;
2229
2230 d = isl_dim_total(qp->dim);
2231 len = qp->div->n_col - 2;
2232 ctx = isl_qpolynomial_get_ctx(qp);
2233 active = isl_calloc_array(ctx, int, len);
2234 if (!active)
2235 goto error;
2236
2237 if (up_set_active(qp->upoly, active, len) < 0)
2238 goto error;
2239
2240 for (i = qp->div->n_row - 1; i >= 0; --i) {
2241 if (!active[d + i]) {
2242 redundant = 1;
2243 continue;
2244 }
2245 for (j = 0; j < i; ++j) {
2246 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2247 continue;
2248 active[d + j] = 1;
2249 break;
2250 }
2251 }
2252
2253 if (!redundant) {
2254 free(active);
2255 return qp;
2256 }
2257
2258 reordering = isl_alloc_array(qp->div->ctx, int, len);
2259 if (!reordering)
2260 goto error;
2261
2262 for (i = 0; i < d; ++i)
2263 reordering[i] = i;
2264
2265 skip = 0;
2266 n_div = qp->div->n_row;
2267 for (i = 0; i < n_div; ++i) {
2268 if (!active[d + i]) {
2269 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2270 qp->div = isl_mat_drop_cols(qp->div,
2271 2 + d + i - skip, 1);
2272 skip++;
2273 }
2274 reordering[d + i] = d + i - skip;
2275 }
2276
2277 qp->upoly = reorder(qp->upoly, reordering);
2278
2279 if (!qp->upoly || !qp->div)
2280 goto error;
2281
2282 free(active);
2283 free(reordering);
2284
2285 return qp;
2286 error:
2287 free(active);
2288 free(reordering);
2289 isl_qpolynomial_free(qp);
2290 return NULL;
2291 }
2292
2293 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2294 unsigned first, unsigned n)
2295 {
2296 int i;
2297 struct isl_upoly_rec *rec;
2298
2299 if (!up)
2300 return NULL;
2301 if (n == 0 || up->var < 0 || up->var < first)
2302 return up;
2303 if (up->var < first + n) {
2304 up = replace_by_constant_term(up);
2305 return isl_upoly_drop(up, first, n);
2306 }
2307 up = isl_upoly_cow(up);
2308 if (!up)
2309 return NULL;
2310 up->var -= n;
2311 rec = isl_upoly_as_rec(up);
2312 if (!rec)
2313 goto error;
2314
2315 for (i = 0; i < rec->n; ++i) {
2316 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2317 if (!rec->p[i])
2318 goto error;
2319 }
2320
2321 return up;
2322 error:
2323 isl_upoly_free(up);
2324 return NULL;
2325 }
2326
2327 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2328 __isl_take isl_qpolynomial *qp,
2329 enum isl_dim_type type, unsigned pos, const char *s)
2330 {
2331 qp = isl_qpolynomial_cow(qp);
2332 if (!qp)
2333 return NULL;
2334 qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
2335 if (!qp->dim)
2336 goto error;
2337 return qp;
2338 error:
2339 isl_qpolynomial_free(qp);
2340 return NULL;
2341 }
2342
2343 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2344 __isl_take isl_qpolynomial *qp,
2345 enum isl_dim_type type, unsigned first, unsigned n)
2346 {
2347 if (!qp)
2348 return NULL;
2349 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2350 return qp;
2351
2352 qp = isl_qpolynomial_cow(qp);
2353 if (!qp)
2354 return NULL;
2355
2356 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
2357 goto error);
2358 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2359 type == isl_dim_set, goto error);
2360
2361 qp->dim = isl_dim_drop(qp->dim, type, first, n);
2362 if (!qp->dim)
2363 goto error;
2364
2365 if (type == isl_dim_set)
2366 first += isl_dim_size(qp->dim, isl_dim_param);
2367
2368 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2369 if (!qp->div)
2370 goto error;
2371
2372 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2373 if (!qp->upoly)
2374 goto error;
2375
2376 return qp;
2377 error:
2378 isl_qpolynomial_free(qp);
2379 return NULL;
2380 }
2381
2382 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2383 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2384 {
2385 int i, j, k;
2386 isl_int denom;
2387 unsigned total;
2388 unsigned n_div;
2389 struct isl_upoly *up;
2390
2391 if (!eq)
2392 goto error;
2393 if (eq->n_eq == 0) {
2394 isl_basic_set_free(eq);
2395 return qp;
2396 }
2397
2398 qp = isl_qpolynomial_cow(qp);
2399 if (!qp)
2400 goto error;
2401 qp->div = isl_mat_cow(qp->div);
2402 if (!qp->div)
2403 goto error;
2404
2405 total = 1 + isl_dim_total(eq->dim);
2406 n_div = eq->n_div;
2407 isl_int_init(denom);
2408 for (i = 0; i < eq->n_eq; ++i) {
2409 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2410 if (j < 0 || j == 0 || j >= total)
2411 continue;
2412
2413 for (k = 0; k < qp->div->n_row; ++k) {
2414 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2415 continue;
2416 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2417 &qp->div->row[k][0]);
2418 normalize_div(qp, k);
2419 }
2420
2421 if (isl_int_is_pos(eq->eq[i][j]))
2422 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2423 isl_int_abs(denom, eq->eq[i][j]);
2424 isl_int_set_si(eq->eq[i][j], 0);
2425
2426 up = isl_upoly_from_affine(qp->dim->ctx,
2427 eq->eq[i], denom, total);
2428 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2429 isl_upoly_free(up);
2430 }
2431 isl_int_clear(denom);
2432
2433 if (!qp->upoly)
2434 goto error;
2435
2436 isl_basic_set_free(eq);
2437
2438 qp = substitute_non_divs(qp);
2439 qp = sort_divs(qp);
2440
2441 return qp;
2442 error:
2443 isl_basic_set_free(eq);
2444 isl_qpolynomial_free(qp);
2445 return NULL;
2446 }
2447
2448 static __isl_give isl_basic_set *add_div_constraints(
2449 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2450 {
2451 int i;
2452 unsigned total;
2453
2454 if (!bset || !div)
2455 goto error;
2456
2457 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2458 if (!bset)
2459 goto error;
2460 total = isl_basic_set_total_dim(bset);
2461 for (i = 0; i < div->n_row; ++i)
2462 if (isl_basic_set_add_div_constraints_var(bset,
2463 total - div->n_row + i, div->row[i]) < 0)
2464 goto error;
2465
2466 isl_mat_free(div);
2467 return bset;
2468 error:
2469 isl_mat_free(div);
2470 isl_basic_set_free(bset);
2471 return NULL;
2472 }
2473
2474 /* Look for equalities among the variables shared by context and qp
2475 * and the integer divisions of qp, if any.
2476 * The equalities are then used to eliminate variables and/or integer
2477 * divisions from qp.
2478 */
2479 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2480 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2481 {
2482 isl_basic_set *aff;
2483
2484 if (!qp)
2485 goto error;
2486 if (qp->div->n_row > 0) {
2487 isl_basic_set *bset;
2488 context = isl_set_add_dims(context, isl_dim_set,
2489 qp->div->n_row);
2490 bset = isl_basic_set_universe(isl_set_get_dim(context));
2491 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2492 context = isl_set_intersect(context,
2493 isl_set_from_basic_set(bset));
2494 }
2495
2496 aff = isl_set_affine_hull(context);
2497 return isl_qpolynomial_substitute_equalities(qp, aff);
2498 error:
2499 isl_qpolynomial_free(qp);
2500 isl_set_free(context);
2501 return NULL;
2502 }
2503
2504 #undef PW
2505 #define PW isl_pw_qpolynomial
2506 #undef EL
2507 #define EL isl_qpolynomial
2508 #undef EL_IS_ZERO
2509 #define EL_IS_ZERO is_zero
2510 #undef ZERO
2511 #define ZERO zero
2512 #undef IS_ZERO
2513 #define IS_ZERO is_zero
2514 #undef FIELD
2515 #define FIELD qp
2516
2517 #include <isl_pw_templ.c>
2518
2519 #undef UNION
2520 #define UNION isl_union_pw_qpolynomial
2521 #undef PART
2522 #define PART isl_pw_qpolynomial
2523 #undef PARTS
2524 #define PARTS pw_qpolynomial
2525
2526 #include <isl_union_templ.c>
2527
2528 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2529 {
2530 if (!pwqp)
2531 return -1;
2532
2533 if (pwqp->n != -1)
2534 return 0;
2535
2536 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2537 return 0;
2538
2539 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2540 }
2541
2542 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2543 __isl_take isl_pw_qpolynomial *pwqp1,
2544 __isl_take isl_pw_qpolynomial *pwqp2)
2545 {
2546 int i, j, n;
2547 struct isl_pw_qpolynomial *res;
2548
2549 if (!pwqp1 || !pwqp2)
2550 goto error;
2551
2552 isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
2553 goto error);
2554
2555 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2556 isl_pw_qpolynomial_free(pwqp2);
2557 return pwqp1;
2558 }
2559
2560 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2561 isl_pw_qpolynomial_free(pwqp1);
2562 return pwqp2;
2563 }
2564
2565 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2566 isl_pw_qpolynomial_free(pwqp1);
2567 return pwqp2;
2568 }
2569
2570 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2571 isl_pw_qpolynomial_free(pwqp2);
2572 return pwqp1;
2573 }
2574
2575 n = pwqp1->n * pwqp2->n;
2576 res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
2577
2578 for (i = 0; i < pwqp1->n; ++i) {
2579 for (j = 0; j < pwqp2->n; ++j) {
2580 struct isl_set *common;
2581 struct isl_qpolynomial *prod;
2582 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2583 isl_set_copy(pwqp2->p[j].set));
2584 if (isl_set_plain_is_empty(common)) {
2585 isl_set_free(common);
2586 continue;
2587 }
2588
2589 prod = isl_qpolynomial_mul(
2590 isl_qpolynomial_copy(pwqp1->p[i].qp),
2591 isl_qpolynomial_copy(pwqp2->p[j].qp));
2592
2593 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2594 }
2595 }
2596
2597 isl_pw_qpolynomial_free(pwqp1);
2598 isl_pw_qpolynomial_free(pwqp2);
2599
2600 return res;
2601 error:
2602 isl_pw_qpolynomial_free(pwqp1);
2603 isl_pw_qpolynomial_free(pwqp2);
2604 return NULL;
2605 }
2606
2607 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2608 __isl_take isl_pw_qpolynomial *pwqp1,
2609 __isl_take isl_pw_qpolynomial *pwqp2)
2610 {
2611 return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
2612 }
2613
2614 __isl_give struct isl_upoly *isl_upoly_eval(
2615 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2616 {
2617 int i;
2618 struct isl_upoly_rec *rec;
2619 struct isl_upoly *res;
2620 struct isl_upoly *base;
2621
2622 if (isl_upoly_is_cst(up)) {
2623 isl_vec_free(vec);
2624 return up;
2625 }
2626
2627 rec = isl_upoly_as_rec(up);
2628 if (!rec)
2629 goto error;
2630
2631 isl_assert(up->ctx, rec->n >= 1, goto error);
2632
2633 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2634
2635 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2636 isl_vec_copy(vec));
2637
2638 for (i = rec->n - 2; i >= 0; --i) {
2639 res = isl_upoly_mul(res, isl_upoly_copy(base));
2640 res = isl_upoly_sum(res,
2641 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2642 isl_vec_copy(vec)));
2643 }
2644
2645 isl_upoly_free(base);
2646 isl_upoly_free(up);
2647 isl_vec_free(vec);
2648 return res;
2649 error:
2650 isl_upoly_free(up);
2651 isl_vec_free(vec);
2652 return NULL;
2653 }
2654
2655 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2656 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2657 {
2658 isl_vec *ext;
2659 struct isl_upoly *up;
2660 isl_dim *dim;
2661
2662 if (!qp || !pnt)
2663 goto error;
2664 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
2665
2666 if (qp->div->n_row == 0)
2667 ext = isl_vec_copy(pnt->vec);
2668 else {
2669 int i;
2670 unsigned dim = isl_dim_total(qp->dim);
2671 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2672 if (!ext)
2673 goto error;
2674
2675 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2676 for (i = 0; i < qp->div->n_row; ++i) {
2677 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2678 1 + dim + i, &ext->el[1+dim+i]);
2679 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2680 qp->div->row[i][0]);
2681 }
2682 }
2683
2684 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2685 if (!up)
2686 goto error;
2687
2688 dim = isl_dim_copy(qp->dim);
2689 isl_qpolynomial_free(qp);
2690 isl_point_free(pnt);
2691
2692 return isl_qpolynomial_alloc(dim, 0, up);
2693 error:
2694 isl_qpolynomial_free(qp);
2695 isl_point_free(pnt);
2696 return NULL;
2697 }
2698
2699 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2700 __isl_keep struct isl_upoly_cst *cst2)
2701 {
2702 int cmp;
2703 isl_int t;
2704 isl_int_init(t);
2705 isl_int_mul(t, cst1->n, cst2->d);
2706 isl_int_submul(t, cst2->n, cst1->d);
2707 cmp = isl_int_sgn(t);
2708 isl_int_clear(t);
2709 return cmp;
2710 }
2711
2712 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2713 __isl_keep isl_qpolynomial *qp2)
2714 {
2715 struct isl_upoly_cst *cst1, *cst2;
2716
2717 if (!qp1 || !qp2)
2718 return -1;
2719 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2720 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2721 if (isl_qpolynomial_is_nan(qp1))
2722 return -1;
2723 if (isl_qpolynomial_is_nan(qp2))
2724 return -1;
2725 cst1 = isl_upoly_as_cst(qp1->upoly);
2726 cst2 = isl_upoly_as_cst(qp2->upoly);
2727
2728 return isl_upoly_cmp(cst1, cst2) <= 0;
2729 }
2730
2731 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2732 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2733 {
2734 struct isl_upoly_cst *cst1, *cst2;
2735 int cmp;
2736
2737 if (!qp1 || !qp2)
2738 goto error;
2739 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2740 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2741 cst1 = isl_upoly_as_cst(qp1->upoly);
2742 cst2 = isl_upoly_as_cst(qp2->upoly);
2743 cmp = isl_upoly_cmp(cst1, cst2);
2744
2745 if (cmp <= 0) {
2746 isl_qpolynomial_free(qp2);
2747 } else {
2748 isl_qpolynomial_free(qp1);
2749 qp1 = qp2;
2750 }
2751 return qp1;
2752 error:
2753 isl_qpolynomial_free(qp1);
2754 isl_qpolynomial_free(qp2);
2755 return NULL;
2756 }
2757
2758 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2759 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2760 {
2761 struct isl_upoly_cst *cst1, *cst2;
2762 int cmp;
2763
2764 if (!qp1 || !qp2)
2765 goto error;
2766 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2767 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2768 cst1 = isl_upoly_as_cst(qp1->upoly);
2769 cst2 = isl_upoly_as_cst(qp2->upoly);
2770 cmp = isl_upoly_cmp(cst1, cst2);
2771
2772 if (cmp >= 0) {
2773 isl_qpolynomial_free(qp2);
2774 } else {
2775 isl_qpolynomial_free(qp1);
2776 qp1 = qp2;
2777 }
2778 return qp1;
2779 error:
2780 isl_qpolynomial_free(qp1);
2781 isl_qpolynomial_free(qp2);
2782 return NULL;
2783 }
2784
2785 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2786 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2787 unsigned first, unsigned n)
2788 {
2789 unsigned total;
2790 unsigned g_pos;
2791 int *exp;
2792
2793 if (n == 0 && !isl_dim_is_named_or_nested(qp->dim, type))
2794 return qp;
2795
2796 qp = isl_qpolynomial_cow(qp);
2797 if (!qp)
2798 return NULL;
2799
2800 isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
2801 goto error);
2802
2803 g_pos = pos(qp->dim, type) + first;
2804
2805 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2806 if (!qp->div)
2807 goto error;
2808
2809 total = qp->div->n_col - 2;
2810 if (total > g_pos) {
2811 int i;
2812 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2813 if (!exp)
2814 goto error;
2815 for (i = 0; i < total - g_pos; ++i)
2816 exp[i] = i + n;
2817 qp->upoly = expand(qp->upoly, exp, g_pos);
2818 free(exp);
2819 if (!qp->upoly)
2820 goto error;
2821 }
2822
2823 qp->dim = isl_dim_insert(qp->dim, type, first, n);
2824 if (!qp->dim)
2825 goto error;
2826
2827 return qp;
2828 error:
2829 isl_qpolynomial_free(qp);
2830 return NULL;
2831 }
2832
2833 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
2834 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
2835 {
2836 unsigned pos;
2837
2838 pos = isl_qpolynomial_dim(qp, type);
2839
2840 return isl_qpolynomial_insert_dims(qp, type, pos, n);
2841 }
2842
2843 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
2844 __isl_take isl_pw_qpolynomial *pwqp,
2845 enum isl_dim_type type, unsigned n)
2846 {
2847 unsigned pos;
2848
2849 pos = isl_pw_qpolynomial_dim(pwqp, type);
2850
2851 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
2852 }
2853
2854 static int *reordering_move(isl_ctx *ctx,
2855 unsigned len, unsigned dst, unsigned src, unsigned n)
2856 {
2857 int i;
2858 int *reordering;
2859
2860 reordering = isl_alloc_array(ctx, int, len);
2861 if (!reordering)
2862 return NULL;
2863
2864 if (dst <= src) {
2865 for (i = 0; i < dst; ++i)
2866 reordering[i] = i;
2867 for (i = 0; i < n; ++i)
2868 reordering[src + i] = dst + i;
2869 for (i = 0; i < src - dst; ++i)
2870 reordering[dst + i] = dst + n + i;
2871 for (i = 0; i < len - src - n; ++i)
2872 reordering[src + n + i] = src + n + i;
2873 } else {
2874 for (i = 0; i < src; ++i)
2875 reordering[i] = i;
2876 for (i = 0; i < n; ++i)
2877 reordering[src + i] = dst + i;
2878 for (i = 0; i < dst - src; ++i)
2879 reordering[src + n + i] = src + i;
2880 for (i = 0; i < len - dst - n; ++i)
2881 reordering[dst + n + i] = dst + n + i;
2882 }
2883
2884 return reordering;
2885 }
2886
2887 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
2888 __isl_take isl_qpolynomial *qp,
2889 enum isl_dim_type dst_type, unsigned dst_pos,
2890 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
2891 {
2892 unsigned g_dst_pos;
2893 unsigned g_src_pos;
2894 int *reordering;
2895
2896 qp = isl_qpolynomial_cow(qp);
2897 if (!qp)
2898 return NULL;
2899
2900 isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
2901 goto error);
2902
2903 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
2904 g_src_pos = pos(qp->dim, src_type) + src_pos;
2905 if (dst_type > src_type)
2906 g_dst_pos -= n;
2907
2908 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
2909 if (!qp->div)
2910 goto error;
2911 qp = sort_divs(qp);
2912 if (!qp)
2913 goto error;
2914
2915 reordering = reordering_move(qp->dim->ctx,
2916 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
2917 if (!reordering)
2918 goto error;
2919
2920 qp->upoly = reorder(qp->upoly, reordering);
2921 free(reordering);
2922 if (!qp->upoly)
2923 goto error;
2924
2925 qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
2926 if (!qp->dim)
2927 goto error;
2928
2929 return qp;
2930 error:
2931 isl_qpolynomial_free(qp);
2932 return NULL;
2933 }
2934
2935 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
2936 isl_int *f, isl_int denom)
2937 {
2938 struct isl_upoly *up;
2939
2940 if (!dim)
2941 return NULL;
2942
2943 up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
2944
2945 return isl_qpolynomial_alloc(dim, 0, up);
2946 }
2947
2948 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
2949 {
2950 isl_ctx *ctx;
2951 struct isl_upoly *up;
2952 isl_qpolynomial *qp;
2953
2954 if (!aff)
2955 return NULL;
2956
2957 ctx = isl_aff_get_ctx(aff);
2958 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
2959 aff->v->size - 1);
2960
2961 qp = isl_qpolynomial_alloc(isl_aff_get_dim(aff),
2962 aff->ls->div->n_row, up);
2963 if (!qp)
2964 goto error;
2965
2966 isl_mat_free(qp->div);
2967 qp->div = isl_mat_copy(aff->ls->div);
2968 qp->div = isl_mat_cow(qp->div);
2969 if (!qp->div)
2970 goto error;
2971
2972 isl_aff_free(aff);
2973 qp = reduce_divs(qp);
2974 qp = remove_redundant_divs(qp);
2975 return qp;
2976 error:
2977 isl_aff_free(aff);
2978 return NULL;
2979 }
2980
2981 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
2982 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
2983 {
2984 isl_aff *aff;
2985
2986 aff = isl_constraint_get_bound(c, type, pos);
2987 isl_constraint_free(c);
2988 return isl_qpolynomial_from_aff(aff);
2989 }
2990
2991 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
2992 * in "qp" by subs[i].
2993 */
2994 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
2995 __isl_take isl_qpolynomial *qp,
2996 enum isl_dim_type type, unsigned first, unsigned n,
2997 __isl_keep isl_qpolynomial **subs)
2998 {
2999 int i;
3000 struct isl_upoly **ups;
3001
3002 if (n == 0)
3003 return qp;
3004
3005 qp = isl_qpolynomial_cow(qp);
3006 if (!qp)
3007 return NULL;
3008 for (i = 0; i < n; ++i)
3009 if (!subs[i])
3010 goto error;
3011
3012 isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
3013 goto error);
3014
3015 for (i = 0; i < n; ++i)
3016 isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
3017 goto error);
3018
3019 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3020 for (i = 0; i < n; ++i)
3021 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3022
3023 first += pos(qp->dim, type);
3024
3025 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3026 if (!ups)
3027 goto error;
3028 for (i = 0; i < n; ++i)
3029 ups[i] = subs[i]->upoly;
3030
3031 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3032
3033 free(ups);
3034
3035 if (!qp->upoly)
3036 goto error;
3037
3038 return qp;
3039 error:
3040 isl_qpolynomial_free(qp);
3041 return NULL;
3042 }
3043
3044 /* Extend "bset" with extra set dimensions for each integer division
3045 * in "qp" and then call "fn" with the extended bset and the polynomial
3046 * that results from replacing each of the integer divisions by the
3047 * corresponding extra set dimension.
3048 */
3049 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3050 __isl_keep isl_basic_set *bset,
3051 int (*fn)(__isl_take isl_basic_set *bset,
3052 __isl_take isl_qpolynomial *poly, void *user), void *user)
3053 {
3054 isl_dim *dim;
3055 isl_mat *div;
3056 isl_qpolynomial *poly;
3057
3058 if (!qp || !bset)
3059 goto error;
3060 if (qp->div->n_row == 0)
3061 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3062 user);
3063
3064 div = isl_mat_copy(qp->div);
3065 dim = isl_dim_copy(qp->dim);
3066 dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
3067 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3068 bset = isl_basic_set_copy(bset);
3069 bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
3070 bset = add_div_constraints(bset, div);
3071
3072 return fn(bset, poly, user);
3073 error:
3074 return -1;
3075 }
3076
3077 /* Return total degree in variables first (inclusive) up to last (exclusive).
3078 */
3079 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3080 {
3081 int deg = -1;
3082 int i;
3083 struct isl_upoly_rec *rec;
3084
3085 if (!up)
3086 return -2;
3087 if (isl_upoly_is_zero(up))
3088 return -1;
3089 if (isl_upoly_is_cst(up) || up->var < first)
3090 return 0;
3091
3092 rec = isl_upoly_as_rec(up);
3093 if (!rec)
3094 return -2;
3095
3096 for (i = 0; i < rec->n; ++i) {
3097 int d;
3098
3099 if (isl_upoly_is_zero(rec->p[i]))
3100 continue;
3101 d = isl_upoly_degree(rec->p[i], first, last);
3102 if (up->var < last)
3103 d += i;
3104 if (d > deg)
3105 deg = d;
3106 }
3107
3108 return deg;
3109 }
3110
3111 /* Return total degree in set variables.
3112 */
3113 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3114 {
3115 unsigned ovar;
3116 unsigned nvar;
3117
3118 if (!poly)
3119 return -2;
3120
3121 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3122 nvar = isl_dim_size(poly->dim, isl_dim_set);
3123 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3124 }
3125
3126 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3127 unsigned pos, int deg)
3128 {
3129 int i;
3130 struct isl_upoly_rec *rec;
3131
3132 if (!up)
3133 return NULL;
3134
3135 if (isl_upoly_is_cst(up) || up->var < pos) {
3136 if (deg == 0)
3137 return isl_upoly_copy(up);
3138 else
3139 return isl_upoly_zero(up->ctx);
3140 }
3141
3142 rec = isl_upoly_as_rec(up);
3143 if (!rec)
3144 return NULL;
3145
3146 if (up->var == pos) {
3147 if (deg < rec->n)
3148 return isl_upoly_copy(rec->p[deg]);
3149 else
3150 return isl_upoly_zero(up->ctx);
3151 }
3152
3153 up = isl_upoly_copy(up);
3154 up = isl_upoly_cow(up);
3155 rec = isl_upoly_as_rec(up);
3156 if (!rec)
3157 goto error;
3158
3159 for (i = 0; i < rec->n; ++i) {
3160 struct isl_upoly *t;
3161 t = isl_upoly_coeff(rec->p[i], pos, deg);
3162 if (!t)
3163 goto error;
3164 isl_upoly_free(rec->p[i]);
3165 rec->p[i] = t;
3166 }
3167
3168 return up;
3169 error:
3170 isl_upoly_free(up);
3171 return NULL;
3172 }
3173
3174 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3175 */
3176 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3177 __isl_keep isl_qpolynomial *qp,
3178 enum isl_dim_type type, unsigned t_pos, int deg)
3179 {
3180 unsigned g_pos;
3181 struct isl_upoly *up;
3182 isl_qpolynomial *c;
3183
3184 if (!qp)
3185 return NULL;
3186
3187 isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
3188 return NULL);
3189
3190 g_pos = pos(qp->dim, type) + t_pos;
3191 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3192
3193 c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
3194 if (!c)
3195 return NULL;
3196 isl_mat_free(c->div);
3197 c->div = isl_mat_copy(qp->div);
3198 if (!c->div)
3199 goto error;
3200 return c;
3201 error:
3202 isl_qpolynomial_free(c);
3203 return NULL;
3204 }
3205
3206 /* Homogenize the polynomial in the variables first (inclusive) up to
3207 * last (exclusive) by inserting powers of variable first.
3208 * Variable first is assumed not to appear in the input.
3209 */
3210 __isl_give struct isl_upoly *isl_upoly_homogenize(
3211 __isl_take struct isl_upoly *up, int deg, int target,
3212 int first, int last)
3213 {
3214 int i;
3215 struct isl_upoly_rec *rec;
3216
3217 if (!up)
3218 return NULL;
3219 if (isl_upoly_is_zero(up))
3220 return up;
3221 if (deg == target)
3222 return up;
3223 if (isl_upoly_is_cst(up) || up->var < first) {
3224 struct isl_upoly *hom;
3225
3226 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3227 if (!hom)
3228 goto error;
3229 rec = isl_upoly_as_rec(hom);
3230 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3231
3232 return hom;
3233 }
3234
3235 up = isl_upoly_cow(up);
3236 rec = isl_upoly_as_rec(up);
3237 if (!rec)
3238 goto error;
3239
3240 for (i = 0; i < rec->n; ++i) {
3241 if (isl_upoly_is_zero(rec->p[i]))
3242 continue;
3243 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3244 up->var < last ? deg + i : i, target,
3245 first, last);
3246 if (!rec->p[i])
3247 goto error;
3248 }
3249
3250 return up;
3251 error:
3252 isl_upoly_free(up);
3253 return NULL;
3254 }
3255
3256 /* Homogenize the polynomial in the set variables by introducing
3257 * powers of an extra set variable at position 0.
3258 */
3259 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3260 __isl_take isl_qpolynomial *poly)
3261 {
3262 unsigned ovar;
3263 unsigned nvar;
3264 int deg = isl_qpolynomial_degree(poly);
3265
3266 if (deg < -1)
3267 goto error;
3268
3269 poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
3270 poly = isl_qpolynomial_cow(poly);
3271 if (!poly)
3272 goto error;
3273
3274 ovar = isl_dim_offset(poly->dim, isl_dim_set);
3275 nvar = isl_dim_size(poly->dim, isl_dim_set);
3276 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3277 ovar, ovar + nvar);
3278 if (!poly->upoly)
3279 goto error;
3280
3281 return poly;
3282 error:
3283 isl_qpolynomial_free(poly);
3284 return NULL;
3285 }
3286
3287 __isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
3288 __isl_take isl_mat *div)
3289 {
3290 isl_term *term;
3291 int n;
3292
3293 if (!dim || !div)
3294 goto error;
3295
3296 n = isl_dim_total(dim) + div->n_row;
3297
3298 term = isl_calloc(dim->ctx, struct isl_term,
3299 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3300 if (!term)
3301 goto error;
3302
3303 term->ref = 1;
3304 term->dim = dim;
3305 term->div = div;
3306 isl_int_init(term->n);
3307 isl_int_init(term->d);
3308
3309 return term;
3310 error:
3311 isl_dim_free(dim);
3312 isl_mat_free(div);
3313 return NULL;
3314 }
3315
3316 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3317 {
3318 if (!term)
3319 return NULL;
3320
3321 term->ref++;
3322 return term;
3323 }
3324
3325 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3326 {
3327 int i;
3328 isl_term *dup;
3329 unsigned total;
3330
3331 if (term)
3332 return NULL;
3333
3334 total = isl_dim_total(term->dim) + term->div->n_row;
3335
3336 dup = isl_term_alloc(isl_dim_copy(term->dim), isl_mat_copy(term->div));
3337 if (!dup)
3338 return NULL;
3339
3340 isl_int_set(dup->n, term->n);
3341 isl_int_set(dup->d, term->d);
3342
3343 for (i = 0; i < total; ++i)
3344 dup->pow[i] = term->pow[i];
3345
3346 return dup;
3347 }
3348
3349 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3350 {
3351 if (!term)
3352 return NULL;
3353
3354 if (term->ref == 1)
3355 return term;
3356 term->ref--;
3357 return isl_term_dup(term);
3358 }
3359
3360 void isl_term_free(__isl_take isl_term *term)
3361 {
3362 if (!term)
3363 return;
3364
3365 if (--term->ref > 0)
3366 return;
3367
3368 isl_dim_free(term->dim);
3369 isl_mat_free(term->div);
3370 isl_int_clear(term->n);
3371 isl_int_clear(term->d);
3372 free(term);
3373 }
3374
3375 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3376 {
3377 if (!term)
3378 return 0;
3379
3380 switch (type) {
3381 case isl_dim_param:
3382 case isl_dim_in:
3383 case isl_dim_out: return isl_dim_size(term->dim, type);
3384 case isl_dim_div: return term->div->n_row;
3385 case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
3386 default: return 0;
3387 }
3388 }
3389
3390 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3391 {
3392 return term ? term->dim->ctx : NULL;
3393 }
3394
3395 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3396 {
3397 if (!term)
3398 return;
3399 isl_int_set(*n, term->n);
3400 }
3401
3402 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3403 {
3404 if (!term)
3405 return;
3406 isl_int_set(*d, term->d);
3407 }
3408
3409 int isl_term_get_exp(__isl_keep isl_term *term,
3410 enum isl_dim_type type, unsigned pos)
3411 {
3412 if (!term)
3413 return -1;
3414
3415 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3416
3417 if (type >= isl_dim_set)
3418 pos += isl_dim_size(term->dim, isl_dim_param);
3419 if (type >= isl_dim_div)
3420 pos += isl_dim_size(term->dim, isl_dim_set);
3421
3422 return term->pow[pos];
3423 }
3424
3425 __isl_give isl_div *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3426 {
3427 isl_basic_map *bmap;
3428 unsigned total;
3429 int k;
3430
3431 if (!term)
3432 return NULL;
3433
3434 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3435 return NULL);
3436
3437 total = term->div->n_col - term->div->n_row - 2;
3438 /* No nested divs for now */
3439 isl_assert(term->dim->ctx,
3440 isl_seq_first_non_zero(term->div->row[pos] + 2 + total,
3441 term->div->n_row) == -1,
3442 return NULL);
3443
3444 bmap = isl_basic_map_alloc_dim(isl_dim_copy(term->dim), 1, 0, 0);
3445 if ((k = isl_basic_map_alloc_div(bmap)) < 0)
3446 goto error;
3447
3448 isl_seq_cpy(bmap->div[k], term->div->row[pos], 2 + total);
3449
3450 return isl_basic_map_div(bmap, k);
3451 error:
3452 isl_basic_map_free(bmap);
3453 return NULL;
3454 }
3455
3456 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3457 int (*fn)(__isl_take isl_term *term, void *user),
3458 __isl_take isl_term *term, void *user)
3459 {
3460 int i;
3461 struct isl_upoly_rec *rec;
3462
3463 if (!up || !term)
3464 goto error;
3465
3466 if (isl_upoly_is_zero(up))
3467 return term;
3468
3469 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3470 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3471 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3472
3473 if (isl_upoly_is_cst(up)) {
3474 struct isl_upoly_cst *cst;
3475 cst = isl_upoly_as_cst(up);
3476 if (!cst)
3477 goto error;
3478 term = isl_term_cow(term);
3479 if (!term)
3480 goto error;
3481 isl_int_set(term->n, cst->n);
3482 isl_int_set(term->d, cst->d);
3483 if (fn(isl_term_copy(term), user) < 0)
3484 goto error;
3485 return term;
3486 }
3487
3488 rec = isl_upoly_as_rec(up);
3489 if (!rec)
3490 goto error;
3491
3492 for (i = 0; i < rec->n; ++i) {
3493 term = isl_term_cow(term);
3494 if (!term)
3495 goto error;
3496 term->pow[up->var] = i;
3497 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3498 if (!term)
3499 goto error;
3500 }
3501 term->pow[up->var] = 0;
3502
3503 return term;
3504 error:
3505 isl_term_free(term);
3506 return NULL;
3507 }
3508
3509 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3510 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3511 {
3512 isl_term *term;
3513
3514 if (!qp)
3515 return -1;
3516
3517 term = isl_term_alloc(isl_dim_copy(qp->dim), isl_mat_copy(qp->div));
3518 if (!term)
3519 return -1;
3520
3521 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3522
3523 isl_term_free(term);
3524
3525 return term ? 0 : -1;
3526 }
3527
3528 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3529 {
3530 struct isl_upoly *up;
3531 isl_qpolynomial *qp;
3532 int i, n;
3533
3534 if (!term)
3535 return NULL;
3536
3537 n = isl_dim_total(term->dim) + term->div->n_row;
3538
3539 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3540 for (i = 0; i < n; ++i) {
3541 if (!term->pow[i])
3542 continue;
3543 up = isl_upoly_mul(up,
3544 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3545 }
3546
3547 qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
3548 if (!qp)
3549 goto error;
3550 isl_mat_free(qp->div);
3551 qp->div = isl_mat_copy(term->div);
3552 if (!qp->div)
3553 goto error;
3554
3555 isl_term_free(term);
3556 return qp;
3557 error:
3558 isl_qpolynomial_free(qp);
3559 isl_term_free(term);
3560 return NULL;
3561 }
3562
3563 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3564 __isl_take isl_dim *dim)
3565 {
3566 int i;
3567 int extra;
3568 unsigned total;
3569
3570 if (!qp || !dim)
3571 goto error;
3572
3573 if (isl_dim_equal(qp->dim, dim)) {
3574 isl_dim_free(dim);
3575 return qp;
3576 }
3577
3578 qp = isl_qpolynomial_cow(qp);
3579 if (!qp)
3580 goto error;
3581
3582 extra = isl_dim_size(dim, isl_dim_set) -
3583 isl_dim_size(qp->dim, isl_dim_set);
3584 total = isl_dim_total(qp->dim);
3585 if (qp->div->n_row) {
3586 int *exp;
3587
3588 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3589 if (!exp)
3590 goto error;
3591 for (i = 0; i < qp->div->n_row; ++i)
3592 exp[i] = extra + i;
3593 qp->upoly = expand(qp->upoly, exp, total);
3594 free(exp);
3595 if (!qp->upoly)
3596 goto error;
3597 }
3598 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3599 if (!qp->div)
3600 goto error;
3601 for (i = 0; i < qp->div->n_row; ++i)
3602 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3603
3604 isl_dim_free(qp->dim);
3605 qp->dim = dim;
3606
3607 return qp;
3608 error:
3609 isl_dim_free(dim);
3610 isl_qpolynomial_free(qp);
3611 return NULL;
3612 }
3613
3614 /* For each parameter or variable that does not appear in qp,
3615 * first eliminate the variable from all constraints and then set it to zero.
3616 */
3617 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3618 __isl_keep isl_qpolynomial *qp)
3619 {
3620 int *active = NULL;
3621 int i;
3622 int d;
3623 unsigned nparam;
3624 unsigned nvar;
3625
3626 if (!set || !qp)
3627 goto error;
3628
3629 d = isl_dim_total(set->dim);
3630 active = isl_calloc_array(set->ctx, int, d);
3631 if (set_active(qp, active) < 0)
3632 goto error;
3633
3634 for (i = 0; i < d; ++i)
3635 if (!active[i])
3636 break;
3637
3638 if (i == d) {
3639 free(active);
3640 return set;
3641 }
3642
3643 nparam = isl_dim_size(set->dim, isl_dim_param);
3644 nvar = isl_dim_size(set->dim, isl_dim_set);
3645 for (i = 0; i < nparam; ++i) {
3646 if (active[i])
3647 continue;
3648 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3649 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3650 }
3651 for (i = 0; i < nvar; ++i) {
3652 if (active[nparam + i])
3653 continue;
3654 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3655 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3656 }
3657
3658 free(active);
3659
3660 return set;
3661 error:
3662 free(active);
3663 isl_set_free(set);
3664 return NULL;
3665 }
3666
3667 struct isl_opt_data {
3668 isl_qpolynomial *qp;
3669 int first;
3670 isl_qpolynomial *opt;
3671 int max;
3672 };
3673
3674 static int opt_fn(__isl_take isl_point *pnt, void *user)
3675 {
3676 struct isl_opt_data *data = (struct isl_opt_data *)user;
3677 isl_qpolynomial *val;
3678
3679 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3680 if (data->first) {
3681 data->first = 0;
3682 data->opt = val;
3683 } else if (data->max) {
3684 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3685 } else {
3686 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3687 }
3688
3689 return 0;
3690 }
3691
3692 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3693 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3694 {
3695 struct isl_opt_data data = { NULL, 1, NULL, max };
3696
3697 if (!set || !qp)
3698 goto error;
3699
3700 if (isl_upoly_is_cst(qp->upoly)) {
3701 isl_set_free(set);
3702 return qp;
3703 }
3704
3705 set = fix_inactive(set, qp);
3706
3707 data.qp = qp;
3708 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3709 goto error;
3710
3711 if (data.first)
3712 data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
3713
3714 isl_set_free(set);
3715 isl_qpolynomial_free(qp);
3716 return data.opt;
3717 error:
3718 isl_set_free(set);
3719 isl_qpolynomial_free(qp);
3720 isl_qpolynomial_free(data.opt);
3721 return NULL;
3722 }
3723
3724 __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
3725 __isl_take isl_morph *morph)
3726 {
3727 int i;
3728 int n_sub;
3729 isl_ctx *ctx;
3730 struct isl_upoly **subs;
3731 isl_mat *mat;
3732
3733 qp = isl_qpolynomial_cow(qp);
3734 if (!qp || !morph)
3735 goto error;
3736
3737 ctx = qp->dim->ctx;
3738 isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
3739
3740 n_sub = morph->inv->n_row - 1;
3741 if (morph->inv->n_row != morph->inv->n_col)
3742 n_sub += qp->div->n_row;
3743 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3744 if (!subs)
3745 goto error;
3746
3747 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3748 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3749 morph->inv->row[0][0], morph->inv->n_col);
3750 if (morph->inv->n_row != morph->inv->n_col)
3751 for (i = 0; i < qp->div->n_row; ++i)
3752 subs[morph->inv->n_row - 1 + i] =
3753 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3754
3755 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3756
3757 for (i = 0; i < n_sub; ++i)
3758 isl_upoly_free(subs[i]);
3759 free(subs);
3760
3761 mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
3762 mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
3763 qp->div = isl_mat_product(qp->div, mat);
3764 isl_dim_free(qp->dim);
3765 qp->dim = isl_dim_copy(morph->ran->dim);
3766
3767 if (!qp->upoly || !qp->div || !qp->dim)
3768 goto error;
3769
3770 isl_morph_free(morph);
3771
3772 return qp;
3773 error:
3774 isl_qpolynomial_free(qp);
3775 isl_morph_free(morph);
3776 return NULL;
3777 }
3778
3779 static int neg_entry(void **entry, void *user)
3780 {
3781 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
3782
3783 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
3784
3785 return *pwqp ? 0 : -1;
3786 }
3787
3788 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
3789 __isl_take isl_union_pw_qpolynomial *upwqp)
3790 {
3791 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
3792 if (!upwqp)
3793 return NULL;
3794
3795 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
3796 &neg_entry, NULL) < 0)
3797 goto error;
3798
3799 return upwqp;
3800 error:
3801 isl_union_pw_qpolynomial_free(upwqp);
3802 return NULL;
3803 }
3804
3805 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3806 __isl_take isl_union_pw_qpolynomial *upwqp1,
3807 __isl_take isl_union_pw_qpolynomial *upwqp2)
3808 {
3809 return isl_union_pw_qpolynomial_add(upwqp1,
3810 isl_union_pw_qpolynomial_neg(upwqp2));
3811 }
3812
3813 static int mul_entry(void **entry, void *user)
3814 {
3815 struct isl_union_pw_qpolynomial_match_bin_data *data = user;
3816 uint32_t hash;
3817 struct isl_hash_table_entry *entry2;
3818 isl_pw_qpolynomial *pwpq = *entry;
3819 int empty;
3820
3821 hash = isl_dim_get_hash(pwpq->dim);
3822 entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
3823 hash, &has_dim, pwpq->dim, 0);
3824 if (!entry2)
3825 return 0;
3826
3827 pwpq = isl_pw_qpolynomial_copy(pwpq);
3828 pwpq = isl_pw_qpolynomial_mul(pwpq,
3829 isl_pw_qpolynomial_copy(entry2->data));
3830
3831 empty = isl_pw_qpolynomial_is_zero(pwpq);
3832 if (empty < 0) {
3833 isl_pw_qpolynomial_free(pwpq);
3834 return -1;
3835 }
3836 if (empty) {
3837 isl_pw_qpolynomial_free(pwpq);
3838 return 0;
3839 }
3840
3841 data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
3842
3843 return 0;
3844 }
3845
3846 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3847 __isl_take isl_union_pw_qpolynomial *upwqp1,
3848 __isl_take isl_union_pw_qpolynomial *upwqp2)
3849 {
3850 return match_bin_op(upwqp1, upwqp2, &mul_entry);
3851 }
3852
3853 /* Reorder the columns of the given div definitions according to the
3854 * given reordering.
3855 */
3856 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
3857 __isl_take isl_reordering *r)
3858 {
3859 int i, j;
3860 isl_mat *mat;
3861 int extra;
3862
3863 if (!div || !r)
3864 goto error;
3865
3866 extra = isl_dim_total(r->dim) + div->n_row - r->len;
3867 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
3868 if (!mat)
3869 goto error;
3870
3871 for (i = 0; i < div->n_row; ++i) {
3872 isl_seq_cpy(mat->row[i], div->row[i], 2);
3873 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
3874 for (j = 0; j < r->len; ++j)
3875 isl_int_set(mat->row[i][2 + r->pos[j]],
3876 div->row[i][2 + j]);
3877 }
3878
3879 isl_reordering_free(r);
3880 isl_mat_free(div);
3881 return mat;
3882 error:
3883 isl_reordering_free(r);
3884 isl_mat_free(div);
3885 return NULL;
3886 }
3887
3888 /* Reorder the dimension of "qp" according to the given reordering.
3889 */
3890 __isl_give isl_qpolynomial *isl_qpolynomial_realign(
3891 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
3892 {
3893 qp = isl_qpolynomial_cow(qp);
3894 if (!qp)
3895 goto error;
3896
3897 r = isl_reordering_extend(r, qp->div->n_row);
3898 if (!r)
3899 goto error;
3900
3901 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
3902 if (!qp->div)
3903 goto error;
3904
3905 qp->upoly = reorder(qp->upoly, r->pos);
3906 if (!qp->upoly)
3907 goto error;
3908
3909 qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
3910
3911 isl_reordering_free(r);
3912 return qp;
3913 error:
3914 isl_qpolynomial_free(qp);
3915 isl_reordering_free(r);
3916 return NULL;
3917 }
3918
3919 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3920 __isl_take isl_qpolynomial *qp, __isl_take isl_dim *model)
3921 {
3922 if (!qp || !model)
3923 goto error;
3924
3925 if (!isl_dim_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
3926 isl_reordering *exp;
3927
3928 model = isl_dim_drop(model, isl_dim_in,
3929 0, isl_dim_size(model, isl_dim_in));
3930 model = isl_dim_drop(model, isl_dim_out,
3931 0, isl_dim_size(model, isl_dim_out));
3932 exp = isl_parameter_alignment_reordering(qp->dim, model);
3933 exp = isl_reordering_extend_dim(exp,
3934 isl_qpolynomial_get_dim(qp));
3935 qp = isl_qpolynomial_realign(qp, exp);
3936 }
3937
3938 isl_dim_free(model);
3939 return qp;
3940 error:
3941 isl_dim_free(model);
3942 isl_qpolynomial_free(qp);
3943 return NULL;
3944 }
3945
3946 struct isl_split_periods_data {
3947 int max_periods;
3948 isl_pw_qpolynomial *res;
3949 };
3950
3951 /* Create a slice where the integer division "div" has the fixed value "v".
3952 * In particular, if "div" refers to floor(f/m), then create a slice
3953 *
3954 * m v <= f <= m v + (m - 1)
3955 *
3956 * or
3957 *
3958 * f - m v >= 0
3959 * -f + m v + (m - 1) >= 0
3960 */
3961 static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
3962 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
3963 {
3964 int total;
3965 isl_basic_set *bset = NULL;
3966 int k;
3967
3968 if (!dim || !qp)
3969 goto error;
3970
3971 total = isl_dim_total(dim);
3972 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
3973
3974 k = isl_basic_set_alloc_inequality(bset);
3975 if (k < 0)
3976 goto error;
3977 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3978 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
3979
3980 k = isl_basic_set_alloc_inequality(bset);
3981 if (k < 0)
3982 goto error;
3983 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
3984 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
3985 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
3986 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
3987
3988 isl_dim_free(dim);
3989 return isl_set_from_basic_set(bset);
3990 error:
3991 isl_basic_set_free(bset);
3992 isl_dim_free(dim);
3993 return NULL;
3994 }
3995
3996 static int split_periods(__isl_take isl_set *set,
3997 __isl_take isl_qpolynomial *qp, void *user);
3998
3999 /* Create a slice of the domain "set" such that integer division "div"
4000 * has the fixed value "v" and add the results to data->res,
4001 * replacing the integer division by "v" in "qp".
4002 */
4003 static int set_div(__isl_take isl_set *set,
4004 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4005 struct isl_split_periods_data *data)
4006 {
4007 int i;
4008 int total;
4009 isl_set *slice;
4010 struct isl_upoly *cst;
4011
4012 slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
4013 set = isl_set_intersect(set, slice);
4014
4015 if (!qp)
4016 goto error;
4017
4018 total = isl_dim_total(qp->dim);
4019
4020 for (i = div + 1; i < qp->div->n_row; ++i) {
4021 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4022 continue;
4023 isl_int_addmul(qp->div->row[i][1],
4024 qp->div->row[i][2 + total + div], v);
4025 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4026 }
4027
4028 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4029 qp = substitute_div(qp, div, cst);
4030
4031 return split_periods(set, qp, data);
4032 error:
4033 isl_set_free(set);
4034 isl_qpolynomial_free(qp);
4035 return -1;
4036 }
4037
4038 /* Split the domain "set" such that integer division "div"
4039 * has a fixed value (ranging from "min" to "max") on each slice
4040 * and add the results to data->res.
4041 */
4042 static int split_div(__isl_take isl_set *set,
4043 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4044 struct isl_split_periods_data *data)
4045 {
4046 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4047 isl_set *set_i = isl_set_copy(set);
4048 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4049
4050 if (set_div(set_i, qp_i, div, min, data) < 0)
4051 goto error;
4052 }
4053 isl_set_free(set);
4054 isl_qpolynomial_free(qp);
4055 return 0;
4056 error:
4057 isl_set_free(set);
4058 isl_qpolynomial_free(qp);
4059 return -1;
4060 }
4061
4062 /* If "qp" refers to any integer division
4063 * that can only attain "max_periods" distinct values on "set"
4064 * then split the domain along those distinct values.
4065 * Add the results (or the original if no splitting occurs)
4066 * to data->res.
4067 */
4068 static int split_periods(__isl_take isl_set *set,
4069 __isl_take isl_qpolynomial *qp, void *user)
4070 {
4071 int i;
4072 isl_pw_qpolynomial *pwqp;
4073 struct isl_split_periods_data *data;
4074 isl_int min, max;
4075 int total;
4076 int r = 0;
4077
4078 data = (struct isl_split_periods_data *)user;
4079
4080 if (!set || !qp)
4081 goto error;
4082
4083 if (qp->div->n_row == 0) {
4084 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4085 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4086 return 0;
4087 }
4088
4089 isl_int_init(min);
4090 isl_int_init(max);
4091 total = isl_dim_total(qp->dim);
4092 for (i = 0; i < qp->div->n_row; ++i) {
4093 enum isl_lp_result lp_res;
4094
4095 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4096 qp->div->n_row) != -1)
4097 continue;
4098
4099 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4100 set->ctx->one, &min, NULL, NULL);
4101 if (lp_res == isl_lp_error)
4102 goto error2;
4103 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4104 continue;
4105 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4106
4107 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4108 set->ctx->one, &max, NULL, NULL);
4109 if (lp_res == isl_lp_error)
4110 goto error2;
4111 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4112 continue;
4113 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4114
4115 isl_int_sub(max, max, min);
4116 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4117 isl_int_add(max, max, min);
4118 break;
4119 }
4120 }
4121
4122 if (i < qp->div->n_row) {
4123 r = split_div(set, qp, i, min, max, data);
4124 } else {
4125 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4126 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4127 }
4128
4129 isl_int_clear(max);
4130 isl_int_clear(min);
4131
4132 return r;
4133 error2:
4134 isl_int_clear(max);
4135 isl_int_clear(min);
4136 error:
4137 isl_set_free(set);
4138 isl_qpolynomial_free(qp);
4139 return -1;
4140 }
4141
4142 /* If any quasi-polynomial in pwqp refers to any integer division
4143 * that can only attain "max_periods" distinct values on its domain
4144 * then split the domain along those distinct values.
4145 */
4146 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4147 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4148 {
4149 struct isl_split_periods_data data;
4150
4151 data.max_periods = max_periods;
4152 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4153
4154 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4155 goto error;
4156
4157 isl_pw_qpolynomial_free(pwqp);
4158
4159 return data.res;
4160 error:
4161 isl_pw_qpolynomial_free(data.res);
4162 isl_pw_qpolynomial_free(pwqp);
4163 return NULL;
4164 }
4165
4166 /* Construct a piecewise quasipolynomial that is constant on the given
4167 * domain. In particular, it is
4168 * 0 if cst == 0
4169 * 1 if cst == 1
4170 * infinity if cst == -1
4171 */
4172 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4173 __isl_take isl_basic_set *bset, int cst)
4174 {
4175 isl_dim *dim;
4176 isl_qpolynomial *qp;
4177
4178 if (!bset)
4179 return NULL;
4180
4181 bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
4182 dim = isl_basic_set_get_dim(bset);
4183 if (cst < 0)
4184 qp = isl_qpolynomial_infty(dim);
4185 else if (cst == 0)
4186 qp = isl_qpolynomial_zero(dim);
4187 else
4188 qp = isl_qpolynomial_one(dim);
4189 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4190 }
4191
4192 /* Factor bset, call fn on each of the factors and return the product.
4193 *
4194 * If no factors can be found, simply call fn on the input.
4195 * Otherwise, construct the factors based on the factorizer,
4196 * call fn on each factor and compute the product.
4197 */
4198 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4199 __isl_take isl_basic_set *bset,
4200 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4201 {
4202 int i, n;
4203 isl_dim *dim;
4204 isl_set *set;
4205 isl_factorizer *f;
4206 isl_qpolynomial *qp;
4207 isl_pw_qpolynomial *pwqp;
4208 unsigned nparam;
4209 unsigned nvar;
4210
4211 f = isl_basic_set_factorizer(bset);
4212 if (!f)
4213 goto error;
4214 if (f->n_group == 0) {
4215 isl_factorizer_free(f);
4216 return fn(bset);
4217 }
4218
4219 nparam = isl_basic_set_dim(bset, isl_dim_param);
4220 nvar = isl_basic_set_dim(bset, isl_dim_set);
4221
4222 dim = isl_basic_set_get_dim(bset);
4223 dim = isl_dim_domain(dim);
4224 set = isl_set_universe(isl_dim_copy(dim));
4225 qp = isl_qpolynomial_one(dim);
4226 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4227
4228 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4229
4230 for (i = 0, n = 0; i < f->n_group; ++i) {
4231 isl_basic_set *bset_i;
4232 isl_pw_qpolynomial *pwqp_i;
4233
4234 bset_i = isl_basic_set_copy(bset);
4235 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4236 nparam + n + f->len[i], nvar - n - f->len[i]);
4237 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4238 nparam, n);
4239 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4240 n + f->len[i], nvar - n - f->len[i]);
4241 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4242
4243 pwqp_i = fn(bset_i);
4244 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4245
4246 n += f->len[i];
4247 }
4248
4249 isl_basic_set_free(bset);
4250 isl_factorizer_free(f);
4251
4252 return pwqp;
4253 error:
4254 isl_basic_set_free(bset);
4255 return NULL;
4256 }
4257
4258 /* Factor bset, call fn on each of the factors and return the product.
4259 * The function is assumed to evaluate to zero on empty domains,
4260 * to one on zero-dimensional domains and to infinity on unbounded domains
4261 * and will not be called explicitly on zero-dimensional or unbounded domains.
4262 *
4263 * We first check for some special cases and remove all equalities.
4264 * Then we hand over control to compressed_multiplicative_call.
4265 */
4266 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4267 __isl_take isl_basic_set *bset,
4268 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4269 {
4270 int bounded;
4271 isl_morph *morph;
4272 isl_pw_qpolynomial *pwqp;
4273 unsigned orig_nvar, final_nvar;
4274
4275 if (!bset)
4276 return NULL;
4277
4278 if (isl_basic_set_plain_is_empty(bset))
4279 return constant_on_domain(bset, 0);
4280
4281 orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
4282
4283 if (orig_nvar == 0)
4284 return constant_on_domain(bset, 1);
4285
4286 bounded = isl_basic_set_is_bounded(bset);
4287 if (bounded < 0)
4288 goto error;
4289 if (!bounded)
4290 return constant_on_domain(bset, -1);
4291
4292 if (bset->n_eq == 0)
4293 return compressed_multiplicative_call(bset, fn);
4294
4295 morph = isl_basic_set_full_compression(bset);
4296 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4297
4298 final_nvar = isl_basic_set_dim(bset, isl_dim_set);
4299
4300 pwqp = compressed_multiplicative_call(bset, fn);
4301
4302 morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
4303 morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
4304 morph = isl_morph_inverse(morph);
4305
4306 pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
4307
4308 return pwqp;
4309 error:
4310 isl_basic_set_free(bset);
4311 return NULL;
4312 }
4313
4314 /* Drop all floors in "qp", turning each integer division [a/m] into
4315 * a rational division a/m. If "down" is set, then the integer division
4316 * is replaces by (a-(m-1))/m instead.
4317 */
4318 static __isl_give isl_qpolynomial *qp_drop_floors(
4319 __isl_take isl_qpolynomial *qp, int down)
4320 {
4321 int i;
4322 struct isl_upoly *s;
4323
4324 if (!qp)
4325 return NULL;
4326 if (qp->div->n_row == 0)
4327 return qp;
4328
4329 qp = isl_qpolynomial_cow(qp);
4330 if (!qp)
4331 return NULL;
4332
4333 for (i = qp->div->n_row - 1; i >= 0; --i) {
4334 if (down) {
4335 isl_int_sub(qp->div->row[i][1],
4336 qp->div->row[i][1], qp->div->row[i][0]);
4337 isl_int_add_ui(qp->div->row[i][1],
4338 qp->div->row[i][1], 1);
4339 }
4340 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4341 qp->div->row[i][0], qp->div->n_col - 1);
4342 qp = substitute_div(qp, i, s);
4343 if (!qp)
4344 return NULL;
4345 }
4346
4347 return qp;
4348 }
4349
4350 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4351 * a rational division a/m.
4352 */
4353 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4354 __isl_take isl_pw_qpolynomial *pwqp)
4355 {
4356 int i;
4357
4358 if (!pwqp)
4359 return NULL;
4360
4361 if (isl_pw_qpolynomial_is_zero(pwqp))
4362 return pwqp;
4363
4364 pwqp = isl_pw_qpolynomial_cow(pwqp);
4365 if (!pwqp)
4366 return NULL;
4367
4368 for (i = 0; i < pwqp->n; ++i) {
4369 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4370 if (!pwqp->p[i].qp)
4371 goto error;
4372 }
4373
4374 return pwqp;
4375 error:
4376 isl_pw_qpolynomial_free(pwqp);
4377 return NULL;
4378 }
4379
4380 /* Adjust all the integer divisions in "qp" such that they are at least
4381 * one over the given orthant (identified by "signs"). This ensures
4382 * that they will still be non-negative even after subtracting (m-1)/m.
4383 *
4384 * In particular, f is replaced by f' + v, changing f = [a/m]
4385 * to f' = [(a - m v)/m].
4386 * If the constant term k in a is smaller than m,
4387 * the constant term of v is set to floor(k/m) - 1.
4388 * For any other term, if the coefficient c and the variable x have
4389 * the same sign, then no changes are needed.
4390 * Otherwise, if the variable is positive (and c is negative),
4391 * then the coefficient of x in v is set to floor(c/m).
4392 * If the variable is negative (and c is positive),
4393 * then the coefficient of x in v is set to ceil(c/m).
4394 */
4395 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4396 int *signs)
4397 {
4398 int i, j;
4399 int total;
4400 isl_vec *v = NULL;
4401 struct isl_upoly *s;
4402
4403 qp = isl_qpolynomial_cow(qp);
4404 if (!qp)
4405 return NULL;
4406 qp->div = isl_mat_cow(qp->div);
4407 if (!qp->div)
4408 goto error;
4409
4410 total = isl_dim_total(qp->dim);
4411 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4412
4413 for (i = 0; i < qp->div->n_row; ++i) {
4414 isl_int *row = qp->div->row[i];
4415 v = isl_vec_clr(v);
4416 if (!v)
4417 goto error;
4418 if (isl_int_lt(row[1], row[0])) {
4419 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4420 isl_int_sub_ui(v->el[0], v->el[0], 1);
4421 isl_int_submul(row[1], row[0], v->el[0]);
4422 }
4423 for (j = 0; j < total; ++j) {
4424 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4425 continue;
4426 if (signs[j] < 0)
4427 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4428 else
4429 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4430 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4431 }
4432 for (j = 0; j < i; ++j) {
4433 if (isl_int_sgn(row[2 + total + j]) >= 0)
4434 continue;
4435 isl_int_fdiv_q(v->el[1 + total + j],
4436 row[2 + total + j], row[0]);
4437 isl_int_submul(row[2 + total + j],
4438 row[0], v->el[1 + total + j]);
4439 }
4440 for (j = i + 1; j < qp->div->n_row; ++j) {
4441 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4442 continue;
4443 isl_seq_combine(qp->div->row[j] + 1,
4444 qp->div->ctx->one, qp->div->row[j] + 1,
4445 qp->div->row[j][2 + total + i], v->el, v->size);
4446 }
4447 isl_int_set_si(v->el[1 + total + i], 1);
4448 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4449 qp->div->ctx->one, v->size);
4450 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4451 isl_upoly_free(s);
4452 if (!qp->upoly)
4453 goto error;
4454 }
4455
4456 isl_vec_free(v);
4457 return qp;
4458 error:
4459 isl_vec_free(v);
4460 isl_qpolynomial_free(qp);
4461 return NULL;
4462 }
4463
4464 struct isl_to_poly_data {
4465 int sign;
4466 isl_pw_qpolynomial *res;
4467 isl_qpolynomial *qp;
4468 };
4469
4470 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4471 * We first make all integer divisions positive and then split the
4472 * quasipolynomials into terms with sign data->sign (the direction
4473 * of the requested approximation) and terms with the opposite sign.
4474 * In the first set of terms, each integer division [a/m] is
4475 * overapproximated by a/m, while in the second it is underapproximated
4476 * by (a-(m-1))/m.
4477 */
4478 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4479 void *user)
4480 {
4481 struct isl_to_poly_data *data = user;
4482 isl_pw_qpolynomial *t;
4483 isl_qpolynomial *qp, *up, *down;
4484
4485 qp = isl_qpolynomial_copy(data->qp);
4486 qp = make_divs_pos(qp, signs);
4487
4488 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4489 up = qp_drop_floors(up, 0);
4490 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4491 down = qp_drop_floors(down, 1);
4492
4493 isl_qpolynomial_free(qp);
4494 qp = isl_qpolynomial_add(up, down);
4495
4496 t = isl_pw_qpolynomial_alloc(orthant, qp);
4497 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4498
4499 return 0;
4500 }
4501
4502 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4503 * the polynomial will be an overapproximation. If "sign" is negative,
4504 * it will be an underapproximation. If "sign" is zero, the approximation
4505 * will lie somewhere in between.
4506 *
4507 * In particular, is sign == 0, we simply drop the floors, turning
4508 * the integer divisions into rational divisions.
4509 * Otherwise, we split the domains into orthants, make all integer divisions
4510 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4511 * depending on the requested sign and the sign of the term in which
4512 * the integer division appears.
4513 */
4514 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4515 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4516 {
4517 int i;
4518 struct isl_to_poly_data data;
4519
4520 if (sign == 0)
4521 return pwqp_drop_floors(pwqp);
4522
4523 if (!pwqp)
4524 return NULL;
4525
4526 data.sign = sign;
4527 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
4528
4529 for (i = 0; i < pwqp->n; ++i) {
4530 if (pwqp->p[i].qp->div->n_row == 0) {
4531 isl_pw_qpolynomial *t;
4532 t = isl_pw_qpolynomial_alloc(
4533 isl_set_copy(pwqp->p[i].set),
4534 isl_qpolynomial_copy(pwqp->p[i].qp));
4535 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4536 continue;
4537 }
4538 data.qp = pwqp->p[i].qp;
4539 if (isl_set_foreach_orthant(pwqp->p[i].set,
4540 &to_polynomial_on_orthant, &data) < 0)
4541 goto error;
4542 }
4543
4544 isl_pw_qpolynomial_free(pwqp);
4545
4546 return data.res;
4547 error:
4548 isl_pw_qpolynomial_free(pwqp);
4549 isl_pw_qpolynomial_free(data.res);
4550 return NULL;
4551 }
4552
4553 static int poly_entry(void **entry, void *user)
4554 {
4555 int *sign = user;
4556 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4557
4558 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4559
4560 return *pwqp ? 0 : -1;
4561 }
4562
4563 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4564 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4565 {
4566 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4567 if (!upwqp)
4568 return NULL;
4569
4570 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4571 &poly_entry, &sign) < 0)
4572 goto error;
4573
4574 return upwqp;
4575 error:
4576 isl_union_pw_qpolynomial_free(upwqp);
4577 return NULL;
4578 }
4579
4580 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4581 __isl_take isl_qpolynomial *qp)
4582 {
4583 int i, k;
4584 isl_dim *dim;
4585 isl_vec *aff = NULL;
4586 isl_basic_map *bmap = NULL;
4587 unsigned pos;
4588 unsigned n_div;
4589
4590 if (!qp)
4591 return NULL;
4592 if (!isl_upoly_is_affine(qp->upoly))
4593 isl_die(qp->dim->ctx, isl_error_invalid,
4594 "input quasi-polynomial not affine", goto error);
4595 aff = isl_qpolynomial_extract_affine(qp);
4596 if (!aff)
4597 goto error;
4598 dim = isl_qpolynomial_get_dim(qp);
4599 dim = isl_dim_from_domain(dim);
4600 pos = 1 + isl_dim_offset(dim, isl_dim_out);
4601 dim = isl_dim_add(dim, isl_dim_out, 1);
4602 n_div = qp->div->n_row;
4603 bmap = isl_basic_map_alloc_dim(dim, n_div, 1, 2 * n_div);
4604
4605 for (i = 0; i < n_div; ++i) {
4606 k = isl_basic_map_alloc_div(bmap);
4607 if (k < 0)
4608 goto error;
4609 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4610 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4611 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4612 goto error;
4613 }
4614 k = isl_basic_map_alloc_equality(bmap);
4615 if (k < 0)
4616 goto error;
4617 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4618 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4619 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4620
4621 isl_vec_free(aff);
4622 isl_qpolynomial_free(qp);
4623 bmap = isl_basic_map_finalize(bmap);
4624 return bmap;
4625 error:
4626 isl_vec_free(aff);
4627 isl_qpolynomial_free(qp);
4628 isl_basic_map_free(bmap);
4629 return NULL;
4630 }
Integer set library