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isl_map_subtract.c: map_subtract: avoid use of isl_map_empty_like
[isl.git] / isl_polynomial.c
blobb3bc8c207523c7fe6ada2244cfad6d3ecf0cc6cb
1 /*
2 * Copyright 2010 INRIA Saclay
3 *
4 * Use of this software is governed by the MIT 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 #define ISL_DIM_H
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl_factorization.h>
16 #include <isl_lp_private.h>
17 #include <isl_seq.h>
18 #include <isl_union_map_private.h>
19 #include <isl_constraint_private.h>
20 #include <isl_polynomial_private.h>
21 #include <isl_point_private.h>
22 #include <isl_space_private.h>
23 #include <isl_mat_private.h>
24 #include <isl_vec_private.h>
25 #include <isl_range.h>
26 #include <isl_local_space_private.h>
27 #include <isl_aff_private.h>
28 #include <isl_val_private.h>
29 #include <isl_config.h>
30 #include <isl/deprecated/polynomial_int.h>
31
32 static unsigned pos(__isl_keep isl_space *dim, enum isl_dim_type type)
33 {
34 switch (type) {
35 case isl_dim_param: return 0;
36 case isl_dim_in: return dim->nparam;
37 case isl_dim_out: return dim->nparam + dim->n_in;
38 default: return 0;
39 }
40 }
41
42 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
43 {
44 if (!up)
45 return -1;
46
47 return up->var < 0;
48 }
49
50 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
51 {
52 if (!up)
53 return NULL;
54
55 isl_assert(up->ctx, up->var < 0, return NULL);
56
57 return (struct isl_upoly_cst *)up;
58 }
59
60 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
61 {
62 if (!up)
63 return NULL;
64
65 isl_assert(up->ctx, up->var >= 0, return NULL);
66
67 return (struct isl_upoly_rec *)up;
68 }
69
70 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
71 __isl_keep struct isl_upoly *up2)
72 {
73 int i;
74 struct isl_upoly_rec *rec1, *rec2;
75
76 if (!up1 || !up2)
77 return -1;
78 if (up1 == up2)
79 return 1;
80 if (up1->var != up2->var)
81 return 0;
82 if (isl_upoly_is_cst(up1)) {
83 struct isl_upoly_cst *cst1, *cst2;
84 cst1 = isl_upoly_as_cst(up1);
85 cst2 = isl_upoly_as_cst(up2);
86 if (!cst1 || !cst2)
87 return -1;
88 return isl_int_eq(cst1->n, cst2->n) &&
89 isl_int_eq(cst1->d, cst2->d);
90 }
91
92 rec1 = isl_upoly_as_rec(up1);
93 rec2 = isl_upoly_as_rec(up2);
94 if (!rec1 || !rec2)
95 return -1;
96
97 if (rec1->n != rec2->n)
98 return 0;
99
100 for (i = 0; i < rec1->n; ++i) {
101 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
102 if (eq < 0 || !eq)
103 return eq;
104 }
105
106 return 1;
107 }
108
109 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
110 {
111 struct isl_upoly_cst *cst;
112
113 if (!up)
114 return -1;
115 if (!isl_upoly_is_cst(up))
116 return 0;
117
118 cst = isl_upoly_as_cst(up);
119 if (!cst)
120 return -1;
121
122 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
123 }
124
125 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
126 {
127 struct isl_upoly_cst *cst;
128
129 if (!up)
130 return 0;
131 if (!isl_upoly_is_cst(up))
132 return 0;
133
134 cst = isl_upoly_as_cst(up);
135 if (!cst)
136 return 0;
137
138 return isl_int_sgn(cst->n);
139 }
140
141 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
142 {
143 struct isl_upoly_cst *cst;
144
145 if (!up)
146 return -1;
147 if (!isl_upoly_is_cst(up))
148 return 0;
149
150 cst = isl_upoly_as_cst(up);
151 if (!cst)
152 return -1;
153
154 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
155 }
156
157 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
158 {
159 struct isl_upoly_cst *cst;
160
161 if (!up)
162 return -1;
163 if (!isl_upoly_is_cst(up))
164 return 0;
165
166 cst = isl_upoly_as_cst(up);
167 if (!cst)
168 return -1;
169
170 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
171 }
172
173 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
174 {
175 struct isl_upoly_cst *cst;
176
177 if (!up)
178 return -1;
179 if (!isl_upoly_is_cst(up))
180 return 0;
181
182 cst = isl_upoly_as_cst(up);
183 if (!cst)
184 return -1;
185
186 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
187 }
188
189 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
190 {
191 struct isl_upoly_cst *cst;
192
193 if (!up)
194 return -1;
195 if (!isl_upoly_is_cst(up))
196 return 0;
197
198 cst = isl_upoly_as_cst(up);
199 if (!cst)
200 return -1;
201
202 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
203 }
204
205 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
206 {
207 struct isl_upoly_cst *cst;
208
209 if (!up)
210 return -1;
211 if (!isl_upoly_is_cst(up))
212 return 0;
213
214 cst = isl_upoly_as_cst(up);
215 if (!cst)
216 return -1;
217
218 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
219 }
220
221 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
222 {
223 struct isl_upoly_cst *cst;
224
225 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
226 if (!cst)
227 return NULL;
228
229 cst->up.ref = 1;
230 cst->up.ctx = ctx;
231 isl_ctx_ref(ctx);
232 cst->up.var = -1;
233
234 isl_int_init(cst->n);
235 isl_int_init(cst->d);
236
237 return cst;
238 }
239
240 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
241 {
242 struct isl_upoly_cst *cst;
243
244 cst = isl_upoly_cst_alloc(ctx);
245 if (!cst)
246 return NULL;
247
248 isl_int_set_si(cst->n, 0);
249 isl_int_set_si(cst->d, 1);
250
251 return &cst->up;
252 }
253
254 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
255 {
256 struct isl_upoly_cst *cst;
257
258 cst = isl_upoly_cst_alloc(ctx);
259 if (!cst)
260 return NULL;
261
262 isl_int_set_si(cst->n, 1);
263 isl_int_set_si(cst->d, 1);
264
265 return &cst->up;
266 }
267
268 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
269 {
270 struct isl_upoly_cst *cst;
271
272 cst = isl_upoly_cst_alloc(ctx);
273 if (!cst)
274 return NULL;
275
276 isl_int_set_si(cst->n, 1);
277 isl_int_set_si(cst->d, 0);
278
279 return &cst->up;
280 }
281
282 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
283 {
284 struct isl_upoly_cst *cst;
285
286 cst = isl_upoly_cst_alloc(ctx);
287 if (!cst)
288 return NULL;
289
290 isl_int_set_si(cst->n, -1);
291 isl_int_set_si(cst->d, 0);
292
293 return &cst->up;
294 }
295
296 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
297 {
298 struct isl_upoly_cst *cst;
299
300 cst = isl_upoly_cst_alloc(ctx);
301 if (!cst)
302 return NULL;
303
304 isl_int_set_si(cst->n, 0);
305 isl_int_set_si(cst->d, 0);
306
307 return &cst->up;
308 }
309
310 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
311 isl_int n, isl_int d)
312 {
313 struct isl_upoly_cst *cst;
314
315 cst = isl_upoly_cst_alloc(ctx);
316 if (!cst)
317 return NULL;
318
319 isl_int_set(cst->n, n);
320 isl_int_set(cst->d, d);
321
322 return &cst->up;
323 }
324
325 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
326 int var, int size)
327 {
328 struct isl_upoly_rec *rec;
329
330 isl_assert(ctx, var >= 0, return NULL);
331 isl_assert(ctx, size >= 0, return NULL);
332 rec = isl_calloc(ctx, struct isl_upoly_rec,
333 sizeof(struct isl_upoly_rec) +
334 size * sizeof(struct isl_upoly *));
335 if (!rec)
336 return NULL;
337
338 rec->up.ref = 1;
339 rec->up.ctx = ctx;
340 isl_ctx_ref(ctx);
341 rec->up.var = var;
342
343 rec->n = 0;
344 rec->size = size;
345
346 return rec;
347 }
348
349 __isl_give isl_qpolynomial *isl_qpolynomial_reset_domain_space(
350 __isl_take isl_qpolynomial *qp, __isl_take isl_space *dim)
351 {
352 qp = isl_qpolynomial_cow(qp);
353 if (!qp || !dim)
354 goto error;
355
356 isl_space_free(qp->dim);
357 qp->dim = dim;
358
359 return qp;
360 error:
361 isl_qpolynomial_free(qp);
362 isl_space_free(dim);
363 return NULL;
364 }
365
366 /* Reset the space of "qp". This function is called from isl_pw_templ.c
367 * and doesn't know if the space of an element object is represented
368 * directly or through its domain. It therefore passes along both.
369 */
370 __isl_give isl_qpolynomial *isl_qpolynomial_reset_space_and_domain(
371 __isl_take isl_qpolynomial *qp, __isl_take isl_space *space,
372 __isl_take isl_space *domain)
373 {
374 isl_space_free(space);
375 return isl_qpolynomial_reset_domain_space(qp, domain);
376 }
377
378 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
379 {
380 return qp ? qp->dim->ctx : NULL;
381 }
382
383 __isl_give isl_space *isl_qpolynomial_get_domain_space(
384 __isl_keep isl_qpolynomial *qp)
385 {
386 return qp ? isl_space_copy(qp->dim) : NULL;
387 }
388
389 __isl_give isl_space *isl_qpolynomial_get_space(__isl_keep isl_qpolynomial *qp)
390 {
391 isl_space *space;
392 if (!qp)
393 return NULL;
394 space = isl_space_copy(qp->dim);
395 space = isl_space_from_domain(space);
396 space = isl_space_add_dims(space, isl_dim_out, 1);
397 return space;
398 }
399
400 /* Externally, an isl_qpolynomial has a map space, but internally, the
401 * ls field corresponds to the domain of that space.
402 */
403 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
404 enum isl_dim_type type)
405 {
406 if (!qp)
407 return 0;
408 if (type == isl_dim_out)
409 return 1;
410 if (type == isl_dim_in)
411 type = isl_dim_set;
412 return isl_space_dim(qp->dim, type);
413 }
414
415 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
416 {
417 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
418 }
419
420 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
421 {
422 return qp ? isl_upoly_is_one(qp->upoly) : -1;
423 }
424
425 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
426 {
427 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
428 }
429
430 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
431 {
432 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
433 }
434
435 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
436 {
437 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
438 }
439
440 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
441 {
442 return qp ? isl_upoly_sgn(qp->upoly) : 0;
443 }
444
445 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
446 {
447 isl_int_clear(cst->n);
448 isl_int_clear(cst->d);
449 }
450
451 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
452 {
453 int i;
454
455 for (i = 0; i < rec->n; ++i)
456 isl_upoly_free(rec->p[i]);
457 }
458
459 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
460 {
461 if (!up)
462 return NULL;
463
464 up->ref++;
465 return up;
466 }
467
468 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
469 {
470 struct isl_upoly_cst *cst;
471 struct isl_upoly_cst *dup;
472
473 cst = isl_upoly_as_cst(up);
474 if (!cst)
475 return NULL;
476
477 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
478 if (!dup)
479 return NULL;
480 isl_int_set(dup->n, cst->n);
481 isl_int_set(dup->d, cst->d);
482
483 return &dup->up;
484 }
485
486 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
487 {
488 int i;
489 struct isl_upoly_rec *rec;
490 struct isl_upoly_rec *dup;
491
492 rec = isl_upoly_as_rec(up);
493 if (!rec)
494 return NULL;
495
496 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
497 if (!dup)
498 return NULL;
499
500 for (i = 0; i < rec->n; ++i) {
501 dup->p[i] = isl_upoly_copy(rec->p[i]);
502 if (!dup->p[i])
503 goto error;
504 dup->n++;
505 }
506
507 return &dup->up;
508 error:
509 isl_upoly_free(&dup->up);
510 return NULL;
511 }
512
513 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
514 {
515 if (!up)
516 return NULL;
517
518 if (isl_upoly_is_cst(up))
519 return isl_upoly_dup_cst(up);
520 else
521 return isl_upoly_dup_rec(up);
522 }
523
524 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
525 {
526 if (!up)
527 return NULL;
528
529 if (up->ref == 1)
530 return up;
531 up->ref--;
532 return isl_upoly_dup(up);
533 }
534
535 void isl_upoly_free(__isl_take struct isl_upoly *up)
536 {
537 if (!up)
538 return;
539
540 if (--up->ref > 0)
541 return;
542
543 if (up->var < 0)
544 upoly_free_cst((struct isl_upoly_cst *)up);
545 else
546 upoly_free_rec((struct isl_upoly_rec *)up);
547
548 isl_ctx_deref(up->ctx);
549 free(up);
550 }
551
552 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
553 {
554 isl_int gcd;
555
556 isl_int_init(gcd);
557 isl_int_gcd(gcd, cst->n, cst->d);
558 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
559 isl_int_divexact(cst->n, cst->n, gcd);
560 isl_int_divexact(cst->d, cst->d, gcd);
561 }
562 isl_int_clear(gcd);
563 }
564
565 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
566 __isl_take struct isl_upoly *up2)
567 {
568 struct isl_upoly_cst *cst1;
569 struct isl_upoly_cst *cst2;
570
571 up1 = isl_upoly_cow(up1);
572 if (!up1 || !up2)
573 goto error;
574
575 cst1 = isl_upoly_as_cst(up1);
576 cst2 = isl_upoly_as_cst(up2);
577
578 if (isl_int_eq(cst1->d, cst2->d))
579 isl_int_add(cst1->n, cst1->n, cst2->n);
580 else {
581 isl_int_mul(cst1->n, cst1->n, cst2->d);
582 isl_int_addmul(cst1->n, cst2->n, cst1->d);
583 isl_int_mul(cst1->d, cst1->d, cst2->d);
584 }
585
586 isl_upoly_cst_reduce(cst1);
587
588 isl_upoly_free(up2);
589 return up1;
590 error:
591 isl_upoly_free(up1);
592 isl_upoly_free(up2);
593 return NULL;
594 }
595
596 static __isl_give struct isl_upoly *replace_by_zero(
597 __isl_take struct isl_upoly *up)
598 {
599 struct isl_ctx *ctx;
600
601 if (!up)
602 return NULL;
603 ctx = up->ctx;
604 isl_upoly_free(up);
605 return isl_upoly_zero(ctx);
606 }
607
608 static __isl_give struct isl_upoly *replace_by_constant_term(
609 __isl_take struct isl_upoly *up)
610 {
611 struct isl_upoly_rec *rec;
612 struct isl_upoly *cst;
613
614 if (!up)
615 return NULL;
616
617 rec = isl_upoly_as_rec(up);
618 if (!rec)
619 goto error;
620 cst = isl_upoly_copy(rec->p[0]);
621 isl_upoly_free(up);
622 return cst;
623 error:
624 isl_upoly_free(up);
625 return NULL;
626 }
627
628 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
629 __isl_take struct isl_upoly *up2)
630 {
631 int i;
632 struct isl_upoly_rec *rec1, *rec2;
633
634 if (!up1 || !up2)
635 goto error;
636
637 if (isl_upoly_is_nan(up1)) {
638 isl_upoly_free(up2);
639 return up1;
640 }
641
642 if (isl_upoly_is_nan(up2)) {
643 isl_upoly_free(up1);
644 return up2;
645 }
646
647 if (isl_upoly_is_zero(up1)) {
648 isl_upoly_free(up1);
649 return up2;
650 }
651
652 if (isl_upoly_is_zero(up2)) {
653 isl_upoly_free(up2);
654 return up1;
655 }
656
657 if (up1->var < up2->var)
658 return isl_upoly_sum(up2, up1);
659
660 if (up2->var < up1->var) {
661 struct isl_upoly_rec *rec;
662 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
663 isl_upoly_free(up1);
664 return up2;
665 }
666 up1 = isl_upoly_cow(up1);
667 rec = isl_upoly_as_rec(up1);
668 if (!rec)
669 goto error;
670 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
671 if (rec->n == 1)
672 up1 = replace_by_constant_term(up1);
673 return up1;
674 }
675
676 if (isl_upoly_is_cst(up1))
677 return isl_upoly_sum_cst(up1, up2);
678
679 rec1 = isl_upoly_as_rec(up1);
680 rec2 = isl_upoly_as_rec(up2);
681 if (!rec1 || !rec2)
682 goto error;
683
684 if (rec1->n < rec2->n)
685 return isl_upoly_sum(up2, up1);
686
687 up1 = isl_upoly_cow(up1);
688 rec1 = isl_upoly_as_rec(up1);
689 if (!rec1)
690 goto error;
691
692 for (i = rec2->n - 1; i >= 0; --i) {
693 rec1->p[i] = isl_upoly_sum(rec1->p[i],
694 isl_upoly_copy(rec2->p[i]));
695 if (!rec1->p[i])
696 goto error;
697 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
698 isl_upoly_free(rec1->p[i]);
699 rec1->n--;
700 }
701 }
702
703 if (rec1->n == 0)
704 up1 = replace_by_zero(up1);
705 else if (rec1->n == 1)
706 up1 = replace_by_constant_term(up1);
707
708 isl_upoly_free(up2);
709
710 return up1;
711 error:
712 isl_upoly_free(up1);
713 isl_upoly_free(up2);
714 return NULL;
715 }
716
717 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
718 __isl_take struct isl_upoly *up, isl_int v)
719 {
720 struct isl_upoly_cst *cst;
721
722 up = isl_upoly_cow(up);
723 if (!up)
724 return NULL;
725
726 cst = isl_upoly_as_cst(up);
727
728 isl_int_addmul(cst->n, cst->d, v);
729
730 return up;
731 }
732
733 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
734 __isl_take struct isl_upoly *up, isl_int v)
735 {
736 struct isl_upoly_rec *rec;
737
738 if (!up)
739 return NULL;
740
741 if (isl_upoly_is_cst(up))
742 return isl_upoly_cst_add_isl_int(up, v);
743
744 up = isl_upoly_cow(up);
745 rec = isl_upoly_as_rec(up);
746 if (!rec)
747 goto error;
748
749 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
750 if (!rec->p[0])
751 goto error;
752
753 return up;
754 error:
755 isl_upoly_free(up);
756 return NULL;
757 }
758
759 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
760 __isl_take struct isl_upoly *up, isl_int v)
761 {
762 struct isl_upoly_cst *cst;
763
764 if (isl_upoly_is_zero(up))
765 return up;
766
767 up = isl_upoly_cow(up);
768 if (!up)
769 return NULL;
770
771 cst = isl_upoly_as_cst(up);
772
773 isl_int_mul(cst->n, cst->n, v);
774
775 return up;
776 }
777
778 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
779 __isl_take struct isl_upoly *up, isl_int v)
780 {
781 int i;
782 struct isl_upoly_rec *rec;
783
784 if (!up)
785 return NULL;
786
787 if (isl_upoly_is_cst(up))
788 return isl_upoly_cst_mul_isl_int(up, v);
789
790 up = isl_upoly_cow(up);
791 rec = isl_upoly_as_rec(up);
792 if (!rec)
793 goto error;
794
795 for (i = 0; i < rec->n; ++i) {
796 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
797 if (!rec->p[i])
798 goto error;
799 }
800
801 return up;
802 error:
803 isl_upoly_free(up);
804 return NULL;
805 }
806
807 /* Multiply the constant polynomial "up" by "v".
808 */
809 static __isl_give struct isl_upoly *isl_upoly_cst_scale_val(
810 __isl_take struct isl_upoly *up, __isl_keep isl_val *v)
811 {
812 struct isl_upoly_cst *cst;
813
814 if (isl_upoly_is_zero(up))
815 return up;
816
817 up = isl_upoly_cow(up);
818 if (!up)
819 return NULL;
820
821 cst = isl_upoly_as_cst(up);
822
823 isl_int_mul(cst->n, cst->n, v->n);
824 isl_int_mul(cst->d, cst->d, v->d);
825 isl_upoly_cst_reduce(cst);
826
827 return up;
828 }
829
830 /* Multiply the polynomial "up" by "v".
831 */
832 static __isl_give struct isl_upoly *isl_upoly_scale_val(
833 __isl_take struct isl_upoly *up, __isl_keep isl_val *v)
834 {
835 int i;
836 struct isl_upoly_rec *rec;
837
838 if (!up)
839 return NULL;
840
841 if (isl_upoly_is_cst(up))
842 return isl_upoly_cst_scale_val(up, v);
843
844 up = isl_upoly_cow(up);
845 rec = isl_upoly_as_rec(up);
846 if (!rec)
847 goto error;
848
849 for (i = 0; i < rec->n; ++i) {
850 rec->p[i] = isl_upoly_scale_val(rec->p[i], v);
851 if (!rec->p[i])
852 goto error;
853 }
854
855 return up;
856 error:
857 isl_upoly_free(up);
858 return NULL;
859 }
860
861 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
862 __isl_take struct isl_upoly *up2)
863 {
864 struct isl_upoly_cst *cst1;
865 struct isl_upoly_cst *cst2;
866
867 up1 = isl_upoly_cow(up1);
868 if (!up1 || !up2)
869 goto error;
870
871 cst1 = isl_upoly_as_cst(up1);
872 cst2 = isl_upoly_as_cst(up2);
873
874 isl_int_mul(cst1->n, cst1->n, cst2->n);
875 isl_int_mul(cst1->d, cst1->d, cst2->d);
876
877 isl_upoly_cst_reduce(cst1);
878
879 isl_upoly_free(up2);
880 return up1;
881 error:
882 isl_upoly_free(up1);
883 isl_upoly_free(up2);
884 return NULL;
885 }
886
887 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
888 __isl_take struct isl_upoly *up2)
889 {
890 struct isl_upoly_rec *rec1;
891 struct isl_upoly_rec *rec2;
892 struct isl_upoly_rec *res = NULL;
893 int i, j;
894 int size;
895
896 rec1 = isl_upoly_as_rec(up1);
897 rec2 = isl_upoly_as_rec(up2);
898 if (!rec1 || !rec2)
899 goto error;
900 size = rec1->n + rec2->n - 1;
901 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
902 if (!res)
903 goto error;
904
905 for (i = 0; i < rec1->n; ++i) {
906 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
907 isl_upoly_copy(rec1->p[i]));
908 if (!res->p[i])
909 goto error;
910 res->n++;
911 }
912 for (; i < size; ++i) {
913 res->p[i] = isl_upoly_zero(up1->ctx);
914 if (!res->p[i])
915 goto error;
916 res->n++;
917 }
918 for (i = 0; i < rec1->n; ++i) {
919 for (j = 1; j < rec2->n; ++j) {
920 struct isl_upoly *up;
921 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
922 isl_upoly_copy(rec1->p[i]));
923 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
924 if (!res->p[i + j])
925 goto error;
926 }
927 }
928
929 isl_upoly_free(up1);
930 isl_upoly_free(up2);
931
932 return &res->up;
933 error:
934 isl_upoly_free(up1);
935 isl_upoly_free(up2);
936 isl_upoly_free(&res->up);
937 return NULL;
938 }
939
940 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
941 __isl_take struct isl_upoly *up2)
942 {
943 if (!up1 || !up2)
944 goto error;
945
946 if (isl_upoly_is_nan(up1)) {
947 isl_upoly_free(up2);
948 return up1;
949 }
950
951 if (isl_upoly_is_nan(up2)) {
952 isl_upoly_free(up1);
953 return up2;
954 }
955
956 if (isl_upoly_is_zero(up1)) {
957 isl_upoly_free(up2);
958 return up1;
959 }
960
961 if (isl_upoly_is_zero(up2)) {
962 isl_upoly_free(up1);
963 return up2;
964 }
965
966 if (isl_upoly_is_one(up1)) {
967 isl_upoly_free(up1);
968 return up2;
969 }
970
971 if (isl_upoly_is_one(up2)) {
972 isl_upoly_free(up2);
973 return up1;
974 }
975
976 if (up1->var < up2->var)
977 return isl_upoly_mul(up2, up1);
978
979 if (up2->var < up1->var) {
980 int i;
981 struct isl_upoly_rec *rec;
982 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
983 isl_ctx *ctx = up1->ctx;
984 isl_upoly_free(up1);
985 isl_upoly_free(up2);
986 return isl_upoly_nan(ctx);
987 }
988 up1 = isl_upoly_cow(up1);
989 rec = isl_upoly_as_rec(up1);
990 if (!rec)
991 goto error;
992
993 for (i = 0; i < rec->n; ++i) {
994 rec->p[i] = isl_upoly_mul(rec->p[i],
995 isl_upoly_copy(up2));
996 if (!rec->p[i])
997 goto error;
998 }
999 isl_upoly_free(up2);
1000 return up1;
1001 }
1002
1003 if (isl_upoly_is_cst(up1))
1004 return isl_upoly_mul_cst(up1, up2);
1005
1006 return isl_upoly_mul_rec(up1, up2);
1007 error:
1008 isl_upoly_free(up1);
1009 isl_upoly_free(up2);
1010 return NULL;
1011 }
1012
1013 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
1014 unsigned power)
1015 {
1016 struct isl_upoly *res;
1017
1018 if (!up)
1019 return NULL;
1020 if (power == 1)
1021 return up;
1022
1023 if (power % 2)
1024 res = isl_upoly_copy(up);
1025 else
1026 res = isl_upoly_one(up->ctx);
1027
1028 while (power >>= 1) {
1029 up = isl_upoly_mul(up, isl_upoly_copy(up));
1030 if (power % 2)
1031 res = isl_upoly_mul(res, isl_upoly_copy(up));
1032 }
1033
1034 isl_upoly_free(up);
1035 return res;
1036 }
1037
1038 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_space *dim,
1039 unsigned n_div, __isl_take struct isl_upoly *up)
1040 {
1041 struct isl_qpolynomial *qp = NULL;
1042 unsigned total;
1043
1044 if (!dim || !up)
1045 goto error;
1046
1047 if (!isl_space_is_set(dim))
1048 isl_die(isl_space_get_ctx(dim), isl_error_invalid,
1049 "domain of polynomial should be a set", goto error);
1050
1051 total = isl_space_dim(dim, isl_dim_all);
1052
1053 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
1054 if (!qp)
1055 goto error;
1056
1057 qp->ref = 1;
1058 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
1059 if (!qp->div)
1060 goto error;
1061
1062 qp->dim = dim;
1063 qp->upoly = up;
1064
1065 return qp;
1066 error:
1067 isl_space_free(dim);
1068 isl_upoly_free(up);
1069 isl_qpolynomial_free(qp);
1070 return NULL;
1071 }
1072
1073 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
1074 {
1075 if (!qp)
1076 return NULL;
1077
1078 qp->ref++;
1079 return qp;
1080 }
1081
1082 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
1083 {
1084 struct isl_qpolynomial *dup;
1085
1086 if (!qp)
1087 return NULL;
1088
1089 dup = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row,
1090 isl_upoly_copy(qp->upoly));
1091 if (!dup)
1092 return NULL;
1093 isl_mat_free(dup->div);
1094 dup->div = isl_mat_copy(qp->div);
1095 if (!dup->div)
1096 goto error;
1097
1098 return dup;
1099 error:
1100 isl_qpolynomial_free(dup);
1101 return NULL;
1102 }
1103
1104 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1105 {
1106 if (!qp)
1107 return NULL;
1108
1109 if (qp->ref == 1)
1110 return qp;
1111 qp->ref--;
1112 return isl_qpolynomial_dup(qp);
1113 }
1114
1115 __isl_null isl_qpolynomial *isl_qpolynomial_free(
1116 __isl_take isl_qpolynomial *qp)
1117 {
1118 if (!qp)
1119 return NULL;
1120
1121 if (--qp->ref > 0)
1122 return NULL;
1123
1124 isl_space_free(qp->dim);
1125 isl_mat_free(qp->div);
1126 isl_upoly_free(qp->upoly);
1127
1128 free(qp);
1129 return NULL;
1130 }
1131
1132 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1133 {
1134 int i;
1135 struct isl_upoly_rec *rec;
1136 struct isl_upoly_cst *cst;
1137
1138 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1139 if (!rec)
1140 return NULL;
1141 for (i = 0; i < 1 + power; ++i) {
1142 rec->p[i] = isl_upoly_zero(ctx);
1143 if (!rec->p[i])
1144 goto error;
1145 rec->n++;
1146 }
1147 cst = isl_upoly_as_cst(rec->p[power]);
1148 isl_int_set_si(cst->n, 1);
1149
1150 return &rec->up;
1151 error:
1152 isl_upoly_free(&rec->up);
1153 return NULL;
1154 }
1155
1156 /* r array maps original positions to new positions.
1157 */
1158 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1159 int *r)
1160 {
1161 int i;
1162 struct isl_upoly_rec *rec;
1163 struct isl_upoly *base;
1164 struct isl_upoly *res;
1165
1166 if (isl_upoly_is_cst(up))
1167 return up;
1168
1169 rec = isl_upoly_as_rec(up);
1170 if (!rec)
1171 goto error;
1172
1173 isl_assert(up->ctx, rec->n >= 1, goto error);
1174
1175 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1176 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1177
1178 for (i = rec->n - 2; i >= 0; --i) {
1179 res = isl_upoly_mul(res, isl_upoly_copy(base));
1180 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1181 }
1182
1183 isl_upoly_free(base);
1184 isl_upoly_free(up);
1185
1186 return res;
1187 error:
1188 isl_upoly_free(up);
1189 return NULL;
1190 }
1191
1192 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1193 {
1194 int n_row, n_col;
1195 int equal;
1196
1197 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1198 div1->n_col >= div2->n_col, return -1);
1199
1200 if (div1->n_row == div2->n_row)
1201 return isl_mat_is_equal(div1, div2);
1202
1203 n_row = div1->n_row;
1204 n_col = div1->n_col;
1205 div1->n_row = div2->n_row;
1206 div1->n_col = div2->n_col;
1207
1208 equal = isl_mat_is_equal(div1, div2);
1209
1210 div1->n_row = n_row;
1211 div1->n_col = n_col;
1212
1213 return equal;
1214 }
1215
1216 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1217 {
1218 int li, lj;
1219
1220 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1221 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1222
1223 if (li != lj)
1224 return li - lj;
1225
1226 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1227 }
1228
1229 struct isl_div_sort_info {
1230 isl_mat *div;
1231 int row;
1232 };
1233
1234 static int div_sort_cmp(const void *p1, const void *p2)
1235 {
1236 const struct isl_div_sort_info *i1, *i2;
1237 i1 = (const struct isl_div_sort_info *) p1;
1238 i2 = (const struct isl_div_sort_info *) p2;
1239
1240 return cmp_row(i1->div, i1->row, i2->row);
1241 }
1242
1243 /* Sort divs and remove duplicates.
1244 */
1245 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1246 {
1247 int i;
1248 int skip;
1249 int len;
1250 struct isl_div_sort_info *array = NULL;
1251 int *pos = NULL, *at = NULL;
1252 int *reordering = NULL;
1253 unsigned div_pos;
1254
1255 if (!qp)
1256 return NULL;
1257 if (qp->div->n_row <= 1)
1258 return qp;
1259
1260 div_pos = isl_space_dim(qp->dim, isl_dim_all);
1261
1262 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1263 qp->div->n_row);
1264 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1265 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1266 len = qp->div->n_col - 2;
1267 reordering = isl_alloc_array(qp->div->ctx, int, len);
1268 if (!array || !pos || !at || !reordering)
1269 goto error;
1270
1271 for (i = 0; i < qp->div->n_row; ++i) {
1272 array[i].div = qp->div;
1273 array[i].row = i;
1274 pos[i] = i;
1275 at[i] = i;
1276 }
1277
1278 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1279 div_sort_cmp);
1280
1281 for (i = 0; i < div_pos; ++i)
1282 reordering[i] = i;
1283
1284 for (i = 0; i < qp->div->n_row; ++i) {
1285 if (pos[array[i].row] == i)
1286 continue;
1287 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1288 pos[at[i]] = pos[array[i].row];
1289 at[pos[array[i].row]] = at[i];
1290 at[i] = array[i].row;
1291 pos[array[i].row] = i;
1292 }
1293
1294 skip = 0;
1295 for (i = 0; i < len - div_pos; ++i) {
1296 if (i > 0 &&
1297 isl_seq_eq(qp->div->row[i - skip - 1],
1298 qp->div->row[i - skip], qp->div->n_col)) {
1299 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1300 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1301 2 + div_pos + i - skip);
1302 qp->div = isl_mat_drop_cols(qp->div,
1303 2 + div_pos + i - skip, 1);
1304 skip++;
1305 }
1306 reordering[div_pos + array[i].row] = div_pos + i - skip;
1307 }
1308
1309 qp->upoly = reorder(qp->upoly, reordering);
1310
1311 if (!qp->upoly || !qp->div)
1312 goto error;
1313
1314 free(at);
1315 free(pos);
1316 free(array);
1317 free(reordering);
1318
1319 return qp;
1320 error:
1321 free(at);
1322 free(pos);
1323 free(array);
1324 free(reordering);
1325 isl_qpolynomial_free(qp);
1326 return NULL;
1327 }
1328
1329 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1330 int *exp, int first)
1331 {
1332 int i;
1333 struct isl_upoly_rec *rec;
1334
1335 if (isl_upoly_is_cst(up))
1336 return up;
1337
1338 if (up->var < first)
1339 return up;
1340
1341 if (exp[up->var - first] == up->var - first)
1342 return up;
1343
1344 up = isl_upoly_cow(up);
1345 if (!up)
1346 goto error;
1347
1348 up->var = exp[up->var - first] + first;
1349
1350 rec = isl_upoly_as_rec(up);
1351 if (!rec)
1352 goto error;
1353
1354 for (i = 0; i < rec->n; ++i) {
1355 rec->p[i] = expand(rec->p[i], exp, first);
1356 if (!rec->p[i])
1357 goto error;
1358 }
1359
1360 return up;
1361 error:
1362 isl_upoly_free(up);
1363 return NULL;
1364 }
1365
1366 static __isl_give isl_qpolynomial *with_merged_divs(
1367 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1368 __isl_take isl_qpolynomial *qp2),
1369 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1370 {
1371 int *exp1 = NULL;
1372 int *exp2 = NULL;
1373 isl_mat *div = NULL;
1374 int n_div1, n_div2;
1375
1376 qp1 = isl_qpolynomial_cow(qp1);
1377 qp2 = isl_qpolynomial_cow(qp2);
1378
1379 if (!qp1 || !qp2)
1380 goto error;
1381
1382 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1383 qp1->div->n_col >= qp2->div->n_col, goto error);
1384
1385 n_div1 = qp1->div->n_row;
1386 n_div2 = qp2->div->n_row;
1387 exp1 = isl_alloc_array(qp1->div->ctx, int, n_div1);
1388 exp2 = isl_alloc_array(qp2->div->ctx, int, n_div2);
1389 if ((n_div1 && !exp1) || (n_div2 && !exp2))
1390 goto error;
1391
1392 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1393 if (!div)
1394 goto error;
1395
1396 isl_mat_free(qp1->div);
1397 qp1->div = isl_mat_copy(div);
1398 isl_mat_free(qp2->div);
1399 qp2->div = isl_mat_copy(div);
1400
1401 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1402 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1403
1404 if (!qp1->upoly || !qp2->upoly)
1405 goto error;
1406
1407 isl_mat_free(div);
1408 free(exp1);
1409 free(exp2);
1410
1411 return fn(qp1, qp2);
1412 error:
1413 isl_mat_free(div);
1414 free(exp1);
1415 free(exp2);
1416 isl_qpolynomial_free(qp1);
1417 isl_qpolynomial_free(qp2);
1418 return NULL;
1419 }
1420
1421 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1422 __isl_take isl_qpolynomial *qp2)
1423 {
1424 qp1 = isl_qpolynomial_cow(qp1);
1425
1426 if (!qp1 || !qp2)
1427 goto error;
1428
1429 if (qp1->div->n_row < qp2->div->n_row)
1430 return isl_qpolynomial_add(qp2, qp1);
1431
1432 isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1433 if (!compatible_divs(qp1->div, qp2->div))
1434 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1435
1436 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1437 if (!qp1->upoly)
1438 goto error;
1439
1440 isl_qpolynomial_free(qp2);
1441
1442 return qp1;
1443 error:
1444 isl_qpolynomial_free(qp1);
1445 isl_qpolynomial_free(qp2);
1446 return NULL;
1447 }
1448
1449 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1450 __isl_keep isl_set *dom,
1451 __isl_take isl_qpolynomial *qp1,
1452 __isl_take isl_qpolynomial *qp2)
1453 {
1454 qp1 = isl_qpolynomial_add(qp1, qp2);
1455 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1456 return qp1;
1457 }
1458
1459 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1460 __isl_take isl_qpolynomial *qp2)
1461 {
1462 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1463 }
1464
1465 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1466 __isl_take isl_qpolynomial *qp, isl_int v)
1467 {
1468 if (isl_int_is_zero(v))
1469 return qp;
1470
1471 qp = isl_qpolynomial_cow(qp);
1472 if (!qp)
1473 return NULL;
1474
1475 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1476 if (!qp->upoly)
1477 goto error;
1478
1479 return qp;
1480 error:
1481 isl_qpolynomial_free(qp);
1482 return NULL;
1483
1484 }
1485
1486 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1487 {
1488 if (!qp)
1489 return NULL;
1490
1491 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1492 }
1493
1494 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1495 __isl_take isl_qpolynomial *qp, isl_int v)
1496 {
1497 if (isl_int_is_one(v))
1498 return qp;
1499
1500 if (qp && isl_int_is_zero(v)) {
1501 isl_qpolynomial *zero;
1502 zero = isl_qpolynomial_zero_on_domain(isl_space_copy(qp->dim));
1503 isl_qpolynomial_free(qp);
1504 return zero;
1505 }
1506
1507 qp = isl_qpolynomial_cow(qp);
1508 if (!qp)
1509 return NULL;
1510
1511 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1512 if (!qp->upoly)
1513 goto error;
1514
1515 return qp;
1516 error:
1517 isl_qpolynomial_free(qp);
1518 return NULL;
1519 }
1520
1521 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
1522 __isl_take isl_qpolynomial *qp, isl_int v)
1523 {
1524 return isl_qpolynomial_mul_isl_int(qp, v);
1525 }
1526
1527 /* Multiply "qp" by "v".
1528 */
1529 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
1530 __isl_take isl_qpolynomial *qp, __isl_take isl_val *v)
1531 {
1532 if (!qp || !v)
1533 goto error;
1534
1535 if (!isl_val_is_rat(v))
1536 isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
1537 "expecting rational factor", goto error);
1538
1539 if (isl_val_is_one(v)) {
1540 isl_val_free(v);
1541 return qp;
1542 }
1543
1544 if (isl_val_is_zero(v)) {
1545 isl_space *space;
1546
1547 space = isl_qpolynomial_get_domain_space(qp);
1548 isl_qpolynomial_free(qp);
1549 isl_val_free(v);
1550 return isl_qpolynomial_zero_on_domain(space);
1551 }
1552
1553 qp = isl_qpolynomial_cow(qp);
1554 if (!qp)
1555 goto error;
1556
1557 qp->upoly = isl_upoly_scale_val(qp->upoly, v);
1558 if (!qp->upoly)
1559 qp = isl_qpolynomial_free(qp);
1560
1561 isl_val_free(v);
1562 return qp;
1563 error:
1564 isl_val_free(v);
1565 isl_qpolynomial_free(qp);
1566 return NULL;
1567 }
1568
1569 /* Divide "qp" by "v".
1570 */
1571 __isl_give isl_qpolynomial *isl_qpolynomial_scale_down_val(
1572 __isl_take isl_qpolynomial *qp, __isl_take isl_val *v)
1573 {
1574 if (!qp || !v)
1575 goto error;
1576
1577 if (!isl_val_is_rat(v))
1578 isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
1579 "expecting rational factor", goto error);
1580 if (isl_val_is_zero(v))
1581 isl_die(isl_val_get_ctx(v), isl_error_invalid,
1582 "cannot scale down by zero", goto error);
1583
1584 return isl_qpolynomial_scale_val(qp, isl_val_inv(v));
1585 error:
1586 isl_val_free(v);
1587 isl_qpolynomial_free(qp);
1588 return NULL;
1589 }
1590
1591 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1592 __isl_take isl_qpolynomial *qp2)
1593 {
1594 qp1 = isl_qpolynomial_cow(qp1);
1595
1596 if (!qp1 || !qp2)
1597 goto error;
1598
1599 if (qp1->div->n_row < qp2->div->n_row)
1600 return isl_qpolynomial_mul(qp2, qp1);
1601
1602 isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1603 if (!compatible_divs(qp1->div, qp2->div))
1604 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1605
1606 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1607 if (!qp1->upoly)
1608 goto error;
1609
1610 isl_qpolynomial_free(qp2);
1611
1612 return qp1;
1613 error:
1614 isl_qpolynomial_free(qp1);
1615 isl_qpolynomial_free(qp2);
1616 return NULL;
1617 }
1618
1619 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1620 unsigned power)
1621 {
1622 qp = isl_qpolynomial_cow(qp);
1623
1624 if (!qp)
1625 return NULL;
1626
1627 qp->upoly = isl_upoly_pow(qp->upoly, power);
1628 if (!qp->upoly)
1629 goto error;
1630
1631 return qp;
1632 error:
1633 isl_qpolynomial_free(qp);
1634 return NULL;
1635 }
1636
1637 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
1638 __isl_take isl_pw_qpolynomial *pwqp, unsigned power)
1639 {
1640 int i;
1641
1642 if (power == 1)
1643 return pwqp;
1644
1645 pwqp = isl_pw_qpolynomial_cow(pwqp);
1646 if (!pwqp)
1647 return NULL;
1648
1649 for (i = 0; i < pwqp->n; ++i) {
1650 pwqp->p[i].qp = isl_qpolynomial_pow(pwqp->p[i].qp, power);
1651 if (!pwqp->p[i].qp)
1652 return isl_pw_qpolynomial_free(pwqp);
1653 }
1654
1655 return pwqp;
1656 }
1657
1658 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
1659 __isl_take isl_space *dim)
1660 {
1661 if (!dim)
1662 return NULL;
1663 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1664 }
1665
1666 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
1667 __isl_take isl_space *dim)
1668 {
1669 if (!dim)
1670 return NULL;
1671 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1672 }
1673
1674 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
1675 __isl_take isl_space *dim)
1676 {
1677 if (!dim)
1678 return NULL;
1679 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1680 }
1681
1682 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
1683 __isl_take isl_space *dim)
1684 {
1685 if (!dim)
1686 return NULL;
1687 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1688 }
1689
1690 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
1691 __isl_take isl_space *dim)
1692 {
1693 if (!dim)
1694 return NULL;
1695 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1696 }
1697
1698 __isl_give isl_qpolynomial *isl_qpolynomial_cst_on_domain(
1699 __isl_take isl_space *dim,
1700 isl_int v)
1701 {
1702 struct isl_qpolynomial *qp;
1703 struct isl_upoly_cst *cst;
1704
1705 if (!dim)
1706 return NULL;
1707
1708 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1709 if (!qp)
1710 return NULL;
1711
1712 cst = isl_upoly_as_cst(qp->upoly);
1713 isl_int_set(cst->n, v);
1714
1715 return qp;
1716 }
1717
1718 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1719 isl_int *n, isl_int *d)
1720 {
1721 struct isl_upoly_cst *cst;
1722
1723 if (!qp)
1724 return -1;
1725
1726 if (!isl_upoly_is_cst(qp->upoly))
1727 return 0;
1728
1729 cst = isl_upoly_as_cst(qp->upoly);
1730 if (!cst)
1731 return -1;
1732
1733 if (n)
1734 isl_int_set(*n, cst->n);
1735 if (d)
1736 isl_int_set(*d, cst->d);
1737
1738 return 1;
1739 }
1740
1741 /* Return the constant term of "up".
1742 */
1743 static __isl_give isl_val *isl_upoly_get_constant_val(
1744 __isl_keep struct isl_upoly *up)
1745 {
1746 struct isl_upoly_cst *cst;
1747
1748 if (!up)
1749 return NULL;
1750
1751 while (!isl_upoly_is_cst(up)) {
1752 struct isl_upoly_rec *rec;
1753
1754 rec = isl_upoly_as_rec(up);
1755 if (!rec)
1756 return NULL;
1757 up = rec->p[0];
1758 }
1759
1760 cst = isl_upoly_as_cst(up);
1761 if (!cst)
1762 return NULL;
1763 return isl_val_rat_from_isl_int(cst->up.ctx, cst->n, cst->d);
1764 }
1765
1766 /* Return the constant term of "qp".
1767 */
1768 __isl_give isl_val *isl_qpolynomial_get_constant_val(
1769 __isl_keep isl_qpolynomial *qp)
1770 {
1771 if (!qp)
1772 return NULL;
1773
1774 return isl_upoly_get_constant_val(qp->upoly);
1775 }
1776
1777 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1778 {
1779 int is_cst;
1780 struct isl_upoly_rec *rec;
1781
1782 if (!up)
1783 return -1;
1784
1785 if (up->var < 0)
1786 return 1;
1787
1788 rec = isl_upoly_as_rec(up);
1789 if (!rec)
1790 return -1;
1791
1792 if (rec->n > 2)
1793 return 0;
1794
1795 isl_assert(up->ctx, rec->n > 1, return -1);
1796
1797 is_cst = isl_upoly_is_cst(rec->p[1]);
1798 if (is_cst < 0)
1799 return -1;
1800 if (!is_cst)
1801 return 0;
1802
1803 return isl_upoly_is_affine(rec->p[0]);
1804 }
1805
1806 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1807 {
1808 if (!qp)
1809 return -1;
1810
1811 if (qp->div->n_row > 0)
1812 return 0;
1813
1814 return isl_upoly_is_affine(qp->upoly);
1815 }
1816
1817 static void update_coeff(__isl_keep isl_vec *aff,
1818 __isl_keep struct isl_upoly_cst *cst, int pos)
1819 {
1820 isl_int gcd;
1821 isl_int f;
1822
1823 if (isl_int_is_zero(cst->n))
1824 return;
1825
1826 isl_int_init(gcd);
1827 isl_int_init(f);
1828 isl_int_gcd(gcd, cst->d, aff->el[0]);
1829 isl_int_divexact(f, cst->d, gcd);
1830 isl_int_divexact(gcd, aff->el[0], gcd);
1831 isl_seq_scale(aff->el, aff->el, f, aff->size);
1832 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1833 isl_int_clear(gcd);
1834 isl_int_clear(f);
1835 }
1836
1837 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1838 __isl_keep isl_vec *aff)
1839 {
1840 struct isl_upoly_cst *cst;
1841 struct isl_upoly_rec *rec;
1842
1843 if (!up || !aff)
1844 return -1;
1845
1846 if (up->var < 0) {
1847 struct isl_upoly_cst *cst;
1848
1849 cst = isl_upoly_as_cst(up);
1850 if (!cst)
1851 return -1;
1852 update_coeff(aff, cst, 0);
1853 return 0;
1854 }
1855
1856 rec = isl_upoly_as_rec(up);
1857 if (!rec)
1858 return -1;
1859 isl_assert(up->ctx, rec->n == 2, return -1);
1860
1861 cst = isl_upoly_as_cst(rec->p[1]);
1862 if (!cst)
1863 return -1;
1864 update_coeff(aff, cst, 1 + up->var);
1865
1866 return isl_upoly_update_affine(rec->p[0], aff);
1867 }
1868
1869 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1870 __isl_keep isl_qpolynomial *qp)
1871 {
1872 isl_vec *aff;
1873 unsigned d;
1874
1875 if (!qp)
1876 return NULL;
1877
1878 d = isl_space_dim(qp->dim, isl_dim_all);
1879 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1880 if (!aff)
1881 return NULL;
1882
1883 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1884 isl_int_set_si(aff->el[0], 1);
1885
1886 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1887 goto error;
1888
1889 return aff;
1890 error:
1891 isl_vec_free(aff);
1892 return NULL;
1893 }
1894
1895 /* Is "qp1" obviously equal to "qp2"?
1896 *
1897 * NaN is not equal to anything, not even to another NaN.
1898 */
1899 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1900 __isl_keep isl_qpolynomial *qp2)
1901 {
1902 int equal;
1903
1904 if (!qp1 || !qp2)
1905 return -1;
1906
1907 if (isl_qpolynomial_is_nan(qp1) || isl_qpolynomial_is_nan(qp2))
1908 return 0;
1909
1910 equal = isl_space_is_equal(qp1->dim, qp2->dim);
1911 if (equal < 0 || !equal)
1912 return equal;
1913
1914 equal = isl_mat_is_equal(qp1->div, qp2->div);
1915 if (equal < 0 || !equal)
1916 return equal;
1917
1918 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1919 }
1920
1921 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1922 {
1923 int i;
1924 struct isl_upoly_rec *rec;
1925
1926 if (isl_upoly_is_cst(up)) {
1927 struct isl_upoly_cst *cst;
1928 cst = isl_upoly_as_cst(up);
1929 if (!cst)
1930 return;
1931 isl_int_lcm(*d, *d, cst->d);
1932 return;
1933 }
1934
1935 rec = isl_upoly_as_rec(up);
1936 if (!rec)
1937 return;
1938
1939 for (i = 0; i < rec->n; ++i)
1940 upoly_update_den(rec->p[i], d);
1941 }
1942
1943 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1944 {
1945 isl_int_set_si(*d, 1);
1946 if (!qp)
1947 return;
1948 upoly_update_den(qp->upoly, d);
1949 }
1950
1951 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow_on_domain(
1952 __isl_take isl_space *dim, int pos, int power)
1953 {
1954 struct isl_ctx *ctx;
1955
1956 if (!dim)
1957 return NULL;
1958
1959 ctx = dim->ctx;
1960
1961 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1962 }
1963
1964 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(__isl_take isl_space *dim,
1965 enum isl_dim_type type, unsigned pos)
1966 {
1967 if (!dim)
1968 return NULL;
1969
1970 isl_assert(dim->ctx, isl_space_dim(dim, isl_dim_in) == 0, goto error);
1971 isl_assert(dim->ctx, pos < isl_space_dim(dim, type), goto error);
1972
1973 if (type == isl_dim_set)
1974 pos += isl_space_dim(dim, isl_dim_param);
1975
1976 return isl_qpolynomial_var_pow_on_domain(dim, pos, 1);
1977 error:
1978 isl_space_free(dim);
1979 return NULL;
1980 }
1981
1982 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1983 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1984 {
1985 int i;
1986 struct isl_upoly_rec *rec;
1987 struct isl_upoly *base, *res;
1988
1989 if (!up)
1990 return NULL;
1991
1992 if (isl_upoly_is_cst(up))
1993 return up;
1994
1995 if (up->var < first)
1996 return up;
1997
1998 rec = isl_upoly_as_rec(up);
1999 if (!rec)
2000 goto error;
2001
2002 isl_assert(up->ctx, rec->n >= 1, goto error);
2003
2004 if (up->var >= first + n)
2005 base = isl_upoly_var_pow(up->ctx, up->var, 1);
2006 else
2007 base = isl_upoly_copy(subs[up->var - first]);
2008
2009 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
2010 for (i = rec->n - 2; i >= 0; --i) {
2011 struct isl_upoly *t;
2012 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
2013 res = isl_upoly_mul(res, isl_upoly_copy(base));
2014 res = isl_upoly_sum(res, t);
2015 }
2016
2017 isl_upoly_free(base);
2018 isl_upoly_free(up);
2019
2020 return res;
2021 error:
2022 isl_upoly_free(up);
2023 return NULL;
2024 }
2025
2026 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
2027 isl_int denom, unsigned len)
2028 {
2029 int i;
2030 struct isl_upoly *up;
2031
2032 isl_assert(ctx, len >= 1, return NULL);
2033
2034 up = isl_upoly_rat_cst(ctx, f[0], denom);
2035 for (i = 0; i < len - 1; ++i) {
2036 struct isl_upoly *t;
2037 struct isl_upoly *c;
2038
2039 if (isl_int_is_zero(f[1 + i]))
2040 continue;
2041
2042 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
2043 t = isl_upoly_var_pow(ctx, i, 1);
2044 t = isl_upoly_mul(c, t);
2045 up = isl_upoly_sum(up, t);
2046 }
2047
2048 return up;
2049 }
2050
2051 /* Remove common factor of non-constant terms and denominator.
2052 */
2053 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
2054 {
2055 isl_ctx *ctx = qp->div->ctx;
2056 unsigned total = qp->div->n_col - 2;
2057
2058 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
2059 isl_int_gcd(ctx->normalize_gcd,
2060 ctx->normalize_gcd, qp->div->row[div][0]);
2061 if (isl_int_is_one(ctx->normalize_gcd))
2062 return;
2063
2064 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
2065 ctx->normalize_gcd, total);
2066 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
2067 ctx->normalize_gcd);
2068 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
2069 ctx->normalize_gcd);
2070 }
2071
2072 /* Replace the integer division identified by "div" by the polynomial "s".
2073 * The integer division is assumed not to appear in the definition
2074 * of any other integer divisions.
2075 */
2076 static __isl_give isl_qpolynomial *substitute_div(
2077 __isl_take isl_qpolynomial *qp,
2078 int div, __isl_take struct isl_upoly *s)
2079 {
2080 int i;
2081 int total;
2082 int *reordering;
2083
2084 if (!qp || !s)
2085 goto error;
2086
2087 qp = isl_qpolynomial_cow(qp);
2088 if (!qp)
2089 goto error;
2090
2091 total = isl_space_dim(qp->dim, isl_dim_all);
2092 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
2093 if (!qp->upoly)
2094 goto error;
2095
2096 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
2097 if (!reordering)
2098 goto error;
2099 for (i = 0; i < total + div; ++i)
2100 reordering[i] = i;
2101 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
2102 reordering[i] = i - 1;
2103 qp->div = isl_mat_drop_rows(qp->div, div, 1);
2104 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
2105 qp->upoly = reorder(qp->upoly, reordering);
2106 free(reordering);
2107
2108 if (!qp->upoly || !qp->div)
2109 goto error;
2110
2111 isl_upoly_free(s);
2112 return qp;
2113 error:
2114 isl_qpolynomial_free(qp);
2115 isl_upoly_free(s);
2116 return NULL;
2117 }
2118
2119 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2120 * divisions because d is equal to 1 by their definition, i.e., e.
2121 */
2122 static __isl_give isl_qpolynomial *substitute_non_divs(
2123 __isl_take isl_qpolynomial *qp)
2124 {
2125 int i, j;
2126 int total;
2127 struct isl_upoly *s;
2128
2129 if (!qp)
2130 return NULL;
2131
2132 total = isl_space_dim(qp->dim, isl_dim_all);
2133 for (i = 0; qp && i < qp->div->n_row; ++i) {
2134 if (!isl_int_is_one(qp->div->row[i][0]))
2135 continue;
2136 for (j = i + 1; j < qp->div->n_row; ++j) {
2137 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
2138 continue;
2139 isl_seq_combine(qp->div->row[j] + 1,
2140 qp->div->ctx->one, qp->div->row[j] + 1,
2141 qp->div->row[j][2 + total + i],
2142 qp->div->row[i] + 1, 1 + total + i);
2143 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
2144 normalize_div(qp, j);
2145 }
2146 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
2147 qp->div->row[i][0], qp->div->n_col - 1);
2148 qp = substitute_div(qp, i, s);
2149 --i;
2150 }
2151
2152 return qp;
2153 }
2154
2155 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2156 * with d the denominator. When replacing the coefficient e of x by
2157 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2158 * inside the division, so we need to add floor(e/d) * x outside.
2159 * That is, we replace q by q' + floor(e/d) * x and we therefore need
2160 * to adjust the coefficient of x in each later div that depends on the
2161 * current div "div" and also in the affine expression "aff"
2162 * (if it too depends on "div").
2163 */
2164 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
2165 __isl_keep isl_vec *aff)
2166 {
2167 int i, j;
2168 isl_int v;
2169 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2170
2171 isl_int_init(v);
2172 for (i = 0; i < 1 + total + div; ++i) {
2173 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
2174 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
2175 continue;
2176 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
2177 isl_int_fdiv_r(qp->div->row[div][1 + i],
2178 qp->div->row[div][1 + i], qp->div->row[div][0]);
2179 if (!isl_int_is_zero(aff->el[1 + total + div]))
2180 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
2181 for (j = div + 1; j < qp->div->n_row; ++j) {
2182 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
2183 continue;
2184 isl_int_addmul(qp->div->row[j][1 + i],
2185 v, qp->div->row[j][2 + total + div]);
2186 }
2187 }
2188 isl_int_clear(v);
2189 }
2190
2191 /* Check if the last non-zero coefficient is bigger that half of the
2192 * denominator. If so, we will invert the div to further reduce the number
2193 * of distinct divs that may appear.
2194 * If the last non-zero coefficient is exactly half the denominator,
2195 * then we continue looking for earlier coefficients that are bigger
2196 * than half the denominator.
2197 */
2198 static int needs_invert(__isl_keep isl_mat *div, int row)
2199 {
2200 int i;
2201 int cmp;
2202
2203 for (i = div->n_col - 1; i >= 1; --i) {
2204 if (isl_int_is_zero(div->row[row][i]))
2205 continue;
2206 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
2207 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
2208 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
2209 if (cmp)
2210 return cmp > 0;
2211 if (i == 1)
2212 return 1;
2213 }
2214
2215 return 0;
2216 }
2217
2218 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2219 * We only invert the coefficients of e (and the coefficient of q in
2220 * later divs and in "aff"). After calling this function, the
2221 * coefficients of e should be reduced again.
2222 */
2223 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
2224 __isl_keep isl_vec *aff)
2225 {
2226 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2227
2228 isl_seq_neg(qp->div->row[div] + 1,
2229 qp->div->row[div] + 1, qp->div->n_col - 1);
2230 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2231 isl_int_add(qp->div->row[div][1],
2232 qp->div->row[div][1], qp->div->row[div][0]);
2233 if (!isl_int_is_zero(aff->el[1 + total + div]))
2234 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2235 isl_mat_col_mul(qp->div, 2 + total + div,
2236 qp->div->ctx->negone, 2 + total + div);
2237 }
2238
2239 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2240 * in the interval [0, d-1], with d the denominator and such that the
2241 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2242 *
2243 * After the reduction, some divs may have become redundant or identical,
2244 * so we call substitute_non_divs and sort_divs. If these functions
2245 * eliminate divs or merge two or more divs into one, the coefficients
2246 * of the enclosing divs may have to be reduced again, so we call
2247 * ourselves recursively if the number of divs decreases.
2248 */
2249 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2250 {
2251 int i;
2252 isl_vec *aff = NULL;
2253 struct isl_upoly *s;
2254 unsigned n_div;
2255
2256 if (!qp)
2257 return NULL;
2258
2259 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2260 aff = isl_vec_clr(aff);
2261 if (!aff)
2262 goto error;
2263
2264 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2265
2266 for (i = 0; i < qp->div->n_row; ++i) {
2267 normalize_div(qp, i);
2268 reduce_div(qp, i, aff);
2269 if (needs_invert(qp->div, i)) {
2270 invert_div(qp, i, aff);
2271 reduce_div(qp, i, aff);
2272 }
2273 }
2274
2275 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2276 qp->div->ctx->one, aff->size);
2277 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2278 isl_upoly_free(s);
2279 if (!qp->upoly)
2280 goto error;
2281
2282 isl_vec_free(aff);
2283
2284 n_div = qp->div->n_row;
2285 qp = substitute_non_divs(qp);
2286 qp = sort_divs(qp);
2287 if (qp && qp->div->n_row < n_div)
2288 return reduce_divs(qp);
2289
2290 return qp;
2291 error:
2292 isl_qpolynomial_free(qp);
2293 isl_vec_free(aff);
2294 return NULL;
2295 }
2296
2297 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
2298 __isl_take isl_space *dim, const isl_int n, const isl_int d)
2299 {
2300 struct isl_qpolynomial *qp;
2301 struct isl_upoly_cst *cst;
2302
2303 if (!dim)
2304 return NULL;
2305
2306 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2307 if (!qp)
2308 return NULL;
2309
2310 cst = isl_upoly_as_cst(qp->upoly);
2311 isl_int_set(cst->n, n);
2312 isl_int_set(cst->d, d);
2313
2314 return qp;
2315 }
2316
2317 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2318 */
2319 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2320 __isl_take isl_space *domain, __isl_take isl_val *val)
2321 {
2322 isl_qpolynomial *qp;
2323 struct isl_upoly_cst *cst;
2324
2325 if (!domain || !val)
2326 goto error;
2327
2328 qp = isl_qpolynomial_alloc(isl_space_copy(domain), 0,
2329 isl_upoly_zero(domain->ctx));
2330 if (!qp)
2331 goto error;
2332
2333 cst = isl_upoly_as_cst(qp->upoly);
2334 isl_int_set(cst->n, val->n);
2335 isl_int_set(cst->d, val->d);
2336
2337 isl_space_free(domain);
2338 isl_val_free(val);
2339 return qp;
2340 error:
2341 isl_space_free(domain);
2342 isl_val_free(val);
2343 return NULL;
2344 }
2345
2346 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2347 {
2348 struct isl_upoly_rec *rec;
2349 int i;
2350
2351 if (!up)
2352 return -1;
2353
2354 if (isl_upoly_is_cst(up))
2355 return 0;
2356
2357 if (up->var < d)
2358 active[up->var] = 1;
2359
2360 rec = isl_upoly_as_rec(up);
2361 for (i = 0; i < rec->n; ++i)
2362 if (up_set_active(rec->p[i], active, d) < 0)
2363 return -1;
2364
2365 return 0;
2366 }
2367
2368 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2369 {
2370 int i, j;
2371 int d = isl_space_dim(qp->dim, isl_dim_all);
2372
2373 if (!qp || !active)
2374 return -1;
2375
2376 for (i = 0; i < d; ++i)
2377 for (j = 0; j < qp->div->n_row; ++j) {
2378 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2379 continue;
2380 active[i] = 1;
2381 break;
2382 }
2383
2384 return up_set_active(qp->upoly, active, d);
2385 }
2386
2387 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2388 enum isl_dim_type type, unsigned first, unsigned n)
2389 {
2390 int i;
2391 int *active = NULL;
2392 int involves = 0;
2393
2394 if (!qp)
2395 return -1;
2396 if (n == 0)
2397 return 0;
2398
2399 isl_assert(qp->dim->ctx,
2400 first + n <= isl_qpolynomial_dim(qp, type), return -1);
2401 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2402 type == isl_dim_in, return -1);
2403
2404 active = isl_calloc_array(qp->dim->ctx, int,
2405 isl_space_dim(qp->dim, isl_dim_all));
2406 if (set_active(qp, active) < 0)
2407 goto error;
2408
2409 if (type == isl_dim_in)
2410 first += isl_space_dim(qp->dim, isl_dim_param);
2411 for (i = 0; i < n; ++i)
2412 if (active[first + i]) {
2413 involves = 1;
2414 break;
2415 }
2416
2417 free(active);
2418
2419 return involves;
2420 error:
2421 free(active);
2422 return -1;
2423 }
2424
2425 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2426 * of the divs that do appear in the quasi-polynomial.
2427 */
2428 static __isl_give isl_qpolynomial *remove_redundant_divs(
2429 __isl_take isl_qpolynomial *qp)
2430 {
2431 int i, j;
2432 int d;
2433 int len;
2434 int skip;
2435 int *active = NULL;
2436 int *reordering = NULL;
2437 int redundant = 0;
2438 int n_div;
2439 isl_ctx *ctx;
2440
2441 if (!qp)
2442 return NULL;
2443 if (qp->div->n_row == 0)
2444 return qp;
2445
2446 d = isl_space_dim(qp->dim, isl_dim_all);
2447 len = qp->div->n_col - 2;
2448 ctx = isl_qpolynomial_get_ctx(qp);
2449 active = isl_calloc_array(ctx, int, len);
2450 if (!active)
2451 goto error;
2452
2453 if (up_set_active(qp->upoly, active, len) < 0)
2454 goto error;
2455
2456 for (i = qp->div->n_row - 1; i >= 0; --i) {
2457 if (!active[d + i]) {
2458 redundant = 1;
2459 continue;
2460 }
2461 for (j = 0; j < i; ++j) {
2462 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2463 continue;
2464 active[d + j] = 1;
2465 break;
2466 }
2467 }
2468
2469 if (!redundant) {
2470 free(active);
2471 return qp;
2472 }
2473
2474 reordering = isl_alloc_array(qp->div->ctx, int, len);
2475 if (!reordering)
2476 goto error;
2477
2478 for (i = 0; i < d; ++i)
2479 reordering[i] = i;
2480
2481 skip = 0;
2482 n_div = qp->div->n_row;
2483 for (i = 0; i < n_div; ++i) {
2484 if (!active[d + i]) {
2485 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2486 qp->div = isl_mat_drop_cols(qp->div,
2487 2 + d + i - skip, 1);
2488 skip++;
2489 }
2490 reordering[d + i] = d + i - skip;
2491 }
2492
2493 qp->upoly = reorder(qp->upoly, reordering);
2494
2495 if (!qp->upoly || !qp->div)
2496 goto error;
2497
2498 free(active);
2499 free(reordering);
2500
2501 return qp;
2502 error:
2503 free(active);
2504 free(reordering);
2505 isl_qpolynomial_free(qp);
2506 return NULL;
2507 }
2508
2509 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2510 unsigned first, unsigned n)
2511 {
2512 int i;
2513 struct isl_upoly_rec *rec;
2514
2515 if (!up)
2516 return NULL;
2517 if (n == 0 || up->var < 0 || up->var < first)
2518 return up;
2519 if (up->var < first + n) {
2520 up = replace_by_constant_term(up);
2521 return isl_upoly_drop(up, first, n);
2522 }
2523 up = isl_upoly_cow(up);
2524 if (!up)
2525 return NULL;
2526 up->var -= n;
2527 rec = isl_upoly_as_rec(up);
2528 if (!rec)
2529 goto error;
2530
2531 for (i = 0; i < rec->n; ++i) {
2532 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2533 if (!rec->p[i])
2534 goto error;
2535 }
2536
2537 return up;
2538 error:
2539 isl_upoly_free(up);
2540 return NULL;
2541 }
2542
2543 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2544 __isl_take isl_qpolynomial *qp,
2545 enum isl_dim_type type, unsigned pos, const char *s)
2546 {
2547 qp = isl_qpolynomial_cow(qp);
2548 if (!qp)
2549 return NULL;
2550 qp->dim = isl_space_set_dim_name(qp->dim, type, pos, s);
2551 if (!qp->dim)
2552 goto error;
2553 return qp;
2554 error:
2555 isl_qpolynomial_free(qp);
2556 return NULL;
2557 }
2558
2559 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2560 __isl_take isl_qpolynomial *qp,
2561 enum isl_dim_type type, unsigned first, unsigned n)
2562 {
2563 if (!qp)
2564 return NULL;
2565 if (type == isl_dim_out)
2566 isl_die(qp->dim->ctx, isl_error_invalid,
2567 "cannot drop output/set dimension",
2568 goto error);
2569 if (type == isl_dim_in)
2570 type = isl_dim_set;
2571 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2572 return qp;
2573
2574 qp = isl_qpolynomial_cow(qp);
2575 if (!qp)
2576 return NULL;
2577
2578 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
2579 goto error);
2580 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2581 type == isl_dim_set, goto error);
2582
2583 qp->dim = isl_space_drop_dims(qp->dim, type, first, n);
2584 if (!qp->dim)
2585 goto error;
2586
2587 if (type == isl_dim_set)
2588 first += isl_space_dim(qp->dim, isl_dim_param);
2589
2590 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2591 if (!qp->div)
2592 goto error;
2593
2594 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2595 if (!qp->upoly)
2596 goto error;
2597
2598 return qp;
2599 error:
2600 isl_qpolynomial_free(qp);
2601 return NULL;
2602 }
2603
2604 /* Project the domain of the quasi-polynomial onto its parameter space.
2605 * The quasi-polynomial may not involve any of the domain dimensions.
2606 */
2607 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
2608 __isl_take isl_qpolynomial *qp)
2609 {
2610 isl_space *space;
2611 unsigned n;
2612 int involves;
2613
2614 n = isl_qpolynomial_dim(qp, isl_dim_in);
2615 involves = isl_qpolynomial_involves_dims(qp, isl_dim_in, 0, n);
2616 if (involves < 0)
2617 return isl_qpolynomial_free(qp);
2618 if (involves)
2619 isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
2620 "polynomial involves some of the domain dimensions",
2621 return isl_qpolynomial_free(qp));
2622 qp = isl_qpolynomial_drop_dims(qp, isl_dim_in, 0, n);
2623 space = isl_qpolynomial_get_domain_space(qp);
2624 space = isl_space_params(space);
2625 qp = isl_qpolynomial_reset_domain_space(qp, space);
2626 return qp;
2627 }
2628
2629 static __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities_lifted(
2630 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2631 {
2632 int i, j, k;
2633 isl_int denom;
2634 unsigned total;
2635 unsigned n_div;
2636 struct isl_upoly *up;
2637
2638 if (!eq)
2639 goto error;
2640 if (eq->n_eq == 0) {
2641 isl_basic_set_free(eq);
2642 return qp;
2643 }
2644
2645 qp = isl_qpolynomial_cow(qp);
2646 if (!qp)
2647 goto error;
2648 qp->div = isl_mat_cow(qp->div);
2649 if (!qp->div)
2650 goto error;
2651
2652 total = 1 + isl_space_dim(eq->dim, isl_dim_all);
2653 n_div = eq->n_div;
2654 isl_int_init(denom);
2655 for (i = 0; i < eq->n_eq; ++i) {
2656 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2657 if (j < 0 || j == 0 || j >= total)
2658 continue;
2659
2660 for (k = 0; k < qp->div->n_row; ++k) {
2661 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2662 continue;
2663 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2664 &qp->div->row[k][0]);
2665 normalize_div(qp, k);
2666 }
2667
2668 if (isl_int_is_pos(eq->eq[i][j]))
2669 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2670 isl_int_abs(denom, eq->eq[i][j]);
2671 isl_int_set_si(eq->eq[i][j], 0);
2672
2673 up = isl_upoly_from_affine(qp->dim->ctx,
2674 eq->eq[i], denom, total);
2675 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2676 isl_upoly_free(up);
2677 }
2678 isl_int_clear(denom);
2679
2680 if (!qp->upoly)
2681 goto error;
2682
2683 isl_basic_set_free(eq);
2684
2685 qp = substitute_non_divs(qp);
2686 qp = sort_divs(qp);
2687
2688 return qp;
2689 error:
2690 isl_basic_set_free(eq);
2691 isl_qpolynomial_free(qp);
2692 return NULL;
2693 }
2694
2695 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2696 */
2697 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2698 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2699 {
2700 if (!qp || !eq)
2701 goto error;
2702 if (qp->div->n_row > 0)
2703 eq = isl_basic_set_add_dims(eq, isl_dim_set, qp->div->n_row);
2704 return isl_qpolynomial_substitute_equalities_lifted(qp, eq);
2705 error:
2706 isl_basic_set_free(eq);
2707 isl_qpolynomial_free(qp);
2708 return NULL;
2709 }
2710
2711 static __isl_give isl_basic_set *add_div_constraints(
2712 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2713 {
2714 int i;
2715 unsigned total;
2716
2717 if (!bset || !div)
2718 goto error;
2719
2720 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2721 if (!bset)
2722 goto error;
2723 total = isl_basic_set_total_dim(bset);
2724 for (i = 0; i < div->n_row; ++i)
2725 if (isl_basic_set_add_div_constraints_var(bset,
2726 total - div->n_row + i, div->row[i]) < 0)
2727 goto error;
2728
2729 isl_mat_free(div);
2730 return bset;
2731 error:
2732 isl_mat_free(div);
2733 isl_basic_set_free(bset);
2734 return NULL;
2735 }
2736
2737 /* Look for equalities among the variables shared by context and qp
2738 * and the integer divisions of qp, if any.
2739 * The equalities are then used to eliminate variables and/or integer
2740 * divisions from qp.
2741 */
2742 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2743 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2744 {
2745 isl_basic_set *aff;
2746
2747 if (!qp)
2748 goto error;
2749 if (qp->div->n_row > 0) {
2750 isl_basic_set *bset;
2751 context = isl_set_add_dims(context, isl_dim_set,
2752 qp->div->n_row);
2753 bset = isl_basic_set_universe(isl_set_get_space(context));
2754 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2755 context = isl_set_intersect(context,
2756 isl_set_from_basic_set(bset));
2757 }
2758
2759 aff = isl_set_affine_hull(context);
2760 return isl_qpolynomial_substitute_equalities_lifted(qp, aff);
2761 error:
2762 isl_qpolynomial_free(qp);
2763 isl_set_free(context);
2764 return NULL;
2765 }
2766
2767 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
2768 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2769 {
2770 isl_space *space = isl_qpolynomial_get_domain_space(qp);
2771 isl_set *dom_context = isl_set_universe(space);
2772 dom_context = isl_set_intersect_params(dom_context, context);
2773 return isl_qpolynomial_gist(qp, dom_context);
2774 }
2775
2776 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2777 __isl_take isl_qpolynomial *qp)
2778 {
2779 isl_set *dom;
2780
2781 if (!qp)
2782 return NULL;
2783 if (isl_qpolynomial_is_zero(qp)) {
2784 isl_space *dim = isl_qpolynomial_get_space(qp);
2785 isl_qpolynomial_free(qp);
2786 return isl_pw_qpolynomial_zero(dim);
2787 }
2788
2789 dom = isl_set_universe(isl_qpolynomial_get_domain_space(qp));
2790 return isl_pw_qpolynomial_alloc(dom, qp);
2791 }
2792
2793 #undef PW
2794 #define PW isl_pw_qpolynomial
2795 #undef EL
2796 #define EL isl_qpolynomial
2797 #undef EL_IS_ZERO
2798 #define EL_IS_ZERO is_zero
2799 #undef ZERO
2800 #define ZERO zero
2801 #undef IS_ZERO
2802 #define IS_ZERO is_zero
2803 #undef FIELD
2804 #define FIELD qp
2805 #undef DEFAULT_IS_ZERO
2806 #define DEFAULT_IS_ZERO 1
2807
2808 #define NO_PULLBACK
2809
2810 #include <isl_pw_templ.c>
2811
2812 #undef UNION
2813 #define UNION isl_union_pw_qpolynomial
2814 #undef PART
2815 #define PART isl_pw_qpolynomial
2816 #undef PARTS
2817 #define PARTS pw_qpolynomial
2818
2819 #include <isl_union_templ.c>
2820
2821 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2822 {
2823 if (!pwqp)
2824 return -1;
2825
2826 if (pwqp->n != -1)
2827 return 0;
2828
2829 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2830 return 0;
2831
2832 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2833 }
2834
2835 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2836 __isl_take isl_pw_qpolynomial *pwqp1,
2837 __isl_take isl_pw_qpolynomial *pwqp2)
2838 {
2839 return isl_pw_qpolynomial_union_add_(pwqp1, pwqp2);
2840 }
2841
2842 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2843 __isl_take isl_pw_qpolynomial *pwqp1,
2844 __isl_take isl_pw_qpolynomial *pwqp2)
2845 {
2846 int i, j, n;
2847 struct isl_pw_qpolynomial *res;
2848
2849 if (!pwqp1 || !pwqp2)
2850 goto error;
2851
2852 isl_assert(pwqp1->dim->ctx, isl_space_is_equal(pwqp1->dim, pwqp2->dim),
2853 goto error);
2854
2855 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2856 isl_pw_qpolynomial_free(pwqp2);
2857 return pwqp1;
2858 }
2859
2860 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2861 isl_pw_qpolynomial_free(pwqp1);
2862 return pwqp2;
2863 }
2864
2865 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2866 isl_pw_qpolynomial_free(pwqp1);
2867 return pwqp2;
2868 }
2869
2870 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2871 isl_pw_qpolynomial_free(pwqp2);
2872 return pwqp1;
2873 }
2874
2875 n = pwqp1->n * pwqp2->n;
2876 res = isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1->dim), n);
2877
2878 for (i = 0; i < pwqp1->n; ++i) {
2879 for (j = 0; j < pwqp2->n; ++j) {
2880 struct isl_set *common;
2881 struct isl_qpolynomial *prod;
2882 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2883 isl_set_copy(pwqp2->p[j].set));
2884 if (isl_set_plain_is_empty(common)) {
2885 isl_set_free(common);
2886 continue;
2887 }
2888
2889 prod = isl_qpolynomial_mul(
2890 isl_qpolynomial_copy(pwqp1->p[i].qp),
2891 isl_qpolynomial_copy(pwqp2->p[j].qp));
2892
2893 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2894 }
2895 }
2896
2897 isl_pw_qpolynomial_free(pwqp1);
2898 isl_pw_qpolynomial_free(pwqp2);
2899
2900 return res;
2901 error:
2902 isl_pw_qpolynomial_free(pwqp1);
2903 isl_pw_qpolynomial_free(pwqp2);
2904 return NULL;
2905 }
2906
2907 __isl_give isl_val *isl_upoly_eval(__isl_take struct isl_upoly *up,
2908 __isl_take isl_vec *vec)
2909 {
2910 int i;
2911 struct isl_upoly_rec *rec;
2912 isl_val *res;
2913 isl_val *base;
2914
2915 if (isl_upoly_is_cst(up)) {
2916 isl_vec_free(vec);
2917 res = isl_upoly_get_constant_val(up);
2918 isl_upoly_free(up);
2919 return res;
2920 }
2921
2922 rec = isl_upoly_as_rec(up);
2923 if (!rec)
2924 goto error;
2925
2926 isl_assert(up->ctx, rec->n >= 1, goto error);
2927
2928 base = isl_val_rat_from_isl_int(up->ctx,
2929 vec->el[1 + up->var], vec->el[0]);
2930
2931 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2932 isl_vec_copy(vec));
2933
2934 for (i = rec->n - 2; i >= 0; --i) {
2935 res = isl_val_mul(res, isl_val_copy(base));
2936 res = isl_val_add(res,
2937 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2938 isl_vec_copy(vec)));
2939 }
2940
2941 isl_val_free(base);
2942 isl_upoly_free(up);
2943 isl_vec_free(vec);
2944 return res;
2945 error:
2946 isl_upoly_free(up);
2947 isl_vec_free(vec);
2948 return NULL;
2949 }
2950
2951 __isl_give isl_val *isl_qpolynomial_eval(__isl_take isl_qpolynomial *qp,
2952 __isl_take isl_point *pnt)
2953 {
2954 isl_vec *ext;
2955 isl_val *v;
2956
2957 if (!qp || !pnt)
2958 goto error;
2959 isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, qp->dim), goto error);
2960
2961 if (qp->div->n_row == 0)
2962 ext = isl_vec_copy(pnt->vec);
2963 else {
2964 int i;
2965 unsigned dim = isl_space_dim(qp->dim, isl_dim_all);
2966 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2967 if (!ext)
2968 goto error;
2969
2970 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2971 for (i = 0; i < qp->div->n_row; ++i) {
2972 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2973 1 + dim + i, &ext->el[1+dim+i]);
2974 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2975 qp->div->row[i][0]);
2976 }
2977 }
2978
2979 v = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2980
2981 isl_qpolynomial_free(qp);
2982 isl_point_free(pnt);
2983
2984 return v;
2985 error:
2986 isl_qpolynomial_free(qp);
2987 isl_point_free(pnt);
2988 return NULL;
2989 }
2990
2991 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2992 __isl_keep struct isl_upoly_cst *cst2)
2993 {
2994 int cmp;
2995 isl_int t;
2996 isl_int_init(t);
2997 isl_int_mul(t, cst1->n, cst2->d);
2998 isl_int_submul(t, cst2->n, cst1->d);
2999 cmp = isl_int_sgn(t);
3000 isl_int_clear(t);
3001 return cmp;
3002 }
3003
3004 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
3005 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
3006 unsigned first, unsigned n)
3007 {
3008 unsigned total;
3009 unsigned g_pos;
3010 int *exp;
3011
3012 if (!qp)
3013 return NULL;
3014 if (type == isl_dim_out)
3015 isl_die(qp->div->ctx, isl_error_invalid,
3016 "cannot insert output/set dimensions",
3017 goto error);
3018 if (type == isl_dim_in)
3019 type = isl_dim_set;
3020 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
3021 return qp;
3022
3023 qp = isl_qpolynomial_cow(qp);
3024 if (!qp)
3025 return NULL;
3026
3027 isl_assert(qp->div->ctx, first <= isl_space_dim(qp->dim, type),
3028 goto error);
3029
3030 g_pos = pos(qp->dim, type) + first;
3031
3032 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
3033 if (!qp->div)
3034 goto error;
3035
3036 total = qp->div->n_col - 2;
3037 if (total > g_pos) {
3038 int i;
3039 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
3040 if (!exp)
3041 goto error;
3042 for (i = 0; i < total - g_pos; ++i)
3043 exp[i] = i + n;
3044 qp->upoly = expand(qp->upoly, exp, g_pos);
3045 free(exp);
3046 if (!qp->upoly)
3047 goto error;
3048 }
3049
3050 qp->dim = isl_space_insert_dims(qp->dim, type, first, n);
3051 if (!qp->dim)
3052 goto error;
3053
3054 return qp;
3055 error:
3056 isl_qpolynomial_free(qp);
3057 return NULL;
3058 }
3059
3060 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
3061 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
3062 {
3063 unsigned pos;
3064
3065 pos = isl_qpolynomial_dim(qp, type);
3066
3067 return isl_qpolynomial_insert_dims(qp, type, pos, n);
3068 }
3069
3070 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
3071 __isl_take isl_pw_qpolynomial *pwqp,
3072 enum isl_dim_type type, unsigned n)
3073 {
3074 unsigned pos;
3075
3076 pos = isl_pw_qpolynomial_dim(pwqp, type);
3077
3078 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
3079 }
3080
3081 static int *reordering_move(isl_ctx *ctx,
3082 unsigned len, unsigned dst, unsigned src, unsigned n)
3083 {
3084 int i;
3085 int *reordering;
3086
3087 reordering = isl_alloc_array(ctx, int, len);
3088 if (!reordering)
3089 return NULL;
3090
3091 if (dst <= src) {
3092 for (i = 0; i < dst; ++i)
3093 reordering[i] = i;
3094 for (i = 0; i < n; ++i)
3095 reordering[src + i] = dst + i;
3096 for (i = 0; i < src - dst; ++i)
3097 reordering[dst + i] = dst + n + i;
3098 for (i = 0; i < len - src - n; ++i)
3099 reordering[src + n + i] = src + n + i;
3100 } else {
3101 for (i = 0; i < src; ++i)
3102 reordering[i] = i;
3103 for (i = 0; i < n; ++i)
3104 reordering[src + i] = dst + i;
3105 for (i = 0; i < dst - src; ++i)
3106 reordering[src + n + i] = src + i;
3107 for (i = 0; i < len - dst - n; ++i)
3108 reordering[dst + n + i] = dst + n + i;
3109 }
3110
3111 return reordering;
3112 }
3113
3114 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
3115 __isl_take isl_qpolynomial *qp,
3116 enum isl_dim_type dst_type, unsigned dst_pos,
3117 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3118 {
3119 unsigned g_dst_pos;
3120 unsigned g_src_pos;
3121 int *reordering;
3122
3123 if (n == 0)
3124 return qp;
3125
3126 qp = isl_qpolynomial_cow(qp);
3127 if (!qp)
3128 return NULL;
3129
3130 if (dst_type == isl_dim_out || src_type == isl_dim_out)
3131 isl_die(qp->dim->ctx, isl_error_invalid,
3132 "cannot move output/set dimension",
3133 goto error);
3134 if (dst_type == isl_dim_in)
3135 dst_type = isl_dim_set;
3136 if (src_type == isl_dim_in)
3137 src_type = isl_dim_set;
3138
3139 isl_assert(qp->dim->ctx, src_pos + n <= isl_space_dim(qp->dim, src_type),
3140 goto error);
3141
3142 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
3143 g_src_pos = pos(qp->dim, src_type) + src_pos;
3144 if (dst_type > src_type)
3145 g_dst_pos -= n;
3146
3147 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
3148 if (!qp->div)
3149 goto error;
3150 qp = sort_divs(qp);
3151 if (!qp)
3152 goto error;
3153
3154 reordering = reordering_move(qp->dim->ctx,
3155 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
3156 if (!reordering)
3157 goto error;
3158
3159 qp->upoly = reorder(qp->upoly, reordering);
3160 free(reordering);
3161 if (!qp->upoly)
3162 goto error;
3163
3164 qp->dim = isl_space_move_dims(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
3165 if (!qp->dim)
3166 goto error;
3167
3168 return qp;
3169 error:
3170 isl_qpolynomial_free(qp);
3171 return NULL;
3172 }
3173
3174 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_space *dim,
3175 isl_int *f, isl_int denom)
3176 {
3177 struct isl_upoly *up;
3178
3179 dim = isl_space_domain(dim);
3180 if (!dim)
3181 return NULL;
3182
3183 up = isl_upoly_from_affine(dim->ctx, f, denom,
3184 1 + isl_space_dim(dim, isl_dim_all));
3185
3186 return isl_qpolynomial_alloc(dim, 0, up);
3187 }
3188
3189 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
3190 {
3191 isl_ctx *ctx;
3192 struct isl_upoly *up;
3193 isl_qpolynomial *qp;
3194
3195 if (!aff)
3196 return NULL;
3197
3198 ctx = isl_aff_get_ctx(aff);
3199 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
3200 aff->v->size - 1);
3201
3202 qp = isl_qpolynomial_alloc(isl_aff_get_domain_space(aff),
3203 aff->ls->div->n_row, up);
3204 if (!qp)
3205 goto error;
3206
3207 isl_mat_free(qp->div);
3208 qp->div = isl_mat_copy(aff->ls->div);
3209 qp->div = isl_mat_cow(qp->div);
3210 if (!qp->div)
3211 goto error;
3212
3213 isl_aff_free(aff);
3214 qp = reduce_divs(qp);
3215 qp = remove_redundant_divs(qp);
3216 return qp;
3217 error:
3218 isl_aff_free(aff);
3219 return isl_qpolynomial_free(qp);
3220 }
3221
3222 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3223 __isl_take isl_pw_aff *pwaff)
3224 {
3225 int i;
3226 isl_pw_qpolynomial *pwqp;
3227
3228 if (!pwaff)
3229 return NULL;
3230
3231 pwqp = isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff),
3232 pwaff->n);
3233
3234 for (i = 0; i < pwaff->n; ++i) {
3235 isl_set *dom;
3236 isl_qpolynomial *qp;
3237
3238 dom = isl_set_copy(pwaff->p[i].set);
3239 qp = isl_qpolynomial_from_aff(isl_aff_copy(pwaff->p[i].aff));
3240 pwqp = isl_pw_qpolynomial_add_piece(pwqp, dom, qp);
3241 }
3242
3243 isl_pw_aff_free(pwaff);
3244 return pwqp;
3245 }
3246
3247 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
3248 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3249 {
3250 isl_aff *aff;
3251
3252 aff = isl_constraint_get_bound(c, type, pos);
3253 isl_constraint_free(c);
3254 return isl_qpolynomial_from_aff(aff);
3255 }
3256
3257 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3258 * in "qp" by subs[i].
3259 */
3260 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3261 __isl_take isl_qpolynomial *qp,
3262 enum isl_dim_type type, unsigned first, unsigned n,
3263 __isl_keep isl_qpolynomial **subs)
3264 {
3265 int i;
3266 struct isl_upoly **ups;
3267
3268 if (n == 0)
3269 return qp;
3270
3271 qp = isl_qpolynomial_cow(qp);
3272 if (!qp)
3273 return NULL;
3274
3275 if (type == isl_dim_out)
3276 isl_die(qp->dim->ctx, isl_error_invalid,
3277 "cannot substitute output/set dimension",
3278 goto error);
3279 if (type == isl_dim_in)
3280 type = isl_dim_set;
3281
3282 for (i = 0; i < n; ++i)
3283 if (!subs[i])
3284 goto error;
3285
3286 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
3287 goto error);
3288
3289 for (i = 0; i < n; ++i)
3290 isl_assert(qp->dim->ctx, isl_space_is_equal(qp->dim, subs[i]->dim),
3291 goto error);
3292
3293 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3294 for (i = 0; i < n; ++i)
3295 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3296
3297 first += pos(qp->dim, type);
3298
3299 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3300 if (!ups)
3301 goto error;
3302 for (i = 0; i < n; ++i)
3303 ups[i] = subs[i]->upoly;
3304
3305 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3306
3307 free(ups);
3308
3309 if (!qp->upoly)
3310 goto error;
3311
3312 return qp;
3313 error:
3314 isl_qpolynomial_free(qp);
3315 return NULL;
3316 }
3317
3318 /* Extend "bset" with extra set dimensions for each integer division
3319 * in "qp" and then call "fn" with the extended bset and the polynomial
3320 * that results from replacing each of the integer divisions by the
3321 * corresponding extra set dimension.
3322 */
3323 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3324 __isl_keep isl_basic_set *bset,
3325 int (*fn)(__isl_take isl_basic_set *bset,
3326 __isl_take isl_qpolynomial *poly, void *user), void *user)
3327 {
3328 isl_space *dim;
3329 isl_mat *div;
3330 isl_qpolynomial *poly;
3331
3332 if (!qp || !bset)
3333 goto error;
3334 if (qp->div->n_row == 0)
3335 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3336 user);
3337
3338 div = isl_mat_copy(qp->div);
3339 dim = isl_space_copy(qp->dim);
3340 dim = isl_space_add_dims(dim, isl_dim_set, qp->div->n_row);
3341 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3342 bset = isl_basic_set_copy(bset);
3343 bset = isl_basic_set_add_dims(bset, isl_dim_set, qp->div->n_row);
3344 bset = add_div_constraints(bset, div);
3345
3346 return fn(bset, poly, user);
3347 error:
3348 return -1;
3349 }
3350
3351 /* Return total degree in variables first (inclusive) up to last (exclusive).
3352 */
3353 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3354 {
3355 int deg = -1;
3356 int i;
3357 struct isl_upoly_rec *rec;
3358
3359 if (!up)
3360 return -2;
3361 if (isl_upoly_is_zero(up))
3362 return -1;
3363 if (isl_upoly_is_cst(up) || up->var < first)
3364 return 0;
3365
3366 rec = isl_upoly_as_rec(up);
3367 if (!rec)
3368 return -2;
3369
3370 for (i = 0; i < rec->n; ++i) {
3371 int d;
3372
3373 if (isl_upoly_is_zero(rec->p[i]))
3374 continue;
3375 d = isl_upoly_degree(rec->p[i], first, last);
3376 if (up->var < last)
3377 d += i;
3378 if (d > deg)
3379 deg = d;
3380 }
3381
3382 return deg;
3383 }
3384
3385 /* Return total degree in set variables.
3386 */
3387 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3388 {
3389 unsigned ovar;
3390 unsigned nvar;
3391
3392 if (!poly)
3393 return -2;
3394
3395 ovar = isl_space_offset(poly->dim, isl_dim_set);
3396 nvar = isl_space_dim(poly->dim, isl_dim_set);
3397 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3398 }
3399
3400 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3401 unsigned pos, int deg)
3402 {
3403 int i;
3404 struct isl_upoly_rec *rec;
3405
3406 if (!up)
3407 return NULL;
3408
3409 if (isl_upoly_is_cst(up) || up->var < pos) {
3410 if (deg == 0)
3411 return isl_upoly_copy(up);
3412 else
3413 return isl_upoly_zero(up->ctx);
3414 }
3415
3416 rec = isl_upoly_as_rec(up);
3417 if (!rec)
3418 return NULL;
3419
3420 if (up->var == pos) {
3421 if (deg < rec->n)
3422 return isl_upoly_copy(rec->p[deg]);
3423 else
3424 return isl_upoly_zero(up->ctx);
3425 }
3426
3427 up = isl_upoly_copy(up);
3428 up = isl_upoly_cow(up);
3429 rec = isl_upoly_as_rec(up);
3430 if (!rec)
3431 goto error;
3432
3433 for (i = 0; i < rec->n; ++i) {
3434 struct isl_upoly *t;
3435 t = isl_upoly_coeff(rec->p[i], pos, deg);
3436 if (!t)
3437 goto error;
3438 isl_upoly_free(rec->p[i]);
3439 rec->p[i] = t;
3440 }
3441
3442 return up;
3443 error:
3444 isl_upoly_free(up);
3445 return NULL;
3446 }
3447
3448 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3449 */
3450 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3451 __isl_keep isl_qpolynomial *qp,
3452 enum isl_dim_type type, unsigned t_pos, int deg)
3453 {
3454 unsigned g_pos;
3455 struct isl_upoly *up;
3456 isl_qpolynomial *c;
3457
3458 if (!qp)
3459 return NULL;
3460
3461 if (type == isl_dim_out)
3462 isl_die(qp->div->ctx, isl_error_invalid,
3463 "output/set dimension does not have a coefficient",
3464 return NULL);
3465 if (type == isl_dim_in)
3466 type = isl_dim_set;
3467
3468 isl_assert(qp->div->ctx, t_pos < isl_space_dim(qp->dim, type),
3469 return NULL);
3470
3471 g_pos = pos(qp->dim, type) + t_pos;
3472 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3473
3474 c = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row, up);
3475 if (!c)
3476 return NULL;
3477 isl_mat_free(c->div);
3478 c->div = isl_mat_copy(qp->div);
3479 if (!c->div)
3480 goto error;
3481 return c;
3482 error:
3483 isl_qpolynomial_free(c);
3484 return NULL;
3485 }
3486
3487 /* Homogenize the polynomial in the variables first (inclusive) up to
3488 * last (exclusive) by inserting powers of variable first.
3489 * Variable first is assumed not to appear in the input.
3490 */
3491 __isl_give struct isl_upoly *isl_upoly_homogenize(
3492 __isl_take struct isl_upoly *up, int deg, int target,
3493 int first, int last)
3494 {
3495 int i;
3496 struct isl_upoly_rec *rec;
3497
3498 if (!up)
3499 return NULL;
3500 if (isl_upoly_is_zero(up))
3501 return up;
3502 if (deg == target)
3503 return up;
3504 if (isl_upoly_is_cst(up) || up->var < first) {
3505 struct isl_upoly *hom;
3506
3507 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3508 if (!hom)
3509 goto error;
3510 rec = isl_upoly_as_rec(hom);
3511 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3512
3513 return hom;
3514 }
3515
3516 up = isl_upoly_cow(up);
3517 rec = isl_upoly_as_rec(up);
3518 if (!rec)
3519 goto error;
3520
3521 for (i = 0; i < rec->n; ++i) {
3522 if (isl_upoly_is_zero(rec->p[i]))
3523 continue;
3524 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3525 up->var < last ? deg + i : i, target,
3526 first, last);
3527 if (!rec->p[i])
3528 goto error;
3529 }
3530
3531 return up;
3532 error:
3533 isl_upoly_free(up);
3534 return NULL;
3535 }
3536
3537 /* Homogenize the polynomial in the set variables by introducing
3538 * powers of an extra set variable at position 0.
3539 */
3540 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3541 __isl_take isl_qpolynomial *poly)
3542 {
3543 unsigned ovar;
3544 unsigned nvar;
3545 int deg = isl_qpolynomial_degree(poly);
3546
3547 if (deg < -1)
3548 goto error;
3549
3550 poly = isl_qpolynomial_insert_dims(poly, isl_dim_in, 0, 1);
3551 poly = isl_qpolynomial_cow(poly);
3552 if (!poly)
3553 goto error;
3554
3555 ovar = isl_space_offset(poly->dim, isl_dim_set);
3556 nvar = isl_space_dim(poly->dim, isl_dim_set);
3557 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3558 ovar, ovar + nvar);
3559 if (!poly->upoly)
3560 goto error;
3561
3562 return poly;
3563 error:
3564 isl_qpolynomial_free(poly);
3565 return NULL;
3566 }
3567
3568 __isl_give isl_term *isl_term_alloc(__isl_take isl_space *dim,
3569 __isl_take isl_mat *div)
3570 {
3571 isl_term *term;
3572 int n;
3573
3574 if (!dim || !div)
3575 goto error;
3576
3577 n = isl_space_dim(dim, isl_dim_all) + div->n_row;
3578
3579 term = isl_calloc(dim->ctx, struct isl_term,
3580 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3581 if (!term)
3582 goto error;
3583
3584 term->ref = 1;
3585 term->dim = dim;
3586 term->div = div;
3587 isl_int_init(term->n);
3588 isl_int_init(term->d);
3589
3590 return term;
3591 error:
3592 isl_space_free(dim);
3593 isl_mat_free(div);
3594 return NULL;
3595 }
3596
3597 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3598 {
3599 if (!term)
3600 return NULL;
3601
3602 term->ref++;
3603 return term;
3604 }
3605
3606 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3607 {
3608 int i;
3609 isl_term *dup;
3610 unsigned total;
3611
3612 if (!term)
3613 return NULL;
3614
3615 total = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3616
3617 dup = isl_term_alloc(isl_space_copy(term->dim), isl_mat_copy(term->div));
3618 if (!dup)
3619 return NULL;
3620
3621 isl_int_set(dup->n, term->n);
3622 isl_int_set(dup->d, term->d);
3623
3624 for (i = 0; i < total; ++i)
3625 dup->pow[i] = term->pow[i];
3626
3627 return dup;
3628 }
3629
3630 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3631 {
3632 if (!term)
3633 return NULL;
3634
3635 if (term->ref == 1)
3636 return term;
3637 term->ref--;
3638 return isl_term_dup(term);
3639 }
3640
3641 void isl_term_free(__isl_take isl_term *term)
3642 {
3643 if (!term)
3644 return;
3645
3646 if (--term->ref > 0)
3647 return;
3648
3649 isl_space_free(term->dim);
3650 isl_mat_free(term->div);
3651 isl_int_clear(term->n);
3652 isl_int_clear(term->d);
3653 free(term);
3654 }
3655
3656 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3657 {
3658 if (!term)
3659 return 0;
3660
3661 switch (type) {
3662 case isl_dim_param:
3663 case isl_dim_in:
3664 case isl_dim_out: return isl_space_dim(term->dim, type);
3665 case isl_dim_div: return term->div->n_row;
3666 case isl_dim_all: return isl_space_dim(term->dim, isl_dim_all) +
3667 term->div->n_row;
3668 default: return 0;
3669 }
3670 }
3671
3672 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3673 {
3674 return term ? term->dim->ctx : NULL;
3675 }
3676
3677 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3678 {
3679 if (!term)
3680 return;
3681 isl_int_set(*n, term->n);
3682 }
3683
3684 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3685 {
3686 if (!term)
3687 return;
3688 isl_int_set(*d, term->d);
3689 }
3690
3691 /* Return the coefficient of the term "term".
3692 */
3693 __isl_give isl_val *isl_term_get_coefficient_val(__isl_keep isl_term *term)
3694 {
3695 if (!term)
3696 return NULL;
3697
3698 return isl_val_rat_from_isl_int(isl_term_get_ctx(term),
3699 term->n, term->d);
3700 }
3701
3702 int isl_term_get_exp(__isl_keep isl_term *term,
3703 enum isl_dim_type type, unsigned pos)
3704 {
3705 if (!term)
3706 return -1;
3707
3708 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3709
3710 if (type >= isl_dim_set)
3711 pos += isl_space_dim(term->dim, isl_dim_param);
3712 if (type >= isl_dim_div)
3713 pos += isl_space_dim(term->dim, isl_dim_set);
3714
3715 return term->pow[pos];
3716 }
3717
3718 __isl_give isl_aff *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3719 {
3720 isl_local_space *ls;
3721 isl_aff *aff;
3722
3723 if (!term)
3724 return NULL;
3725
3726 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3727 return NULL);
3728
3729 ls = isl_local_space_alloc_div(isl_space_copy(term->dim),
3730 isl_mat_copy(term->div));
3731 aff = isl_aff_alloc(ls);
3732 if (!aff)
3733 return NULL;
3734
3735 isl_seq_cpy(aff->v->el, term->div->row[pos], aff->v->size);
3736
3737 aff = isl_aff_normalize(aff);
3738
3739 return aff;
3740 }
3741
3742 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3743 int (*fn)(__isl_take isl_term *term, void *user),
3744 __isl_take isl_term *term, void *user)
3745 {
3746 int i;
3747 struct isl_upoly_rec *rec;
3748
3749 if (!up || !term)
3750 goto error;
3751
3752 if (isl_upoly_is_zero(up))
3753 return term;
3754
3755 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3756 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3757 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3758
3759 if (isl_upoly_is_cst(up)) {
3760 struct isl_upoly_cst *cst;
3761 cst = isl_upoly_as_cst(up);
3762 if (!cst)
3763 goto error;
3764 term = isl_term_cow(term);
3765 if (!term)
3766 goto error;
3767 isl_int_set(term->n, cst->n);
3768 isl_int_set(term->d, cst->d);
3769 if (fn(isl_term_copy(term), user) < 0)
3770 goto error;
3771 return term;
3772 }
3773
3774 rec = isl_upoly_as_rec(up);
3775 if (!rec)
3776 goto error;
3777
3778 for (i = 0; i < rec->n; ++i) {
3779 term = isl_term_cow(term);
3780 if (!term)
3781 goto error;
3782 term->pow[up->var] = i;
3783 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3784 if (!term)
3785 goto error;
3786 }
3787 term->pow[up->var] = 0;
3788
3789 return term;
3790 error:
3791 isl_term_free(term);
3792 return NULL;
3793 }
3794
3795 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3796 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3797 {
3798 isl_term *term;
3799
3800 if (!qp)
3801 return -1;
3802
3803 term = isl_term_alloc(isl_space_copy(qp->dim), isl_mat_copy(qp->div));
3804 if (!term)
3805 return -1;
3806
3807 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3808
3809 isl_term_free(term);
3810
3811 return term ? 0 : -1;
3812 }
3813
3814 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3815 {
3816 struct isl_upoly *up;
3817 isl_qpolynomial *qp;
3818 int i, n;
3819
3820 if (!term)
3821 return NULL;
3822
3823 n = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3824
3825 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3826 for (i = 0; i < n; ++i) {
3827 if (!term->pow[i])
3828 continue;
3829 up = isl_upoly_mul(up,
3830 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3831 }
3832
3833 qp = isl_qpolynomial_alloc(isl_space_copy(term->dim), term->div->n_row, up);
3834 if (!qp)
3835 goto error;
3836 isl_mat_free(qp->div);
3837 qp->div = isl_mat_copy(term->div);
3838 if (!qp->div)
3839 goto error;
3840
3841 isl_term_free(term);
3842 return qp;
3843 error:
3844 isl_qpolynomial_free(qp);
3845 isl_term_free(term);
3846 return NULL;
3847 }
3848
3849 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3850 __isl_take isl_space *dim)
3851 {
3852 int i;
3853 int extra;
3854 unsigned total;
3855
3856 if (!qp || !dim)
3857 goto error;
3858
3859 if (isl_space_is_equal(qp->dim, dim)) {
3860 isl_space_free(dim);
3861 return qp;
3862 }
3863
3864 qp = isl_qpolynomial_cow(qp);
3865 if (!qp)
3866 goto error;
3867
3868 extra = isl_space_dim(dim, isl_dim_set) -
3869 isl_space_dim(qp->dim, isl_dim_set);
3870 total = isl_space_dim(qp->dim, isl_dim_all);
3871 if (qp->div->n_row) {
3872 int *exp;
3873
3874 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3875 if (!exp)
3876 goto error;
3877 for (i = 0; i < qp->div->n_row; ++i)
3878 exp[i] = extra + i;
3879 qp->upoly = expand(qp->upoly, exp, total);
3880 free(exp);
3881 if (!qp->upoly)
3882 goto error;
3883 }
3884 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3885 if (!qp->div)
3886 goto error;
3887 for (i = 0; i < qp->div->n_row; ++i)
3888 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3889
3890 isl_space_free(qp->dim);
3891 qp->dim = dim;
3892
3893 return qp;
3894 error:
3895 isl_space_free(dim);
3896 isl_qpolynomial_free(qp);
3897 return NULL;
3898 }
3899
3900 /* For each parameter or variable that does not appear in qp,
3901 * first eliminate the variable from all constraints and then set it to zero.
3902 */
3903 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3904 __isl_keep isl_qpolynomial *qp)
3905 {
3906 int *active = NULL;
3907 int i;
3908 int d;
3909 unsigned nparam;
3910 unsigned nvar;
3911
3912 if (!set || !qp)
3913 goto error;
3914
3915 d = isl_space_dim(set->dim, isl_dim_all);
3916 active = isl_calloc_array(set->ctx, int, d);
3917 if (set_active(qp, active) < 0)
3918 goto error;
3919
3920 for (i = 0; i < d; ++i)
3921 if (!active[i])
3922 break;
3923
3924 if (i == d) {
3925 free(active);
3926 return set;
3927 }
3928
3929 nparam = isl_space_dim(set->dim, isl_dim_param);
3930 nvar = isl_space_dim(set->dim, isl_dim_set);
3931 for (i = 0; i < nparam; ++i) {
3932 if (active[i])
3933 continue;
3934 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3935 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3936 }
3937 for (i = 0; i < nvar; ++i) {
3938 if (active[nparam + i])
3939 continue;
3940 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3941 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3942 }
3943
3944 free(active);
3945
3946 return set;
3947 error:
3948 free(active);
3949 isl_set_free(set);
3950 return NULL;
3951 }
3952
3953 struct isl_opt_data {
3954 isl_qpolynomial *qp;
3955 int first;
3956 isl_val *opt;
3957 int max;
3958 };
3959
3960 static int opt_fn(__isl_take isl_point *pnt, void *user)
3961 {
3962 struct isl_opt_data *data = (struct isl_opt_data *)user;
3963 isl_val *val;
3964
3965 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3966 if (data->first) {
3967 data->first = 0;
3968 data->opt = val;
3969 } else if (data->max) {
3970 data->opt = isl_val_max(data->opt, val);
3971 } else {
3972 data->opt = isl_val_min(data->opt, val);
3973 }
3974
3975 return 0;
3976 }
3977
3978 __isl_give isl_val *isl_qpolynomial_opt_on_domain(
3979 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3980 {
3981 struct isl_opt_data data = { NULL, 1, NULL, max };
3982
3983 if (!set || !qp)
3984 goto error;
3985
3986 if (isl_upoly_is_cst(qp->upoly)) {
3987 isl_set_free(set);
3988 data.opt = isl_qpolynomial_get_constant_val(qp);
3989 isl_qpolynomial_free(qp);
3990 return data.opt;
3991 }
3992
3993 set = fix_inactive(set, qp);
3994
3995 data.qp = qp;
3996 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3997 goto error;
3998
3999 if (data.first)
4000 data.opt = isl_val_zero(isl_set_get_ctx(set));
4001
4002 isl_set_free(set);
4003 isl_qpolynomial_free(qp);
4004 return data.opt;
4005 error:
4006 isl_set_free(set);
4007 isl_qpolynomial_free(qp);
4008 isl_val_free(data.opt);
4009 return NULL;
4010 }
4011
4012 __isl_give isl_qpolynomial *isl_qpolynomial_morph_domain(
4013 __isl_take isl_qpolynomial *qp, __isl_take isl_morph *morph)
4014 {
4015 int i;
4016 int n_sub;
4017 isl_ctx *ctx;
4018 struct isl_upoly **subs;
4019 isl_mat *mat, *diag;
4020
4021 qp = isl_qpolynomial_cow(qp);
4022 if (!qp || !morph)
4023 goto error;
4024
4025 ctx = qp->dim->ctx;
4026 isl_assert(ctx, isl_space_is_equal(qp->dim, morph->dom->dim), goto error);
4027
4028 n_sub = morph->inv->n_row - 1;
4029 if (morph->inv->n_row != morph->inv->n_col)
4030 n_sub += qp->div->n_row;
4031 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
4032 if (n_sub && !subs)
4033 goto error;
4034
4035 for (i = 0; 1 + i < morph->inv->n_row; ++i)
4036 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
4037 morph->inv->row[0][0], morph->inv->n_col);
4038 if (morph->inv->n_row != morph->inv->n_col)
4039 for (i = 0; i < qp->div->n_row; ++i)
4040 subs[morph->inv->n_row - 1 + i] =
4041 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
4042
4043 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
4044
4045 for (i = 0; i < n_sub; ++i)
4046 isl_upoly_free(subs[i]);
4047 free(subs);
4048
4049 diag = isl_mat_diag(ctx, 1, morph->inv->row[0][0]);
4050 mat = isl_mat_diagonal(diag, isl_mat_copy(morph->inv));
4051 diag = isl_mat_diag(ctx, qp->div->n_row, morph->inv->row[0][0]);
4052 mat = isl_mat_diagonal(mat, diag);
4053 qp->div = isl_mat_product(qp->div, mat);
4054 isl_space_free(qp->dim);
4055 qp->dim = isl_space_copy(morph->ran->dim);
4056
4057 if (!qp->upoly || !qp->div || !qp->dim)
4058 goto error;
4059
4060 isl_morph_free(morph);
4061
4062 return qp;
4063 error:
4064 isl_qpolynomial_free(qp);
4065 isl_morph_free(morph);
4066 return NULL;
4067 }
4068
4069 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4070 __isl_take isl_union_pw_qpolynomial *upwqp1,
4071 __isl_take isl_union_pw_qpolynomial *upwqp2)
4072 {
4073 return isl_union_pw_qpolynomial_match_bin_op(upwqp1, upwqp2,
4074 &isl_pw_qpolynomial_mul);
4075 }
4076
4077 /* Reorder the columns of the given div definitions according to the
4078 * given reordering.
4079 */
4080 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
4081 __isl_take isl_reordering *r)
4082 {
4083 int i, j;
4084 isl_mat *mat;
4085 int extra;
4086
4087 if (!div || !r)
4088 goto error;
4089
4090 extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
4091 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
4092 if (!mat)
4093 goto error;
4094
4095 for (i = 0; i < div->n_row; ++i) {
4096 isl_seq_cpy(mat->row[i], div->row[i], 2);
4097 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
4098 for (j = 0; j < r->len; ++j)
4099 isl_int_set(mat->row[i][2 + r->pos[j]],
4100 div->row[i][2 + j]);
4101 }
4102
4103 isl_reordering_free(r);
4104 isl_mat_free(div);
4105 return mat;
4106 error:
4107 isl_reordering_free(r);
4108 isl_mat_free(div);
4109 return NULL;
4110 }
4111
4112 /* Reorder the dimension of "qp" according to the given reordering.
4113 */
4114 __isl_give isl_qpolynomial *isl_qpolynomial_realign_domain(
4115 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
4116 {
4117 qp = isl_qpolynomial_cow(qp);
4118 if (!qp)
4119 goto error;
4120
4121 r = isl_reordering_extend(r, qp->div->n_row);
4122 if (!r)
4123 goto error;
4124
4125 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
4126 if (!qp->div)
4127 goto error;
4128
4129 qp->upoly = reorder(qp->upoly, r->pos);
4130 if (!qp->upoly)
4131 goto error;
4132
4133 qp = isl_qpolynomial_reset_domain_space(qp, isl_space_copy(r->dim));
4134
4135 isl_reordering_free(r);
4136 return qp;
4137 error:
4138 isl_qpolynomial_free(qp);
4139 isl_reordering_free(r);
4140 return NULL;
4141 }
4142
4143 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4144 __isl_take isl_qpolynomial *qp, __isl_take isl_space *model)
4145 {
4146 if (!qp || !model)
4147 goto error;
4148
4149 if (!isl_space_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
4150 isl_reordering *exp;
4151
4152 model = isl_space_drop_dims(model, isl_dim_in,
4153 0, isl_space_dim(model, isl_dim_in));
4154 model = isl_space_drop_dims(model, isl_dim_out,
4155 0, isl_space_dim(model, isl_dim_out));
4156 exp = isl_parameter_alignment_reordering(qp->dim, model);
4157 exp = isl_reordering_extend_space(exp,
4158 isl_qpolynomial_get_domain_space(qp));
4159 qp = isl_qpolynomial_realign_domain(qp, exp);
4160 }
4161
4162 isl_space_free(model);
4163 return qp;
4164 error:
4165 isl_space_free(model);
4166 isl_qpolynomial_free(qp);
4167 return NULL;
4168 }
4169
4170 struct isl_split_periods_data {
4171 int max_periods;
4172 isl_pw_qpolynomial *res;
4173 };
4174
4175 /* Create a slice where the integer division "div" has the fixed value "v".
4176 * In particular, if "div" refers to floor(f/m), then create a slice
4177 *
4178 * m v <= f <= m v + (m - 1)
4179 *
4180 * or
4181 *
4182 * f - m v >= 0
4183 * -f + m v + (m - 1) >= 0
4184 */
4185 static __isl_give isl_set *set_div_slice(__isl_take isl_space *dim,
4186 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4187 {
4188 int total;
4189 isl_basic_set *bset = NULL;
4190 int k;
4191
4192 if (!dim || !qp)
4193 goto error;
4194
4195 total = isl_space_dim(dim, isl_dim_all);
4196 bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0, 0, 2);
4197
4198 k = isl_basic_set_alloc_inequality(bset);
4199 if (k < 0)
4200 goto error;
4201 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4202 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4203
4204 k = isl_basic_set_alloc_inequality(bset);
4205 if (k < 0)
4206 goto error;
4207 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4208 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4209 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4210 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4211
4212 isl_space_free(dim);
4213 return isl_set_from_basic_set(bset);
4214 error:
4215 isl_basic_set_free(bset);
4216 isl_space_free(dim);
4217 return NULL;
4218 }
4219
4220 static int split_periods(__isl_take isl_set *set,
4221 __isl_take isl_qpolynomial *qp, void *user);
4222
4223 /* Create a slice of the domain "set" such that integer division "div"
4224 * has the fixed value "v" and add the results to data->res,
4225 * replacing the integer division by "v" in "qp".
4226 */
4227 static int set_div(__isl_take isl_set *set,
4228 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4229 struct isl_split_periods_data *data)
4230 {
4231 int i;
4232 int total;
4233 isl_set *slice;
4234 struct isl_upoly *cst;
4235
4236 slice = set_div_slice(isl_set_get_space(set), qp, div, v);
4237 set = isl_set_intersect(set, slice);
4238
4239 if (!qp)
4240 goto error;
4241
4242 total = isl_space_dim(qp->dim, isl_dim_all);
4243
4244 for (i = div + 1; i < qp->div->n_row; ++i) {
4245 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4246 continue;
4247 isl_int_addmul(qp->div->row[i][1],
4248 qp->div->row[i][2 + total + div], v);
4249 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4250 }
4251
4252 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4253 qp = substitute_div(qp, div, cst);
4254
4255 return split_periods(set, qp, data);
4256 error:
4257 isl_set_free(set);
4258 isl_qpolynomial_free(qp);
4259 return -1;
4260 }
4261
4262 /* Split the domain "set" such that integer division "div"
4263 * has a fixed value (ranging from "min" to "max") on each slice
4264 * and add the results to data->res.
4265 */
4266 static int split_div(__isl_take isl_set *set,
4267 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4268 struct isl_split_periods_data *data)
4269 {
4270 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4271 isl_set *set_i = isl_set_copy(set);
4272 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4273
4274 if (set_div(set_i, qp_i, div, min, data) < 0)
4275 goto error;
4276 }
4277 isl_set_free(set);
4278 isl_qpolynomial_free(qp);
4279 return 0;
4280 error:
4281 isl_set_free(set);
4282 isl_qpolynomial_free(qp);
4283 return -1;
4284 }
4285
4286 /* If "qp" refers to any integer division
4287 * that can only attain "max_periods" distinct values on "set"
4288 * then split the domain along those distinct values.
4289 * Add the results (or the original if no splitting occurs)
4290 * to data->res.
4291 */
4292 static int split_periods(__isl_take isl_set *set,
4293 __isl_take isl_qpolynomial *qp, void *user)
4294 {
4295 int i;
4296 isl_pw_qpolynomial *pwqp;
4297 struct isl_split_periods_data *data;
4298 isl_int min, max;
4299 int total;
4300 int r = 0;
4301
4302 data = (struct isl_split_periods_data *)user;
4303
4304 if (!set || !qp)
4305 goto error;
4306
4307 if (qp->div->n_row == 0) {
4308 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4309 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4310 return 0;
4311 }
4312
4313 isl_int_init(min);
4314 isl_int_init(max);
4315 total = isl_space_dim(qp->dim, isl_dim_all);
4316 for (i = 0; i < qp->div->n_row; ++i) {
4317 enum isl_lp_result lp_res;
4318
4319 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4320 qp->div->n_row) != -1)
4321 continue;
4322
4323 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4324 set->ctx->one, &min, NULL, NULL);
4325 if (lp_res == isl_lp_error)
4326 goto error2;
4327 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4328 continue;
4329 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4330
4331 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4332 set->ctx->one, &max, NULL, NULL);
4333 if (lp_res == isl_lp_error)
4334 goto error2;
4335 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4336 continue;
4337 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4338
4339 isl_int_sub(max, max, min);
4340 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4341 isl_int_add(max, max, min);
4342 break;
4343 }
4344 }
4345
4346 if (i < qp->div->n_row) {
4347 r = split_div(set, qp, i, min, max, data);
4348 } else {
4349 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4350 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4351 }
4352
4353 isl_int_clear(max);
4354 isl_int_clear(min);
4355
4356 return r;
4357 error2:
4358 isl_int_clear(max);
4359 isl_int_clear(min);
4360 error:
4361 isl_set_free(set);
4362 isl_qpolynomial_free(qp);
4363 return -1;
4364 }
4365
4366 /* If any quasi-polynomial in pwqp refers to any integer division
4367 * that can only attain "max_periods" distinct values on its domain
4368 * then split the domain along those distinct values.
4369 */
4370 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4371 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4372 {
4373 struct isl_split_periods_data data;
4374
4375 data.max_periods = max_periods;
4376 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4377
4378 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4379 goto error;
4380
4381 isl_pw_qpolynomial_free(pwqp);
4382
4383 return data.res;
4384 error:
4385 isl_pw_qpolynomial_free(data.res);
4386 isl_pw_qpolynomial_free(pwqp);
4387 return NULL;
4388 }
4389
4390 /* Construct a piecewise quasipolynomial that is constant on the given
4391 * domain. In particular, it is
4392 * 0 if cst == 0
4393 * 1 if cst == 1
4394 * infinity if cst == -1
4395 */
4396 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4397 __isl_take isl_basic_set *bset, int cst)
4398 {
4399 isl_space *dim;
4400 isl_qpolynomial *qp;
4401
4402 if (!bset)
4403 return NULL;
4404
4405 bset = isl_basic_set_params(bset);
4406 dim = isl_basic_set_get_space(bset);
4407 if (cst < 0)
4408 qp = isl_qpolynomial_infty_on_domain(dim);
4409 else if (cst == 0)
4410 qp = isl_qpolynomial_zero_on_domain(dim);
4411 else
4412 qp = isl_qpolynomial_one_on_domain(dim);
4413 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4414 }
4415
4416 /* Factor bset, call fn on each of the factors and return the product.
4417 *
4418 * If no factors can be found, simply call fn on the input.
4419 * Otherwise, construct the factors based on the factorizer,
4420 * call fn on each factor and compute the product.
4421 */
4422 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4423 __isl_take isl_basic_set *bset,
4424 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4425 {
4426 int i, n;
4427 isl_space *dim;
4428 isl_set *set;
4429 isl_factorizer *f;
4430 isl_qpolynomial *qp;
4431 isl_pw_qpolynomial *pwqp;
4432 unsigned nparam;
4433 unsigned nvar;
4434
4435 f = isl_basic_set_factorizer(bset);
4436 if (!f)
4437 goto error;
4438 if (f->n_group == 0) {
4439 isl_factorizer_free(f);
4440 return fn(bset);
4441 }
4442
4443 nparam = isl_basic_set_dim(bset, isl_dim_param);
4444 nvar = isl_basic_set_dim(bset, isl_dim_set);
4445
4446 dim = isl_basic_set_get_space(bset);
4447 dim = isl_space_domain(dim);
4448 set = isl_set_universe(isl_space_copy(dim));
4449 qp = isl_qpolynomial_one_on_domain(dim);
4450 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4451
4452 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4453
4454 for (i = 0, n = 0; i < f->n_group; ++i) {
4455 isl_basic_set *bset_i;
4456 isl_pw_qpolynomial *pwqp_i;
4457
4458 bset_i = isl_basic_set_copy(bset);
4459 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4460 nparam + n + f->len[i], nvar - n - f->len[i]);
4461 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4462 nparam, n);
4463 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4464 n + f->len[i], nvar - n - f->len[i]);
4465 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4466
4467 pwqp_i = fn(bset_i);
4468 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4469
4470 n += f->len[i];
4471 }
4472
4473 isl_basic_set_free(bset);
4474 isl_factorizer_free(f);
4475
4476 return pwqp;
4477 error:
4478 isl_basic_set_free(bset);
4479 return NULL;
4480 }
4481
4482 /* Factor bset, call fn on each of the factors and return the product.
4483 * The function is assumed to evaluate to zero on empty domains,
4484 * to one on zero-dimensional domains and to infinity on unbounded domains
4485 * and will not be called explicitly on zero-dimensional or unbounded domains.
4486 *
4487 * We first check for some special cases and remove all equalities.
4488 * Then we hand over control to compressed_multiplicative_call.
4489 */
4490 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4491 __isl_take isl_basic_set *bset,
4492 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4493 {
4494 int bounded;
4495 isl_morph *morph;
4496 isl_pw_qpolynomial *pwqp;
4497
4498 if (!bset)
4499 return NULL;
4500
4501 if (isl_basic_set_plain_is_empty(bset))
4502 return constant_on_domain(bset, 0);
4503
4504 if (isl_basic_set_dim(bset, isl_dim_set) == 0)
4505 return constant_on_domain(bset, 1);
4506
4507 bounded = isl_basic_set_is_bounded(bset);
4508 if (bounded < 0)
4509 goto error;
4510 if (!bounded)
4511 return constant_on_domain(bset, -1);
4512
4513 if (bset->n_eq == 0)
4514 return compressed_multiplicative_call(bset, fn);
4515
4516 morph = isl_basic_set_full_compression(bset);
4517 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4518
4519 pwqp = compressed_multiplicative_call(bset, fn);
4520
4521 morph = isl_morph_dom_params(morph);
4522 morph = isl_morph_ran_params(morph);
4523 morph = isl_morph_inverse(morph);
4524
4525 pwqp = isl_pw_qpolynomial_morph_domain(pwqp, morph);
4526
4527 return pwqp;
4528 error:
4529 isl_basic_set_free(bset);
4530 return NULL;
4531 }
4532
4533 /* Drop all floors in "qp", turning each integer division [a/m] into
4534 * a rational division a/m. If "down" is set, then the integer division
4535 * is replaced by (a-(m-1))/m instead.
4536 */
4537 static __isl_give isl_qpolynomial *qp_drop_floors(
4538 __isl_take isl_qpolynomial *qp, int down)
4539 {
4540 int i;
4541 struct isl_upoly *s;
4542
4543 if (!qp)
4544 return NULL;
4545 if (qp->div->n_row == 0)
4546 return qp;
4547
4548 qp = isl_qpolynomial_cow(qp);
4549 if (!qp)
4550 return NULL;
4551
4552 for (i = qp->div->n_row - 1; i >= 0; --i) {
4553 if (down) {
4554 isl_int_sub(qp->div->row[i][1],
4555 qp->div->row[i][1], qp->div->row[i][0]);
4556 isl_int_add_ui(qp->div->row[i][1],
4557 qp->div->row[i][1], 1);
4558 }
4559 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4560 qp->div->row[i][0], qp->div->n_col - 1);
4561 qp = substitute_div(qp, i, s);
4562 if (!qp)
4563 return NULL;
4564 }
4565
4566 return qp;
4567 }
4568
4569 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4570 * a rational division a/m.
4571 */
4572 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4573 __isl_take isl_pw_qpolynomial *pwqp)
4574 {
4575 int i;
4576
4577 if (!pwqp)
4578 return NULL;
4579
4580 if (isl_pw_qpolynomial_is_zero(pwqp))
4581 return pwqp;
4582
4583 pwqp = isl_pw_qpolynomial_cow(pwqp);
4584 if (!pwqp)
4585 return NULL;
4586
4587 for (i = 0; i < pwqp->n; ++i) {
4588 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4589 if (!pwqp->p[i].qp)
4590 goto error;
4591 }
4592
4593 return pwqp;
4594 error:
4595 isl_pw_qpolynomial_free(pwqp);
4596 return NULL;
4597 }
4598
4599 /* Adjust all the integer divisions in "qp" such that they are at least
4600 * one over the given orthant (identified by "signs"). This ensures
4601 * that they will still be non-negative even after subtracting (m-1)/m.
4602 *
4603 * In particular, f is replaced by f' + v, changing f = [a/m]
4604 * to f' = [(a - m v)/m].
4605 * If the constant term k in a is smaller than m,
4606 * the constant term of v is set to floor(k/m) - 1.
4607 * For any other term, if the coefficient c and the variable x have
4608 * the same sign, then no changes are needed.
4609 * Otherwise, if the variable is positive (and c is negative),
4610 * then the coefficient of x in v is set to floor(c/m).
4611 * If the variable is negative (and c is positive),
4612 * then the coefficient of x in v is set to ceil(c/m).
4613 */
4614 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4615 int *signs)
4616 {
4617 int i, j;
4618 int total;
4619 isl_vec *v = NULL;
4620 struct isl_upoly *s;
4621
4622 qp = isl_qpolynomial_cow(qp);
4623 if (!qp)
4624 return NULL;
4625 qp->div = isl_mat_cow(qp->div);
4626 if (!qp->div)
4627 goto error;
4628
4629 total = isl_space_dim(qp->dim, isl_dim_all);
4630 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4631
4632 for (i = 0; i < qp->div->n_row; ++i) {
4633 isl_int *row = qp->div->row[i];
4634 v = isl_vec_clr(v);
4635 if (!v)
4636 goto error;
4637 if (isl_int_lt(row[1], row[0])) {
4638 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4639 isl_int_sub_ui(v->el[0], v->el[0], 1);
4640 isl_int_submul(row[1], row[0], v->el[0]);
4641 }
4642 for (j = 0; j < total; ++j) {
4643 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4644 continue;
4645 if (signs[j] < 0)
4646 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4647 else
4648 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4649 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4650 }
4651 for (j = 0; j < i; ++j) {
4652 if (isl_int_sgn(row[2 + total + j]) >= 0)
4653 continue;
4654 isl_int_fdiv_q(v->el[1 + total + j],
4655 row[2 + total + j], row[0]);
4656 isl_int_submul(row[2 + total + j],
4657 row[0], v->el[1 + total + j]);
4658 }
4659 for (j = i + 1; j < qp->div->n_row; ++j) {
4660 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4661 continue;
4662 isl_seq_combine(qp->div->row[j] + 1,
4663 qp->div->ctx->one, qp->div->row[j] + 1,
4664 qp->div->row[j][2 + total + i], v->el, v->size);
4665 }
4666 isl_int_set_si(v->el[1 + total + i], 1);
4667 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4668 qp->div->ctx->one, v->size);
4669 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4670 isl_upoly_free(s);
4671 if (!qp->upoly)
4672 goto error;
4673 }
4674
4675 isl_vec_free(v);
4676 return qp;
4677 error:
4678 isl_vec_free(v);
4679 isl_qpolynomial_free(qp);
4680 return NULL;
4681 }
4682
4683 struct isl_to_poly_data {
4684 int sign;
4685 isl_pw_qpolynomial *res;
4686 isl_qpolynomial *qp;
4687 };
4688
4689 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4690 * We first make all integer divisions positive and then split the
4691 * quasipolynomials into terms with sign data->sign (the direction
4692 * of the requested approximation) and terms with the opposite sign.
4693 * In the first set of terms, each integer division [a/m] is
4694 * overapproximated by a/m, while in the second it is underapproximated
4695 * by (a-(m-1))/m.
4696 */
4697 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4698 void *user)
4699 {
4700 struct isl_to_poly_data *data = user;
4701 isl_pw_qpolynomial *t;
4702 isl_qpolynomial *qp, *up, *down;
4703
4704 qp = isl_qpolynomial_copy(data->qp);
4705 qp = make_divs_pos(qp, signs);
4706
4707 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4708 up = qp_drop_floors(up, 0);
4709 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4710 down = qp_drop_floors(down, 1);
4711
4712 isl_qpolynomial_free(qp);
4713 qp = isl_qpolynomial_add(up, down);
4714
4715 t = isl_pw_qpolynomial_alloc(orthant, qp);
4716 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4717
4718 return 0;
4719 }
4720
4721 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4722 * the polynomial will be an overapproximation. If "sign" is negative,
4723 * it will be an underapproximation. If "sign" is zero, the approximation
4724 * will lie somewhere in between.
4725 *
4726 * In particular, is sign == 0, we simply drop the floors, turning
4727 * the integer divisions into rational divisions.
4728 * Otherwise, we split the domains into orthants, make all integer divisions
4729 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4730 * depending on the requested sign and the sign of the term in which
4731 * the integer division appears.
4732 */
4733 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4734 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4735 {
4736 int i;
4737 struct isl_to_poly_data data;
4738
4739 if (sign == 0)
4740 return pwqp_drop_floors(pwqp);
4741
4742 if (!pwqp)
4743 return NULL;
4744
4745 data.sign = sign;
4746 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4747
4748 for (i = 0; i < pwqp->n; ++i) {
4749 if (pwqp->p[i].qp->div->n_row == 0) {
4750 isl_pw_qpolynomial *t;
4751 t = isl_pw_qpolynomial_alloc(
4752 isl_set_copy(pwqp->p[i].set),
4753 isl_qpolynomial_copy(pwqp->p[i].qp));
4754 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4755 continue;
4756 }
4757 data.qp = pwqp->p[i].qp;
4758 if (isl_set_foreach_orthant(pwqp->p[i].set,
4759 &to_polynomial_on_orthant, &data) < 0)
4760 goto error;
4761 }
4762
4763 isl_pw_qpolynomial_free(pwqp);
4764
4765 return data.res;
4766 error:
4767 isl_pw_qpolynomial_free(pwqp);
4768 isl_pw_qpolynomial_free(data.res);
4769 return NULL;
4770 }
4771
4772 static int poly_entry(void **entry, void *user)
4773 {
4774 int *sign = user;
4775 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4776
4777 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4778
4779 return *pwqp ? 0 : -1;
4780 }
4781
4782 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4783 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4784 {
4785 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4786 if (!upwqp)
4787 return NULL;
4788
4789 if (isl_hash_table_foreach(upwqp->space->ctx, &upwqp->table,
4790 &poly_entry, &sign) < 0)
4791 goto error;
4792
4793 return upwqp;
4794 error:
4795 isl_union_pw_qpolynomial_free(upwqp);
4796 return NULL;
4797 }
4798
4799 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4800 __isl_take isl_qpolynomial *qp)
4801 {
4802 int i, k;
4803 isl_space *dim;
4804 isl_vec *aff = NULL;
4805 isl_basic_map *bmap = NULL;
4806 unsigned pos;
4807 unsigned n_div;
4808
4809 if (!qp)
4810 return NULL;
4811 if (!isl_upoly_is_affine(qp->upoly))
4812 isl_die(qp->dim->ctx, isl_error_invalid,
4813 "input quasi-polynomial not affine", goto error);
4814 aff = isl_qpolynomial_extract_affine(qp);
4815 if (!aff)
4816 goto error;
4817 dim = isl_qpolynomial_get_space(qp);
4818 pos = 1 + isl_space_offset(dim, isl_dim_out);
4819 n_div = qp->div->n_row;
4820 bmap = isl_basic_map_alloc_space(dim, n_div, 1, 2 * n_div);
4821
4822 for (i = 0; i < n_div; ++i) {
4823 k = isl_basic_map_alloc_div(bmap);
4824 if (k < 0)
4825 goto error;
4826 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4827 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4828 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4829 goto error;
4830 }
4831 k = isl_basic_map_alloc_equality(bmap);
4832 if (k < 0)
4833 goto error;
4834 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4835 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4836 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4837
4838 isl_vec_free(aff);
4839 isl_qpolynomial_free(qp);
4840 bmap = isl_basic_map_finalize(bmap);
4841 return bmap;
4842 error:
4843 isl_vec_free(aff);
4844 isl_qpolynomial_free(qp);
4845 isl_basic_map_free(bmap);
4846 return NULL;
4847 }
Integer set library