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interface: update to move of llvm/Support/Host.h to llvm/TargetParser/Host.h
[isl.git] / isl_polynomial.c
blob7b4eae01489667a5ac0208dda47e07902f5b01bd
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 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl_factorization.h>
15 #include <isl_lp_private.h>
16 #include <isl_seq.h>
17 #include <isl_union_map_private.h>
18 #include <isl_constraint_private.h>
19 #include <isl_polynomial_private.h>
20 #include <isl_point_private.h>
21 #include <isl_space_private.h>
22 #include <isl_mat_private.h>
23 #include <isl_vec_private.h>
24 #include <isl_range.h>
25 #include <isl_local.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
31 #undef EL_BASE
32 #define EL_BASE qpolynomial
33
34 #include <isl_list_templ.c>
35
36 #undef EL_BASE
37 #define EL_BASE pw_qpolynomial
38
39 #include <isl_list_templ.c>
40
41 static unsigned pos(__isl_keep isl_space *space, enum isl_dim_type type)
42 {
43 switch (type) {
44 case isl_dim_param: return 0;
45 case isl_dim_in: return space->nparam;
46 case isl_dim_out: return space->nparam + space->n_in;
47 default: return 0;
48 }
49 }
50
51 isl_bool isl_poly_is_cst(__isl_keep isl_poly *poly)
52 {
53 if (!poly)
54 return isl_bool_error;
55
56 return isl_bool_ok(poly->var < 0);
57 }
58
59 __isl_keep isl_poly_cst *isl_poly_as_cst(__isl_keep isl_poly *poly)
60 {
61 if (!poly)
62 return NULL;
63
64 isl_assert(poly->ctx, poly->var < 0, return NULL);
65
66 return (isl_poly_cst *) poly;
67 }
68
69 __isl_keep isl_poly_rec *isl_poly_as_rec(__isl_keep isl_poly *poly)
70 {
71 if (!poly)
72 return NULL;
73
74 isl_assert(poly->ctx, poly->var >= 0, return NULL);
75
76 return (isl_poly_rec *) poly;
77 }
78
79 /* Compare two polynomials.
80 *
81 * Return -1 if "poly1" is "smaller" than "poly2", 1 if "poly1" is "greater"
82 * than "poly2" and 0 if they are equal.
83 */
84 static int isl_poly_plain_cmp(__isl_keep isl_poly *poly1,
85 __isl_keep isl_poly *poly2)
86 {
87 int i;
88 isl_bool is_cst1;
89 isl_poly_rec *rec1, *rec2;
90
91 if (poly1 == poly2)
92 return 0;
93 is_cst1 = isl_poly_is_cst(poly1);
94 if (is_cst1 < 0)
95 return -1;
96 if (!poly2)
97 return 1;
98 if (poly1->var != poly2->var)
99 return poly1->var - poly2->var;
100
101 if (is_cst1) {
102 isl_poly_cst *cst1, *cst2;
103 int cmp;
104
105 cst1 = isl_poly_as_cst(poly1);
106 cst2 = isl_poly_as_cst(poly2);
107 if (!cst1 || !cst2)
108 return 0;
109 cmp = isl_int_cmp(cst1->n, cst2->n);
110 if (cmp != 0)
111 return cmp;
112 return isl_int_cmp(cst1->d, cst2->d);
113 }
114
115 rec1 = isl_poly_as_rec(poly1);
116 rec2 = isl_poly_as_rec(poly2);
117 if (!rec1 || !rec2)
118 return 0;
119
120 if (rec1->n != rec2->n)
121 return rec1->n - rec2->n;
122
123 for (i = 0; i < rec1->n; ++i) {
124 int cmp = isl_poly_plain_cmp(rec1->p[i], rec2->p[i]);
125 if (cmp != 0)
126 return cmp;
127 }
128
129 return 0;
130 }
131
132 isl_bool isl_poly_is_equal(__isl_keep isl_poly *poly1,
133 __isl_keep isl_poly *poly2)
134 {
135 int i;
136 isl_bool is_cst1;
137 isl_poly_rec *rec1, *rec2;
138
139 is_cst1 = isl_poly_is_cst(poly1);
140 if (is_cst1 < 0 || !poly2)
141 return isl_bool_error;
142 if (poly1 == poly2)
143 return isl_bool_true;
144 if (poly1->var != poly2->var)
145 return isl_bool_false;
146 if (is_cst1) {
147 isl_poly_cst *cst1, *cst2;
148 int r;
149 cst1 = isl_poly_as_cst(poly1);
150 cst2 = isl_poly_as_cst(poly2);
151 if (!cst1 || !cst2)
152 return isl_bool_error;
153 r = isl_int_eq(cst1->n, cst2->n) &&
154 isl_int_eq(cst1->d, cst2->d);
155 return isl_bool_ok(r);
156 }
157
158 rec1 = isl_poly_as_rec(poly1);
159 rec2 = isl_poly_as_rec(poly2);
160 if (!rec1 || !rec2)
161 return isl_bool_error;
162
163 if (rec1->n != rec2->n)
164 return isl_bool_false;
165
166 for (i = 0; i < rec1->n; ++i) {
167 isl_bool eq = isl_poly_is_equal(rec1->p[i], rec2->p[i]);
168 if (eq < 0 || !eq)
169 return eq;
170 }
171
172 return isl_bool_true;
173 }
174
175 isl_bool isl_poly_is_zero(__isl_keep isl_poly *poly)
176 {
177 isl_bool is_cst;
178 isl_poly_cst *cst;
179
180 is_cst = isl_poly_is_cst(poly);
181 if (is_cst < 0 || !is_cst)
182 return is_cst;
183
184 cst = isl_poly_as_cst(poly);
185 if (!cst)
186 return isl_bool_error;
187
188 return isl_bool_ok(isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d));
189 }
190
191 int isl_poly_sgn(__isl_keep isl_poly *poly)
192 {
193 isl_bool is_cst;
194 isl_poly_cst *cst;
195
196 is_cst = isl_poly_is_cst(poly);
197 if (is_cst < 0 || !is_cst)
198 return 0;
199
200 cst = isl_poly_as_cst(poly);
201 if (!cst)
202 return 0;
203
204 return isl_int_sgn(cst->n);
205 }
206
207 isl_bool isl_poly_is_nan(__isl_keep isl_poly *poly)
208 {
209 isl_bool is_cst;
210 isl_poly_cst *cst;
211
212 is_cst = isl_poly_is_cst(poly);
213 if (is_cst < 0 || !is_cst)
214 return is_cst;
215
216 cst = isl_poly_as_cst(poly);
217 if (!cst)
218 return isl_bool_error;
219
220 return isl_bool_ok(isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d));
221 }
222
223 isl_bool isl_poly_is_infty(__isl_keep isl_poly *poly)
224 {
225 isl_bool is_cst;
226 isl_poly_cst *cst;
227
228 is_cst = isl_poly_is_cst(poly);
229 if (is_cst < 0 || !is_cst)
230 return is_cst;
231
232 cst = isl_poly_as_cst(poly);
233 if (!cst)
234 return isl_bool_error;
235
236 return isl_bool_ok(isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d));
237 }
238
239 isl_bool isl_poly_is_neginfty(__isl_keep isl_poly *poly)
240 {
241 isl_bool is_cst;
242 isl_poly_cst *cst;
243
244 is_cst = isl_poly_is_cst(poly);
245 if (is_cst < 0 || !is_cst)
246 return is_cst;
247
248 cst = isl_poly_as_cst(poly);
249 if (!cst)
250 return isl_bool_error;
251
252 return isl_bool_ok(isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d));
253 }
254
255 isl_bool isl_poly_is_one(__isl_keep isl_poly *poly)
256 {
257 isl_bool is_cst;
258 isl_poly_cst *cst;
259 int r;
260
261 is_cst = isl_poly_is_cst(poly);
262 if (is_cst < 0 || !is_cst)
263 return is_cst;
264
265 cst = isl_poly_as_cst(poly);
266 if (!cst)
267 return isl_bool_error;
268
269 r = isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
270 return isl_bool_ok(r);
271 }
272
273 isl_bool isl_poly_is_negone(__isl_keep isl_poly *poly)
274 {
275 isl_bool is_cst;
276 isl_poly_cst *cst;
277
278 is_cst = isl_poly_is_cst(poly);
279 if (is_cst < 0 || !is_cst)
280 return is_cst;
281
282 cst = isl_poly_as_cst(poly);
283 if (!cst)
284 return isl_bool_error;
285
286 return isl_bool_ok(isl_int_is_negone(cst->n) && isl_int_is_one(cst->d));
287 }
288
289 __isl_give isl_poly_cst *isl_poly_cst_alloc(isl_ctx *ctx)
290 {
291 isl_poly_cst *cst;
292
293 cst = isl_alloc_type(ctx, struct isl_poly_cst);
294 if (!cst)
295 return NULL;
296
297 cst->poly.ref = 1;
298 cst->poly.ctx = ctx;
299 isl_ctx_ref(ctx);
300 cst->poly.var = -1;
301
302 isl_int_init(cst->n);
303 isl_int_init(cst->d);
304
305 return cst;
306 }
307
308 __isl_give isl_poly *isl_poly_zero(isl_ctx *ctx)
309 {
310 isl_poly_cst *cst;
311
312 cst = isl_poly_cst_alloc(ctx);
313 if (!cst)
314 return NULL;
315
316 isl_int_set_si(cst->n, 0);
317 isl_int_set_si(cst->d, 1);
318
319 return &cst->poly;
320 }
321
322 __isl_give isl_poly *isl_poly_one(isl_ctx *ctx)
323 {
324 isl_poly_cst *cst;
325
326 cst = isl_poly_cst_alloc(ctx);
327 if (!cst)
328 return NULL;
329
330 isl_int_set_si(cst->n, 1);
331 isl_int_set_si(cst->d, 1);
332
333 return &cst->poly;
334 }
335
336 __isl_give isl_poly *isl_poly_infty(isl_ctx *ctx)
337 {
338 isl_poly_cst *cst;
339
340 cst = isl_poly_cst_alloc(ctx);
341 if (!cst)
342 return NULL;
343
344 isl_int_set_si(cst->n, 1);
345 isl_int_set_si(cst->d, 0);
346
347 return &cst->poly;
348 }
349
350 __isl_give isl_poly *isl_poly_neginfty(isl_ctx *ctx)
351 {
352 isl_poly_cst *cst;
353
354 cst = isl_poly_cst_alloc(ctx);
355 if (!cst)
356 return NULL;
357
358 isl_int_set_si(cst->n, -1);
359 isl_int_set_si(cst->d, 0);
360
361 return &cst->poly;
362 }
363
364 __isl_give isl_poly *isl_poly_nan(isl_ctx *ctx)
365 {
366 isl_poly_cst *cst;
367
368 cst = isl_poly_cst_alloc(ctx);
369 if (!cst)
370 return NULL;
371
372 isl_int_set_si(cst->n, 0);
373 isl_int_set_si(cst->d, 0);
374
375 return &cst->poly;
376 }
377
378 __isl_give isl_poly *isl_poly_rat_cst(isl_ctx *ctx, isl_int n, isl_int d)
379 {
380 isl_poly_cst *cst;
381
382 cst = isl_poly_cst_alloc(ctx);
383 if (!cst)
384 return NULL;
385
386 isl_int_set(cst->n, n);
387 isl_int_set(cst->d, d);
388
389 return &cst->poly;
390 }
391
392 __isl_give isl_poly_rec *isl_poly_alloc_rec(isl_ctx *ctx, int var, int size)
393 {
394 isl_poly_rec *rec;
395
396 isl_assert(ctx, var >= 0, return NULL);
397 isl_assert(ctx, size >= 0, return NULL);
398 rec = isl_calloc(ctx, struct isl_poly_rec,
399 sizeof(struct isl_poly_rec) +
400 size * sizeof(struct isl_poly *));
401 if (!rec)
402 return NULL;
403
404 rec->poly.ref = 1;
405 rec->poly.ctx = ctx;
406 isl_ctx_ref(ctx);
407 rec->poly.var = var;
408
409 rec->n = 0;
410 rec->size = size;
411
412 return rec;
413 }
414
415 __isl_give isl_qpolynomial *isl_qpolynomial_reset_domain_space(
416 __isl_take isl_qpolynomial *qp, __isl_take isl_space *space)
417 {
418 qp = isl_qpolynomial_cow(qp);
419 if (!qp || !space)
420 goto error;
421
422 isl_space_free(qp->dim);
423 qp->dim = space;
424
425 return qp;
426 error:
427 isl_qpolynomial_free(qp);
428 isl_space_free(space);
429 return NULL;
430 }
431
432 /* Reset the space of "qp". This function is called from isl_pw_templ.c
433 * and doesn't know if the space of an element object is represented
434 * directly or through its domain. It therefore passes along both.
435 */
436 __isl_give isl_qpolynomial *isl_qpolynomial_reset_space_and_domain(
437 __isl_take isl_qpolynomial *qp, __isl_take isl_space *space,
438 __isl_take isl_space *domain)
439 {
440 isl_space_free(space);
441 return isl_qpolynomial_reset_domain_space(qp, domain);
442 }
443
444 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
445 {
446 return qp ? qp->dim->ctx : NULL;
447 }
448
449 /* Return the domain space of "qp".
450 */
451 static __isl_keep isl_space *isl_qpolynomial_peek_domain_space(
452 __isl_keep isl_qpolynomial *qp)
453 {
454 return qp ? qp->dim : NULL;
455 }
456
457 /* Return a copy of the domain space of "qp".
458 */
459 __isl_give isl_space *isl_qpolynomial_get_domain_space(
460 __isl_keep isl_qpolynomial *qp)
461 {
462 return isl_space_copy(isl_qpolynomial_peek_domain_space(qp));
463 }
464
465 #undef TYPE
466 #define TYPE isl_qpolynomial
467 #undef PEEK_SPACE
468 #define PEEK_SPACE peek_domain_space
469
470 static
471 #include "isl_type_has_equal_space_bin_templ.c"
472 static
473 #include "isl_type_check_equal_space_templ.c"
474
475 #undef PEEK_SPACE
476
477 /* Return a copy of the local space on which "qp" is defined.
478 */
479 static __isl_give isl_local_space *isl_qpolynomial_get_domain_local_space(
480 __isl_keep isl_qpolynomial *qp)
481 {
482 isl_space *space;
483
484 if (!qp)
485 return NULL;
486
487 space = isl_qpolynomial_get_domain_space(qp);
488 return isl_local_space_alloc_div(space, isl_mat_copy(qp->div));
489 }
490
491 __isl_give isl_space *isl_qpolynomial_get_space(__isl_keep isl_qpolynomial *qp)
492 {
493 isl_space *space;
494 if (!qp)
495 return NULL;
496 space = isl_space_copy(qp->dim);
497 space = isl_space_from_domain(space);
498 space = isl_space_add_dims(space, isl_dim_out, 1);
499 return space;
500 }
501
502 /* Return the number of variables of the given type in the domain of "qp".
503 */
504 isl_size isl_qpolynomial_domain_dim(__isl_keep isl_qpolynomial *qp,
505 enum isl_dim_type type)
506 {
507 isl_space *space;
508 isl_size dim;
509
510 space = isl_qpolynomial_peek_domain_space(qp);
511
512 if (!space)
513 return isl_size_error;
514 if (type == isl_dim_div)
515 return qp->div->n_row;
516 dim = isl_space_dim(space, type);
517 if (dim < 0)
518 return isl_size_error;
519 if (type == isl_dim_all) {
520 isl_size n_div;
521
522 n_div = isl_qpolynomial_domain_dim(qp, isl_dim_div);
523 if (n_div < 0)
524 return isl_size_error;
525 dim += n_div;
526 }
527 return dim;
528 }
529
530 /* Given the type of a dimension of an isl_qpolynomial,
531 * return the type of the corresponding dimension in its domain.
532 * This function is only called for "type" equal to isl_dim_in or
533 * isl_dim_param.
534 */
535 static enum isl_dim_type domain_type(enum isl_dim_type type)
536 {
537 return type == isl_dim_in ? isl_dim_set : type;
538 }
539
540 /* Externally, an isl_qpolynomial has a map space, but internally, the
541 * ls field corresponds to the domain of that space.
542 */
543 isl_size isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
544 enum isl_dim_type type)
545 {
546 if (!qp)
547 return isl_size_error;
548 if (type == isl_dim_out)
549 return 1;
550 type = domain_type(type);
551 return isl_qpolynomial_domain_dim(qp, type);
552 }
553
554 /* Return the offset of the first variable of type "type" within
555 * the variables of the domain of "qp".
556 */
557 static isl_size isl_qpolynomial_domain_var_offset(
558 __isl_keep isl_qpolynomial *qp, enum isl_dim_type type)
559 {
560 isl_space *space;
561
562 space = isl_qpolynomial_peek_domain_space(qp);
563 if (!space)
564 return isl_size_error;
565
566 switch (type) {
567 case isl_dim_param:
568 case isl_dim_set: return isl_space_offset(space, type);
569 case isl_dim_div: return isl_space_dim(space, isl_dim_all);
570 case isl_dim_cst:
571 default:
572 isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
573 "invalid dimension type", return isl_size_error);
574 }
575 }
576
577 /* Return the offset of the first coefficient of type "type" in
578 * the domain of "qp".
579 */
580 unsigned isl_qpolynomial_domain_offset(__isl_keep isl_qpolynomial *qp,
581 enum isl_dim_type type)
582 {
583 switch (type) {
584 case isl_dim_cst:
585 return 0;
586 case isl_dim_param:
587 case isl_dim_set:
588 case isl_dim_div:
589 return 1 + isl_qpolynomial_domain_var_offset(qp, type);
590 default:
591 return 0;
592 }
593 }
594
595 isl_bool isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
596 {
597 return qp ? isl_poly_is_zero(qp->poly) : isl_bool_error;
598 }
599
600 isl_bool isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
601 {
602 return qp ? isl_poly_is_one(qp->poly) : isl_bool_error;
603 }
604
605 isl_bool isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
606 {
607 return qp ? isl_poly_is_nan(qp->poly) : isl_bool_error;
608 }
609
610 isl_bool isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
611 {
612 return qp ? isl_poly_is_infty(qp->poly) : isl_bool_error;
613 }
614
615 isl_bool isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
616 {
617 return qp ? isl_poly_is_neginfty(qp->poly) : isl_bool_error;
618 }
619
620 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
621 {
622 return qp ? isl_poly_sgn(qp->poly) : 0;
623 }
624
625 static void poly_free_cst(__isl_take isl_poly_cst *cst)
626 {
627 isl_int_clear(cst->n);
628 isl_int_clear(cst->d);
629 }
630
631 static void poly_free_rec(__isl_take isl_poly_rec *rec)
632 {
633 int i;
634
635 for (i = 0; i < rec->n; ++i)
636 isl_poly_free(rec->p[i]);
637 }
638
639 __isl_give isl_poly *isl_poly_copy(__isl_keep isl_poly *poly)
640 {
641 if (!poly)
642 return NULL;
643
644 poly->ref++;
645 return poly;
646 }
647
648 __isl_give isl_poly *isl_poly_dup_cst(__isl_keep isl_poly *poly)
649 {
650 isl_poly_cst *cst;
651 isl_poly_cst *dup;
652
653 cst = isl_poly_as_cst(poly);
654 if (!cst)
655 return NULL;
656
657 dup = isl_poly_as_cst(isl_poly_zero(poly->ctx));
658 if (!dup)
659 return NULL;
660 isl_int_set(dup->n, cst->n);
661 isl_int_set(dup->d, cst->d);
662
663 return &dup->poly;
664 }
665
666 __isl_give isl_poly *isl_poly_dup_rec(__isl_keep isl_poly *poly)
667 {
668 int i;
669 isl_poly_rec *rec;
670 isl_poly_rec *dup;
671
672 rec = isl_poly_as_rec(poly);
673 if (!rec)
674 return NULL;
675
676 dup = isl_poly_alloc_rec(poly->ctx, poly->var, rec->n);
677 if (!dup)
678 return NULL;
679
680 for (i = 0; i < rec->n; ++i) {
681 dup->p[i] = isl_poly_copy(rec->p[i]);
682 if (!dup->p[i])
683 goto error;
684 dup->n++;
685 }
686
687 return &dup->poly;
688 error:
689 isl_poly_free(&dup->poly);
690 return NULL;
691 }
692
693 __isl_give isl_poly *isl_poly_dup(__isl_keep isl_poly *poly)
694 {
695 isl_bool is_cst;
696
697 is_cst = isl_poly_is_cst(poly);
698 if (is_cst < 0)
699 return NULL;
700 if (is_cst)
701 return isl_poly_dup_cst(poly);
702 else
703 return isl_poly_dup_rec(poly);
704 }
705
706 __isl_give isl_poly *isl_poly_cow(__isl_take isl_poly *poly)
707 {
708 if (!poly)
709 return NULL;
710
711 if (poly->ref == 1)
712 return poly;
713 poly->ref--;
714 return isl_poly_dup(poly);
715 }
716
717 __isl_null isl_poly *isl_poly_free(__isl_take isl_poly *poly)
718 {
719 if (!poly)
720 return NULL;
721
722 if (--poly->ref > 0)
723 return NULL;
724
725 if (poly->var < 0)
726 poly_free_cst((isl_poly_cst *) poly);
727 else
728 poly_free_rec((isl_poly_rec *) poly);
729
730 isl_ctx_deref(poly->ctx);
731 free(poly);
732 return NULL;
733 }
734
735 static void isl_poly_cst_reduce(__isl_keep isl_poly_cst *cst)
736 {
737 isl_int gcd;
738
739 isl_int_init(gcd);
740 isl_int_gcd(gcd, cst->n, cst->d);
741 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
742 isl_int_divexact(cst->n, cst->n, gcd);
743 isl_int_divexact(cst->d, cst->d, gcd);
744 }
745 isl_int_clear(gcd);
746 }
747
748 __isl_give isl_poly *isl_poly_sum_cst(__isl_take isl_poly *poly1,
749 __isl_take isl_poly *poly2)
750 {
751 isl_poly_cst *cst1;
752 isl_poly_cst *cst2;
753
754 poly1 = isl_poly_cow(poly1);
755 if (!poly1 || !poly2)
756 goto error;
757
758 cst1 = isl_poly_as_cst(poly1);
759 cst2 = isl_poly_as_cst(poly2);
760
761 if (isl_int_eq(cst1->d, cst2->d))
762 isl_int_add(cst1->n, cst1->n, cst2->n);
763 else {
764 isl_int_mul(cst1->n, cst1->n, cst2->d);
765 isl_int_addmul(cst1->n, cst2->n, cst1->d);
766 isl_int_mul(cst1->d, cst1->d, cst2->d);
767 }
768
769 isl_poly_cst_reduce(cst1);
770
771 isl_poly_free(poly2);
772 return poly1;
773 error:
774 isl_poly_free(poly1);
775 isl_poly_free(poly2);
776 return NULL;
777 }
778
779 static __isl_give isl_poly *replace_by_zero(__isl_take isl_poly *poly)
780 {
781 struct isl_ctx *ctx;
782
783 if (!poly)
784 return NULL;
785 ctx = poly->ctx;
786 isl_poly_free(poly);
787 return isl_poly_zero(ctx);
788 }
789
790 static __isl_give isl_poly *replace_by_constant_term(__isl_take isl_poly *poly)
791 {
792 isl_poly_rec *rec;
793 isl_poly *cst;
794
795 if (!poly)
796 return NULL;
797
798 rec = isl_poly_as_rec(poly);
799 if (!rec)
800 goto error;
801 cst = isl_poly_copy(rec->p[0]);
802 isl_poly_free(poly);
803 return cst;
804 error:
805 isl_poly_free(poly);
806 return NULL;
807 }
808
809 __isl_give isl_poly *isl_poly_sum(__isl_take isl_poly *poly1,
810 __isl_take isl_poly *poly2)
811 {
812 int i;
813 isl_bool is_zero, is_nan, is_cst;
814 isl_poly_rec *rec1, *rec2;
815
816 if (!poly1 || !poly2)
817 goto error;
818
819 is_nan = isl_poly_is_nan(poly1);
820 if (is_nan < 0)
821 goto error;
822 if (is_nan) {
823 isl_poly_free(poly2);
824 return poly1;
825 }
826
827 is_nan = isl_poly_is_nan(poly2);
828 if (is_nan < 0)
829 goto error;
830 if (is_nan) {
831 isl_poly_free(poly1);
832 return poly2;
833 }
834
835 is_zero = isl_poly_is_zero(poly1);
836 if (is_zero < 0)
837 goto error;
838 if (is_zero) {
839 isl_poly_free(poly1);
840 return poly2;
841 }
842
843 is_zero = isl_poly_is_zero(poly2);
844 if (is_zero < 0)
845 goto error;
846 if (is_zero) {
847 isl_poly_free(poly2);
848 return poly1;
849 }
850
851 if (poly1->var < poly2->var)
852 return isl_poly_sum(poly2, poly1);
853
854 if (poly2->var < poly1->var) {
855 isl_poly_rec *rec;
856 isl_bool is_infty;
857
858 is_infty = isl_poly_is_infty(poly2);
859 if (is_infty >= 0 && !is_infty)
860 is_infty = isl_poly_is_neginfty(poly2);
861 if (is_infty < 0)
862 goto error;
863 if (is_infty) {
864 isl_poly_free(poly1);
865 return poly2;
866 }
867 poly1 = isl_poly_cow(poly1);
868 rec = isl_poly_as_rec(poly1);
869 if (!rec)
870 goto error;
871 rec->p[0] = isl_poly_sum(rec->p[0], poly2);
872 if (rec->n == 1)
873 poly1 = replace_by_constant_term(poly1);
874 return poly1;
875 }
876
877 is_cst = isl_poly_is_cst(poly1);
878 if (is_cst < 0)
879 goto error;
880 if (is_cst)
881 return isl_poly_sum_cst(poly1, poly2);
882
883 rec1 = isl_poly_as_rec(poly1);
884 rec2 = isl_poly_as_rec(poly2);
885 if (!rec1 || !rec2)
886 goto error;
887
888 if (rec1->n < rec2->n)
889 return isl_poly_sum(poly2, poly1);
890
891 poly1 = isl_poly_cow(poly1);
892 rec1 = isl_poly_as_rec(poly1);
893 if (!rec1)
894 goto error;
895
896 for (i = rec2->n - 1; i >= 0; --i) {
897 isl_bool is_zero;
898
899 rec1->p[i] = isl_poly_sum(rec1->p[i],
900 isl_poly_copy(rec2->p[i]));
901 if (!rec1->p[i])
902 goto error;
903 if (i != rec1->n - 1)
904 continue;
905 is_zero = isl_poly_is_zero(rec1->p[i]);
906 if (is_zero < 0)
907 goto error;
908 if (is_zero) {
909 isl_poly_free(rec1->p[i]);
910 rec1->n--;
911 }
912 }
913
914 if (rec1->n == 0)
915 poly1 = replace_by_zero(poly1);
916 else if (rec1->n == 1)
917 poly1 = replace_by_constant_term(poly1);
918
919 isl_poly_free(poly2);
920
921 return poly1;
922 error:
923 isl_poly_free(poly1);
924 isl_poly_free(poly2);
925 return NULL;
926 }
927
928 __isl_give isl_poly *isl_poly_cst_add_isl_int(__isl_take isl_poly *poly,
929 isl_int v)
930 {
931 isl_poly_cst *cst;
932
933 poly = isl_poly_cow(poly);
934 if (!poly)
935 return NULL;
936
937 cst = isl_poly_as_cst(poly);
938
939 isl_int_addmul(cst->n, cst->d, v);
940
941 return poly;
942 }
943
944 __isl_give isl_poly *isl_poly_add_isl_int(__isl_take isl_poly *poly, isl_int v)
945 {
946 isl_bool is_cst;
947 isl_poly_rec *rec;
948
949 is_cst = isl_poly_is_cst(poly);
950 if (is_cst < 0)
951 return isl_poly_free(poly);
952 if (is_cst)
953 return isl_poly_cst_add_isl_int(poly, v);
954
955 poly = isl_poly_cow(poly);
956 rec = isl_poly_as_rec(poly);
957 if (!rec)
958 goto error;
959
960 rec->p[0] = isl_poly_add_isl_int(rec->p[0], v);
961 if (!rec->p[0])
962 goto error;
963
964 return poly;
965 error:
966 isl_poly_free(poly);
967 return NULL;
968 }
969
970 __isl_give isl_poly *isl_poly_cst_mul_isl_int(__isl_take isl_poly *poly,
971 isl_int v)
972 {
973 isl_bool is_zero;
974 isl_poly_cst *cst;
975
976 is_zero = isl_poly_is_zero(poly);
977 if (is_zero < 0)
978 return isl_poly_free(poly);
979 if (is_zero)
980 return poly;
981
982 poly = isl_poly_cow(poly);
983 if (!poly)
984 return NULL;
985
986 cst = isl_poly_as_cst(poly);
987
988 isl_int_mul(cst->n, cst->n, v);
989
990 return poly;
991 }
992
993 __isl_give isl_poly *isl_poly_mul_isl_int(__isl_take isl_poly *poly, isl_int v)
994 {
995 int i;
996 isl_bool is_cst;
997 isl_poly_rec *rec;
998
999 is_cst = isl_poly_is_cst(poly);
1000 if (is_cst < 0)
1001 return isl_poly_free(poly);
1002 if (is_cst)
1003 return isl_poly_cst_mul_isl_int(poly, v);
1004
1005 poly = isl_poly_cow(poly);
1006 rec = isl_poly_as_rec(poly);
1007 if (!rec)
1008 goto error;
1009
1010 for (i = 0; i < rec->n; ++i) {
1011 rec->p[i] = isl_poly_mul_isl_int(rec->p[i], v);
1012 if (!rec->p[i])
1013 goto error;
1014 }
1015
1016 return poly;
1017 error:
1018 isl_poly_free(poly);
1019 return NULL;
1020 }
1021
1022 /* Multiply the constant polynomial "poly" by "v".
1023 */
1024 static __isl_give isl_poly *isl_poly_cst_scale_val(__isl_take isl_poly *poly,
1025 __isl_keep isl_val *v)
1026 {
1027 isl_bool is_zero;
1028 isl_poly_cst *cst;
1029
1030 is_zero = isl_poly_is_zero(poly);
1031 if (is_zero < 0)
1032 return isl_poly_free(poly);
1033 if (is_zero)
1034 return poly;
1035
1036 poly = isl_poly_cow(poly);
1037 if (!poly)
1038 return NULL;
1039
1040 cst = isl_poly_as_cst(poly);
1041
1042 isl_int_mul(cst->n, cst->n, v->n);
1043 isl_int_mul(cst->d, cst->d, v->d);
1044 isl_poly_cst_reduce(cst);
1045
1046 return poly;
1047 }
1048
1049 /* Multiply the polynomial "poly" by "v".
1050 */
1051 static __isl_give isl_poly *isl_poly_scale_val(__isl_take isl_poly *poly,
1052 __isl_keep isl_val *v)
1053 {
1054 int i;
1055 isl_bool is_cst;
1056 isl_poly_rec *rec;
1057
1058 is_cst = isl_poly_is_cst(poly);
1059 if (is_cst < 0)
1060 return isl_poly_free(poly);
1061 if (is_cst)
1062 return isl_poly_cst_scale_val(poly, v);
1063
1064 poly = isl_poly_cow(poly);
1065 rec = isl_poly_as_rec(poly);
1066 if (!rec)
1067 goto error;
1068
1069 for (i = 0; i < rec->n; ++i) {
1070 rec->p[i] = isl_poly_scale_val(rec->p[i], v);
1071 if (!rec->p[i])
1072 goto error;
1073 }
1074
1075 return poly;
1076 error:
1077 isl_poly_free(poly);
1078 return NULL;
1079 }
1080
1081 __isl_give isl_poly *isl_poly_mul_cst(__isl_take isl_poly *poly1,
1082 __isl_take isl_poly *poly2)
1083 {
1084 isl_poly_cst *cst1;
1085 isl_poly_cst *cst2;
1086
1087 poly1 = isl_poly_cow(poly1);
1088 if (!poly1 || !poly2)
1089 goto error;
1090
1091 cst1 = isl_poly_as_cst(poly1);
1092 cst2 = isl_poly_as_cst(poly2);
1093
1094 isl_int_mul(cst1->n, cst1->n, cst2->n);
1095 isl_int_mul(cst1->d, cst1->d, cst2->d);
1096
1097 isl_poly_cst_reduce(cst1);
1098
1099 isl_poly_free(poly2);
1100 return poly1;
1101 error:
1102 isl_poly_free(poly1);
1103 isl_poly_free(poly2);
1104 return NULL;
1105 }
1106
1107 __isl_give isl_poly *isl_poly_mul_rec(__isl_take isl_poly *poly1,
1108 __isl_take isl_poly *poly2)
1109 {
1110 isl_poly_rec *rec1;
1111 isl_poly_rec *rec2;
1112 isl_poly_rec *res = NULL;
1113 int i, j;
1114 int size;
1115
1116 rec1 = isl_poly_as_rec(poly1);
1117 rec2 = isl_poly_as_rec(poly2);
1118 if (!rec1 || !rec2)
1119 goto error;
1120 size = rec1->n + rec2->n - 1;
1121 res = isl_poly_alloc_rec(poly1->ctx, poly1->var, size);
1122 if (!res)
1123 goto error;
1124
1125 for (i = 0; i < rec1->n; ++i) {
1126 res->p[i] = isl_poly_mul(isl_poly_copy(rec2->p[0]),
1127 isl_poly_copy(rec1->p[i]));
1128 if (!res->p[i])
1129 goto error;
1130 res->n++;
1131 }
1132 for (; i < size; ++i) {
1133 res->p[i] = isl_poly_zero(poly1->ctx);
1134 if (!res->p[i])
1135 goto error;
1136 res->n++;
1137 }
1138 for (i = 0; i < rec1->n; ++i) {
1139 for (j = 1; j < rec2->n; ++j) {
1140 isl_poly *poly;
1141 poly = isl_poly_mul(isl_poly_copy(rec2->p[j]),
1142 isl_poly_copy(rec1->p[i]));
1143 res->p[i + j] = isl_poly_sum(res->p[i + j], poly);
1144 if (!res->p[i + j])
1145 goto error;
1146 }
1147 }
1148
1149 isl_poly_free(poly1);
1150 isl_poly_free(poly2);
1151
1152 return &res->poly;
1153 error:
1154 isl_poly_free(poly1);
1155 isl_poly_free(poly2);
1156 isl_poly_free(&res->poly);
1157 return NULL;
1158 }
1159
1160 __isl_give isl_poly *isl_poly_mul(__isl_take isl_poly *poly1,
1161 __isl_take isl_poly *poly2)
1162 {
1163 isl_bool is_zero, is_nan, is_one, is_cst;
1164
1165 if (!poly1 || !poly2)
1166 goto error;
1167
1168 is_nan = isl_poly_is_nan(poly1);
1169 if (is_nan < 0)
1170 goto error;
1171 if (is_nan) {
1172 isl_poly_free(poly2);
1173 return poly1;
1174 }
1175
1176 is_nan = isl_poly_is_nan(poly2);
1177 if (is_nan < 0)
1178 goto error;
1179 if (is_nan) {
1180 isl_poly_free(poly1);
1181 return poly2;
1182 }
1183
1184 is_zero = isl_poly_is_zero(poly1);
1185 if (is_zero < 0)
1186 goto error;
1187 if (is_zero) {
1188 isl_poly_free(poly2);
1189 return poly1;
1190 }
1191
1192 is_zero = isl_poly_is_zero(poly2);
1193 if (is_zero < 0)
1194 goto error;
1195 if (is_zero) {
1196 isl_poly_free(poly1);
1197 return poly2;
1198 }
1199
1200 is_one = isl_poly_is_one(poly1);
1201 if (is_one < 0)
1202 goto error;
1203 if (is_one) {
1204 isl_poly_free(poly1);
1205 return poly2;
1206 }
1207
1208 is_one = isl_poly_is_one(poly2);
1209 if (is_one < 0)
1210 goto error;
1211 if (is_one) {
1212 isl_poly_free(poly2);
1213 return poly1;
1214 }
1215
1216 if (poly1->var < poly2->var)
1217 return isl_poly_mul(poly2, poly1);
1218
1219 if (poly2->var < poly1->var) {
1220 int i;
1221 isl_poly_rec *rec;
1222 isl_bool is_infty;
1223
1224 is_infty = isl_poly_is_infty(poly2);
1225 if (is_infty >= 0 && !is_infty)
1226 is_infty = isl_poly_is_neginfty(poly2);
1227 if (is_infty < 0)
1228 goto error;
1229 if (is_infty) {
1230 isl_ctx *ctx = poly1->ctx;
1231 isl_poly_free(poly1);
1232 isl_poly_free(poly2);
1233 return isl_poly_nan(ctx);
1234 }
1235 poly1 = isl_poly_cow(poly1);
1236 rec = isl_poly_as_rec(poly1);
1237 if (!rec)
1238 goto error;
1239
1240 for (i = 0; i < rec->n; ++i) {
1241 rec->p[i] = isl_poly_mul(rec->p[i],
1242 isl_poly_copy(poly2));
1243 if (!rec->p[i])
1244 goto error;
1245 }
1246 isl_poly_free(poly2);
1247 return poly1;
1248 }
1249
1250 is_cst = isl_poly_is_cst(poly1);
1251 if (is_cst < 0)
1252 goto error;
1253 if (is_cst)
1254 return isl_poly_mul_cst(poly1, poly2);
1255
1256 return isl_poly_mul_rec(poly1, poly2);
1257 error:
1258 isl_poly_free(poly1);
1259 isl_poly_free(poly2);
1260 return NULL;
1261 }
1262
1263 __isl_give isl_poly *isl_poly_pow(__isl_take isl_poly *poly, unsigned power)
1264 {
1265 isl_poly *res;
1266
1267 if (!poly)
1268 return NULL;
1269 if (power == 1)
1270 return poly;
1271
1272 if (power % 2)
1273 res = isl_poly_copy(poly);
1274 else
1275 res = isl_poly_one(poly->ctx);
1276
1277 while (power >>= 1) {
1278 poly = isl_poly_mul(poly, isl_poly_copy(poly));
1279 if (power % 2)
1280 res = isl_poly_mul(res, isl_poly_copy(poly));
1281 }
1282
1283 isl_poly_free(poly);
1284 return res;
1285 }
1286
1287 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_space *space,
1288 unsigned n_div, __isl_take isl_poly *poly)
1289 {
1290 struct isl_qpolynomial *qp = NULL;
1291 isl_size total;
1292
1293 total = isl_space_dim(space, isl_dim_all);
1294 if (total < 0 || !poly)
1295 goto error;
1296
1297 if (!isl_space_is_set(space))
1298 isl_die(isl_space_get_ctx(space), isl_error_invalid,
1299 "domain of polynomial should be a set", goto error);
1300
1301 qp = isl_calloc_type(space->ctx, struct isl_qpolynomial);
1302 if (!qp)
1303 goto error;
1304
1305 qp->ref = 1;
1306 qp->div = isl_mat_alloc(space->ctx, n_div, 1 + 1 + total + n_div);
1307 if (!qp->div)
1308 goto error;
1309
1310 qp->dim = space;
1311 qp->poly = poly;
1312
1313 return qp;
1314 error:
1315 isl_space_free(space);
1316 isl_poly_free(poly);
1317 isl_qpolynomial_free(qp);
1318 return NULL;
1319 }
1320
1321 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
1322 {
1323 if (!qp)
1324 return NULL;
1325
1326 qp->ref++;
1327 return qp;
1328 }
1329
1330 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
1331 {
1332 struct isl_qpolynomial *dup;
1333
1334 if (!qp)
1335 return NULL;
1336
1337 dup = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row,
1338 isl_poly_copy(qp->poly));
1339 if (!dup)
1340 return NULL;
1341 isl_mat_free(dup->div);
1342 dup->div = isl_mat_copy(qp->div);
1343 if (!dup->div)
1344 goto error;
1345
1346 return dup;
1347 error:
1348 isl_qpolynomial_free(dup);
1349 return NULL;
1350 }
1351
1352 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1353 {
1354 if (!qp)
1355 return NULL;
1356
1357 if (qp->ref == 1)
1358 return qp;
1359 qp->ref--;
1360 return isl_qpolynomial_dup(qp);
1361 }
1362
1363 __isl_null isl_qpolynomial *isl_qpolynomial_free(
1364 __isl_take isl_qpolynomial *qp)
1365 {
1366 if (!qp)
1367 return NULL;
1368
1369 if (--qp->ref > 0)
1370 return NULL;
1371
1372 isl_space_free(qp->dim);
1373 isl_mat_free(qp->div);
1374 isl_poly_free(qp->poly);
1375
1376 free(qp);
1377 return NULL;
1378 }
1379
1380 __isl_give isl_poly *isl_poly_var_pow(isl_ctx *ctx, int pos, int power)
1381 {
1382 int i;
1383 isl_poly_rec *rec;
1384 isl_poly_cst *cst;
1385
1386 rec = isl_poly_alloc_rec(ctx, pos, 1 + power);
1387 if (!rec)
1388 return NULL;
1389 for (i = 0; i < 1 + power; ++i) {
1390 rec->p[i] = isl_poly_zero(ctx);
1391 if (!rec->p[i])
1392 goto error;
1393 rec->n++;
1394 }
1395 cst = isl_poly_as_cst(rec->p[power]);
1396 isl_int_set_si(cst->n, 1);
1397
1398 return &rec->poly;
1399 error:
1400 isl_poly_free(&rec->poly);
1401 return NULL;
1402 }
1403
1404 /* r array maps original positions to new positions.
1405 */
1406 static __isl_give isl_poly *reorder(__isl_take isl_poly *poly, int *r)
1407 {
1408 int i;
1409 isl_bool is_cst;
1410 isl_poly_rec *rec;
1411 isl_poly *base;
1412 isl_poly *res;
1413
1414 is_cst = isl_poly_is_cst(poly);
1415 if (is_cst < 0)
1416 return isl_poly_free(poly);
1417 if (is_cst)
1418 return poly;
1419
1420 rec = isl_poly_as_rec(poly);
1421 if (!rec)
1422 goto error;
1423
1424 isl_assert(poly->ctx, rec->n >= 1, goto error);
1425
1426 base = isl_poly_var_pow(poly->ctx, r[poly->var], 1);
1427 res = reorder(isl_poly_copy(rec->p[rec->n - 1]), r);
1428
1429 for (i = rec->n - 2; i >= 0; --i) {
1430 res = isl_poly_mul(res, isl_poly_copy(base));
1431 res = isl_poly_sum(res, reorder(isl_poly_copy(rec->p[i]), r));
1432 }
1433
1434 isl_poly_free(base);
1435 isl_poly_free(poly);
1436
1437 return res;
1438 error:
1439 isl_poly_free(poly);
1440 return NULL;
1441 }
1442
1443 static isl_bool compatible_divs(__isl_keep isl_mat *div1,
1444 __isl_keep isl_mat *div2)
1445 {
1446 int n_row, n_col;
1447 isl_bool equal;
1448
1449 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1450 div1->n_col >= div2->n_col,
1451 return isl_bool_error);
1452
1453 if (div1->n_row == div2->n_row)
1454 return isl_mat_is_equal(div1, div2);
1455
1456 n_row = div1->n_row;
1457 n_col = div1->n_col;
1458 div1->n_row = div2->n_row;
1459 div1->n_col = div2->n_col;
1460
1461 equal = isl_mat_is_equal(div1, div2);
1462
1463 div1->n_row = n_row;
1464 div1->n_col = n_col;
1465
1466 return equal;
1467 }
1468
1469 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1470 {
1471 int li, lj;
1472
1473 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1474 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1475
1476 if (li != lj)
1477 return li - lj;
1478
1479 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1480 }
1481
1482 struct isl_div_sort_info {
1483 isl_mat *div;
1484 int row;
1485 };
1486
1487 static int div_sort_cmp(const void *p1, const void *p2)
1488 {
1489 const struct isl_div_sort_info *i1, *i2;
1490 i1 = (const struct isl_div_sort_info *) p1;
1491 i2 = (const struct isl_div_sort_info *) p2;
1492
1493 return cmp_row(i1->div, i1->row, i2->row);
1494 }
1495
1496 /* Sort divs and remove duplicates.
1497 */
1498 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1499 {
1500 int i;
1501 int skip;
1502 int len;
1503 struct isl_div_sort_info *array = NULL;
1504 int *pos = NULL, *at = NULL;
1505 int *reordering = NULL;
1506 isl_size div_pos;
1507
1508 if (!qp)
1509 return NULL;
1510 if (qp->div->n_row <= 1)
1511 return qp;
1512
1513 div_pos = isl_qpolynomial_domain_var_offset(qp, isl_dim_div);
1514 if (div_pos < 0)
1515 return isl_qpolynomial_free(qp);
1516
1517 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1518 qp->div->n_row);
1519 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1520 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1521 len = qp->div->n_col - 2;
1522 reordering = isl_alloc_array(qp->div->ctx, int, len);
1523 if (!array || !pos || !at || !reordering)
1524 goto error;
1525
1526 for (i = 0; i < qp->div->n_row; ++i) {
1527 array[i].div = qp->div;
1528 array[i].row = i;
1529 pos[i] = i;
1530 at[i] = i;
1531 }
1532
1533 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1534 div_sort_cmp);
1535
1536 for (i = 0; i < div_pos; ++i)
1537 reordering[i] = i;
1538
1539 for (i = 0; i < qp->div->n_row; ++i) {
1540 if (pos[array[i].row] == i)
1541 continue;
1542 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1543 pos[at[i]] = pos[array[i].row];
1544 at[pos[array[i].row]] = at[i];
1545 at[i] = array[i].row;
1546 pos[array[i].row] = i;
1547 }
1548
1549 skip = 0;
1550 for (i = 0; i < len - div_pos; ++i) {
1551 if (i > 0 &&
1552 isl_seq_eq(qp->div->row[i - skip - 1],
1553 qp->div->row[i - skip], qp->div->n_col)) {
1554 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1555 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1556 2 + div_pos + i - skip);
1557 qp->div = isl_mat_drop_cols(qp->div,
1558 2 + div_pos + i - skip, 1);
1559 skip++;
1560 }
1561 reordering[div_pos + array[i].row] = div_pos + i - skip;
1562 }
1563
1564 qp->poly = reorder(qp->poly, reordering);
1565
1566 if (!qp->poly || !qp->div)
1567 goto error;
1568
1569 free(at);
1570 free(pos);
1571 free(array);
1572 free(reordering);
1573
1574 return qp;
1575 error:
1576 free(at);
1577 free(pos);
1578 free(array);
1579 free(reordering);
1580 isl_qpolynomial_free(qp);
1581 return NULL;
1582 }
1583
1584 static __isl_give isl_poly *expand(__isl_take isl_poly *poly, int *exp,
1585 int first)
1586 {
1587 int i;
1588 isl_bool is_cst;
1589 isl_poly_rec *rec;
1590
1591 is_cst = isl_poly_is_cst(poly);
1592 if (is_cst < 0)
1593 return isl_poly_free(poly);
1594 if (is_cst)
1595 return poly;
1596
1597 if (poly->var < first)
1598 return poly;
1599
1600 if (exp[poly->var - first] == poly->var - first)
1601 return poly;
1602
1603 poly = isl_poly_cow(poly);
1604 if (!poly)
1605 goto error;
1606
1607 poly->var = exp[poly->var - first] + first;
1608
1609 rec = isl_poly_as_rec(poly);
1610 if (!rec)
1611 goto error;
1612
1613 for (i = 0; i < rec->n; ++i) {
1614 rec->p[i] = expand(rec->p[i], exp, first);
1615 if (!rec->p[i])
1616 goto error;
1617 }
1618
1619 return poly;
1620 error:
1621 isl_poly_free(poly);
1622 return NULL;
1623 }
1624
1625 static __isl_give isl_qpolynomial *with_merged_divs(
1626 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1627 __isl_take isl_qpolynomial *qp2),
1628 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1629 {
1630 int *exp1 = NULL;
1631 int *exp2 = NULL;
1632 isl_mat *div = NULL;
1633 int n_div1, n_div2;
1634
1635 qp1 = isl_qpolynomial_cow(qp1);
1636 qp2 = isl_qpolynomial_cow(qp2);
1637
1638 if (!qp1 || !qp2)
1639 goto error;
1640
1641 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1642 qp1->div->n_col >= qp2->div->n_col, goto error);
1643
1644 n_div1 = qp1->div->n_row;
1645 n_div2 = qp2->div->n_row;
1646 exp1 = isl_alloc_array(qp1->div->ctx, int, n_div1);
1647 exp2 = isl_alloc_array(qp2->div->ctx, int, n_div2);
1648 if ((n_div1 && !exp1) || (n_div2 && !exp2))
1649 goto error;
1650
1651 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1652 if (!div)
1653 goto error;
1654
1655 isl_mat_free(qp1->div);
1656 qp1->div = isl_mat_copy(div);
1657 isl_mat_free(qp2->div);
1658 qp2->div = isl_mat_copy(div);
1659
1660 qp1->poly = expand(qp1->poly, exp1, div->n_col - div->n_row - 2);
1661 qp2->poly = expand(qp2->poly, exp2, div->n_col - div->n_row - 2);
1662
1663 if (!qp1->poly || !qp2->poly)
1664 goto error;
1665
1666 isl_mat_free(div);
1667 free(exp1);
1668 free(exp2);
1669
1670 return fn(qp1, qp2);
1671 error:
1672 isl_mat_free(div);
1673 free(exp1);
1674 free(exp2);
1675 isl_qpolynomial_free(qp1);
1676 isl_qpolynomial_free(qp2);
1677 return NULL;
1678 }
1679
1680 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1681 __isl_take isl_qpolynomial *qp2)
1682 {
1683 isl_bool compatible;
1684
1685 qp1 = isl_qpolynomial_cow(qp1);
1686
1687 if (isl_qpolynomial_check_equal_space(qp1, qp2) < 0)
1688 goto error;
1689
1690 if (qp1->div->n_row < qp2->div->n_row)
1691 return isl_qpolynomial_add(qp2, qp1);
1692
1693 compatible = compatible_divs(qp1->div, qp2->div);
1694 if (compatible < 0)
1695 goto error;
1696 if (!compatible)
1697 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1698
1699 qp1->poly = isl_poly_sum(qp1->poly, isl_poly_copy(qp2->poly));
1700 if (!qp1->poly)
1701 goto error;
1702
1703 isl_qpolynomial_free(qp2);
1704
1705 return qp1;
1706 error:
1707 isl_qpolynomial_free(qp1);
1708 isl_qpolynomial_free(qp2);
1709 return NULL;
1710 }
1711
1712 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1713 __isl_keep isl_set *dom,
1714 __isl_take isl_qpolynomial *qp1,
1715 __isl_take isl_qpolynomial *qp2)
1716 {
1717 qp1 = isl_qpolynomial_add(qp1, qp2);
1718 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1719 return qp1;
1720 }
1721
1722 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1723 __isl_take isl_qpolynomial *qp2)
1724 {
1725 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1726 }
1727
1728 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1729 __isl_take isl_qpolynomial *qp, isl_int v)
1730 {
1731 if (isl_int_is_zero(v))
1732 return qp;
1733
1734 qp = isl_qpolynomial_cow(qp);
1735 if (!qp)
1736 return NULL;
1737
1738 qp->poly = isl_poly_add_isl_int(qp->poly, v);
1739 if (!qp->poly)
1740 goto error;
1741
1742 return qp;
1743 error:
1744 isl_qpolynomial_free(qp);
1745 return NULL;
1746
1747 }
1748
1749 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1750 {
1751 if (!qp)
1752 return NULL;
1753
1754 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1755 }
1756
1757 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1758 __isl_take isl_qpolynomial *qp, isl_int v)
1759 {
1760 if (isl_int_is_one(v))
1761 return qp;
1762
1763 if (qp && isl_int_is_zero(v)) {
1764 isl_qpolynomial *zero;
1765 zero = isl_qpolynomial_zero_on_domain(isl_space_copy(qp->dim));
1766 isl_qpolynomial_free(qp);
1767 return zero;
1768 }
1769
1770 qp = isl_qpolynomial_cow(qp);
1771 if (!qp)
1772 return NULL;
1773
1774 qp->poly = isl_poly_mul_isl_int(qp->poly, v);
1775 if (!qp->poly)
1776 goto error;
1777
1778 return qp;
1779 error:
1780 isl_qpolynomial_free(qp);
1781 return NULL;
1782 }
1783
1784 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
1785 __isl_take isl_qpolynomial *qp, isl_int v)
1786 {
1787 return isl_qpolynomial_mul_isl_int(qp, v);
1788 }
1789
1790 /* Multiply "qp" by "v".
1791 */
1792 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
1793 __isl_take isl_qpolynomial *qp, __isl_take isl_val *v)
1794 {
1795 if (!qp || !v)
1796 goto error;
1797
1798 if (!isl_val_is_rat(v))
1799 isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
1800 "expecting rational factor", goto error);
1801
1802 if (isl_val_is_one(v)) {
1803 isl_val_free(v);
1804 return qp;
1805 }
1806
1807 if (isl_val_is_zero(v)) {
1808 isl_space *space;
1809
1810 space = isl_qpolynomial_get_domain_space(qp);
1811 isl_qpolynomial_free(qp);
1812 isl_val_free(v);
1813 return isl_qpolynomial_zero_on_domain(space);
1814 }
1815
1816 qp = isl_qpolynomial_cow(qp);
1817 if (!qp)
1818 goto error;
1819
1820 qp->poly = isl_poly_scale_val(qp->poly, v);
1821 if (!qp->poly)
1822 qp = isl_qpolynomial_free(qp);
1823
1824 isl_val_free(v);
1825 return qp;
1826 error:
1827 isl_val_free(v);
1828 isl_qpolynomial_free(qp);
1829 return NULL;
1830 }
1831
1832 /* Divide "qp" by "v".
1833 */
1834 __isl_give isl_qpolynomial *isl_qpolynomial_scale_down_val(
1835 __isl_take isl_qpolynomial *qp, __isl_take isl_val *v)
1836 {
1837 if (!qp || !v)
1838 goto error;
1839
1840 if (!isl_val_is_rat(v))
1841 isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
1842 "expecting rational factor", goto error);
1843 if (isl_val_is_zero(v))
1844 isl_die(isl_val_get_ctx(v), isl_error_invalid,
1845 "cannot scale down by zero", goto error);
1846
1847 return isl_qpolynomial_scale_val(qp, isl_val_inv(v));
1848 error:
1849 isl_val_free(v);
1850 isl_qpolynomial_free(qp);
1851 return NULL;
1852 }
1853
1854 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1855 __isl_take isl_qpolynomial *qp2)
1856 {
1857 isl_bool compatible;
1858
1859 qp1 = isl_qpolynomial_cow(qp1);
1860
1861 if (isl_qpolynomial_check_equal_space(qp1, qp2) < 0)
1862 goto error;
1863
1864 if (qp1->div->n_row < qp2->div->n_row)
1865 return isl_qpolynomial_mul(qp2, qp1);
1866
1867 compatible = compatible_divs(qp1->div, qp2->div);
1868 if (compatible < 0)
1869 goto error;
1870 if (!compatible)
1871 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1872
1873 qp1->poly = isl_poly_mul(qp1->poly, isl_poly_copy(qp2->poly));
1874 if (!qp1->poly)
1875 goto error;
1876
1877 isl_qpolynomial_free(qp2);
1878
1879 return qp1;
1880 error:
1881 isl_qpolynomial_free(qp1);
1882 isl_qpolynomial_free(qp2);
1883 return NULL;
1884 }
1885
1886 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1887 unsigned power)
1888 {
1889 qp = isl_qpolynomial_cow(qp);
1890
1891 if (!qp)
1892 return NULL;
1893
1894 qp->poly = isl_poly_pow(qp->poly, power);
1895 if (!qp->poly)
1896 goto error;
1897
1898 return qp;
1899 error:
1900 isl_qpolynomial_free(qp);
1901 return NULL;
1902 }
1903
1904 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
1905 __isl_take isl_pw_qpolynomial *pwqp, unsigned power)
1906 {
1907 int i;
1908
1909 if (power == 1)
1910 return pwqp;
1911
1912 pwqp = isl_pw_qpolynomial_cow(pwqp);
1913 if (!pwqp)
1914 return NULL;
1915
1916 for (i = 0; i < pwqp->n; ++i) {
1917 pwqp->p[i].qp = isl_qpolynomial_pow(pwqp->p[i].qp, power);
1918 if (!pwqp->p[i].qp)
1919 return isl_pw_qpolynomial_free(pwqp);
1920 }
1921
1922 return pwqp;
1923 }
1924
1925 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
1926 __isl_take isl_space *domain)
1927 {
1928 if (!domain)
1929 return NULL;
1930 return isl_qpolynomial_alloc(domain, 0, isl_poly_zero(domain->ctx));
1931 }
1932
1933 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
1934 __isl_take isl_space *domain)
1935 {
1936 if (!domain)
1937 return NULL;
1938 return isl_qpolynomial_alloc(domain, 0, isl_poly_one(domain->ctx));
1939 }
1940
1941 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
1942 __isl_take isl_space *domain)
1943 {
1944 if (!domain)
1945 return NULL;
1946 return isl_qpolynomial_alloc(domain, 0, isl_poly_infty(domain->ctx));
1947 }
1948
1949 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
1950 __isl_take isl_space *domain)
1951 {
1952 if (!domain)
1953 return NULL;
1954 return isl_qpolynomial_alloc(domain, 0, isl_poly_neginfty(domain->ctx));
1955 }
1956
1957 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
1958 __isl_take isl_space *domain)
1959 {
1960 if (!domain)
1961 return NULL;
1962 return isl_qpolynomial_alloc(domain, 0, isl_poly_nan(domain->ctx));
1963 }
1964
1965 __isl_give isl_qpolynomial *isl_qpolynomial_cst_on_domain(
1966 __isl_take isl_space *domain,
1967 isl_int v)
1968 {
1969 struct isl_qpolynomial *qp;
1970 isl_poly_cst *cst;
1971
1972 qp = isl_qpolynomial_zero_on_domain(domain);
1973 if (!qp)
1974 return NULL;
1975
1976 cst = isl_poly_as_cst(qp->poly);
1977 isl_int_set(cst->n, v);
1978
1979 return qp;
1980 }
1981
1982 isl_bool isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1983 isl_int *n, isl_int *d)
1984 {
1985 isl_bool is_cst;
1986 isl_poly_cst *cst;
1987
1988 if (!qp)
1989 return isl_bool_error;
1990
1991 is_cst = isl_poly_is_cst(qp->poly);
1992 if (is_cst < 0 || !is_cst)
1993 return is_cst;
1994
1995 cst = isl_poly_as_cst(qp->poly);
1996 if (!cst)
1997 return isl_bool_error;
1998
1999 if (n)
2000 isl_int_set(*n, cst->n);
2001 if (d)
2002 isl_int_set(*d, cst->d);
2003
2004 return isl_bool_true;
2005 }
2006
2007 /* Return the constant term of "poly".
2008 */
2009 static __isl_give isl_val *isl_poly_get_constant_val(__isl_keep isl_poly *poly)
2010 {
2011 isl_bool is_cst;
2012 isl_poly_cst *cst;
2013
2014 if (!poly)
2015 return NULL;
2016
2017 while ((is_cst = isl_poly_is_cst(poly)) == isl_bool_false) {
2018 isl_poly_rec *rec;
2019
2020 rec = isl_poly_as_rec(poly);
2021 if (!rec)
2022 return NULL;
2023 poly = rec->p[0];
2024 }
2025 if (is_cst < 0)
2026 return NULL;
2027
2028 cst = isl_poly_as_cst(poly);
2029 if (!cst)
2030 return NULL;
2031 return isl_val_rat_from_isl_int(cst->poly.ctx, cst->n, cst->d);
2032 }
2033
2034 /* Return the constant term of "qp".
2035 */
2036 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2037 __isl_keep isl_qpolynomial *qp)
2038 {
2039 if (!qp)
2040 return NULL;
2041
2042 return isl_poly_get_constant_val(qp->poly);
2043 }
2044
2045 isl_bool isl_poly_is_affine(__isl_keep isl_poly *poly)
2046 {
2047 isl_bool is_cst;
2048 isl_poly_rec *rec;
2049
2050 if (!poly)
2051 return isl_bool_error;
2052
2053 if (poly->var < 0)
2054 return isl_bool_true;
2055
2056 rec = isl_poly_as_rec(poly);
2057 if (!rec)
2058 return isl_bool_error;
2059
2060 if (rec->n > 2)
2061 return isl_bool_false;
2062
2063 isl_assert(poly->ctx, rec->n > 1, return isl_bool_error);
2064
2065 is_cst = isl_poly_is_cst(rec->p[1]);
2066 if (is_cst < 0 || !is_cst)
2067 return is_cst;
2068
2069 return isl_poly_is_affine(rec->p[0]);
2070 }
2071
2072 isl_bool isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
2073 {
2074 if (!qp)
2075 return isl_bool_error;
2076
2077 if (qp->div->n_row > 0)
2078 return isl_bool_false;
2079
2080 return isl_poly_is_affine(qp->poly);
2081 }
2082
2083 static void update_coeff(__isl_keep isl_vec *aff,
2084 __isl_keep isl_poly_cst *cst, int pos)
2085 {
2086 isl_int gcd;
2087 isl_int f;
2088
2089 if (isl_int_is_zero(cst->n))
2090 return;
2091
2092 isl_int_init(gcd);
2093 isl_int_init(f);
2094 isl_int_gcd(gcd, cst->d, aff->el[0]);
2095 isl_int_divexact(f, cst->d, gcd);
2096 isl_int_divexact(gcd, aff->el[0], gcd);
2097 isl_seq_scale(aff->el, aff->el, f, aff->size);
2098 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
2099 isl_int_clear(gcd);
2100 isl_int_clear(f);
2101 }
2102
2103 int isl_poly_update_affine(__isl_keep isl_poly *poly, __isl_keep isl_vec *aff)
2104 {
2105 isl_poly_cst *cst;
2106 isl_poly_rec *rec;
2107
2108 if (!poly || !aff)
2109 return -1;
2110
2111 if (poly->var < 0) {
2112 isl_poly_cst *cst;
2113
2114 cst = isl_poly_as_cst(poly);
2115 if (!cst)
2116 return -1;
2117 update_coeff(aff, cst, 0);
2118 return 0;
2119 }
2120
2121 rec = isl_poly_as_rec(poly);
2122 if (!rec)
2123 return -1;
2124 isl_assert(poly->ctx, rec->n == 2, return -1);
2125
2126 cst = isl_poly_as_cst(rec->p[1]);
2127 if (!cst)
2128 return -1;
2129 update_coeff(aff, cst, 1 + poly->var);
2130
2131 return isl_poly_update_affine(rec->p[0], aff);
2132 }
2133
2134 __isl_give isl_vec *isl_qpolynomial_extract_affine(
2135 __isl_keep isl_qpolynomial *qp)
2136 {
2137 isl_vec *aff;
2138 isl_size d;
2139
2140 d = isl_qpolynomial_domain_dim(qp, isl_dim_all);
2141 if (d < 0)
2142 return NULL;
2143
2144 aff = isl_vec_alloc(qp->div->ctx, 2 + d);
2145 if (!aff)
2146 return NULL;
2147
2148 isl_seq_clr(aff->el + 1, 1 + d);
2149 isl_int_set_si(aff->el[0], 1);
2150
2151 if (isl_poly_update_affine(qp->poly, aff) < 0)
2152 goto error;
2153
2154 return aff;
2155 error:
2156 isl_vec_free(aff);
2157 return NULL;
2158 }
2159
2160 /* Compare two quasi-polynomials.
2161 *
2162 * Return -1 if "qp1" is "smaller" than "qp2", 1 if "qp1" is "greater"
2163 * than "qp2" and 0 if they are equal.
2164 */
2165 int isl_qpolynomial_plain_cmp(__isl_keep isl_qpolynomial *qp1,
2166 __isl_keep isl_qpolynomial *qp2)
2167 {
2168 int cmp;
2169
2170 if (qp1 == qp2)
2171 return 0;
2172 if (!qp1)
2173 return -1;
2174 if (!qp2)
2175 return 1;
2176
2177 cmp = isl_space_cmp(qp1->dim, qp2->dim);
2178 if (cmp != 0)
2179 return cmp;
2180
2181 cmp = isl_local_cmp(qp1->div, qp2->div);
2182 if (cmp != 0)
2183 return cmp;
2184
2185 return isl_poly_plain_cmp(qp1->poly, qp2->poly);
2186 }
2187
2188 /* Is "qp1" obviously equal to "qp2"?
2189 *
2190 * NaN is not equal to anything, not even to another NaN.
2191 */
2192 isl_bool isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
2193 __isl_keep isl_qpolynomial *qp2)
2194 {
2195 isl_bool equal;
2196
2197 if (!qp1 || !qp2)
2198 return isl_bool_error;
2199
2200 if (isl_qpolynomial_is_nan(qp1) || isl_qpolynomial_is_nan(qp2))
2201 return isl_bool_false;
2202
2203 equal = isl_space_is_equal(qp1->dim, qp2->dim);
2204 if (equal < 0 || !equal)
2205 return equal;
2206
2207 equal = isl_mat_is_equal(qp1->div, qp2->div);
2208 if (equal < 0 || !equal)
2209 return equal;
2210
2211 return isl_poly_is_equal(qp1->poly, qp2->poly);
2212 }
2213
2214 static isl_stat poly_update_den(__isl_keep isl_poly *poly, isl_int *d)
2215 {
2216 int i;
2217 isl_bool is_cst;
2218 isl_poly_rec *rec;
2219
2220 is_cst = isl_poly_is_cst(poly);
2221 if (is_cst < 0)
2222 return isl_stat_error;
2223 if (is_cst) {
2224 isl_poly_cst *cst;
2225 cst = isl_poly_as_cst(poly);
2226 if (!cst)
2227 return isl_stat_error;
2228 isl_int_lcm(*d, *d, cst->d);
2229 return isl_stat_ok;
2230 }
2231
2232 rec = isl_poly_as_rec(poly);
2233 if (!rec)
2234 return isl_stat_error;
2235
2236 for (i = 0; i < rec->n; ++i)
2237 poly_update_den(rec->p[i], d);
2238
2239 return isl_stat_ok;
2240 }
2241
2242 __isl_give isl_val *isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp)
2243 {
2244 isl_val *d;
2245
2246 if (!qp)
2247 return NULL;
2248 d = isl_val_one(isl_qpolynomial_get_ctx(qp));
2249 if (!d)
2250 return NULL;
2251 if (poly_update_den(qp->poly, &d->n) < 0)
2252 return isl_val_free(d);
2253 return d;
2254 }
2255
2256 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow_on_domain(
2257 __isl_take isl_space *domain, int pos, int power)
2258 {
2259 struct isl_ctx *ctx;
2260
2261 if (!domain)
2262 return NULL;
2263
2264 ctx = domain->ctx;
2265
2266 return isl_qpolynomial_alloc(domain, 0,
2267 isl_poly_var_pow(ctx, pos, power));
2268 }
2269
2270 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2271 __isl_take isl_space *domain, enum isl_dim_type type, unsigned pos)
2272 {
2273 if (isl_space_check_is_set(domain ) < 0)
2274 goto error;
2275 if (isl_space_check_range(domain, type, pos, 1) < 0)
2276 goto error;
2277
2278 pos += isl_space_offset(domain, type);
2279
2280 return isl_qpolynomial_var_pow_on_domain(domain, pos, 1);
2281 error:
2282 isl_space_free(domain);
2283 return NULL;
2284 }
2285
2286 __isl_give isl_poly *isl_poly_subs(__isl_take isl_poly *poly,
2287 unsigned first, unsigned n, __isl_keep isl_poly **subs)
2288 {
2289 int i;
2290 isl_bool is_cst;
2291 isl_poly_rec *rec;
2292 isl_poly *base, *res;
2293
2294 is_cst = isl_poly_is_cst(poly);
2295 if (is_cst < 0)
2296 return isl_poly_free(poly);
2297 if (is_cst)
2298 return poly;
2299
2300 if (poly->var < first)
2301 return poly;
2302
2303 rec = isl_poly_as_rec(poly);
2304 if (!rec)
2305 goto error;
2306
2307 isl_assert(poly->ctx, rec->n >= 1, goto error);
2308
2309 if (poly->var >= first + n)
2310 base = isl_poly_var_pow(poly->ctx, poly->var, 1);
2311 else
2312 base = isl_poly_copy(subs[poly->var - first]);
2313
2314 res = isl_poly_subs(isl_poly_copy(rec->p[rec->n - 1]), first, n, subs);
2315 for (i = rec->n - 2; i >= 0; --i) {
2316 isl_poly *t;
2317 t = isl_poly_subs(isl_poly_copy(rec->p[i]), first, n, subs);
2318 res = isl_poly_mul(res, isl_poly_copy(base));
2319 res = isl_poly_sum(res, t);
2320 }
2321
2322 isl_poly_free(base);
2323 isl_poly_free(poly);
2324
2325 return res;
2326 error:
2327 isl_poly_free(poly);
2328 return NULL;
2329 }
2330
2331 __isl_give isl_poly *isl_poly_from_affine(isl_ctx *ctx, isl_int *f,
2332 isl_int denom, unsigned len)
2333 {
2334 int i;
2335 isl_poly *poly;
2336
2337 isl_assert(ctx, len >= 1, return NULL);
2338
2339 poly = isl_poly_rat_cst(ctx, f[0], denom);
2340 for (i = 0; i < len - 1; ++i) {
2341 isl_poly *t;
2342 isl_poly *c;
2343
2344 if (isl_int_is_zero(f[1 + i]))
2345 continue;
2346
2347 c = isl_poly_rat_cst(ctx, f[1 + i], denom);
2348 t = isl_poly_var_pow(ctx, i, 1);
2349 t = isl_poly_mul(c, t);
2350 poly = isl_poly_sum(poly, t);
2351 }
2352
2353 return poly;
2354 }
2355
2356 /* Remove common factor of non-constant terms and denominator.
2357 */
2358 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
2359 {
2360 isl_ctx *ctx = qp->div->ctx;
2361 unsigned total = qp->div->n_col - 2;
2362
2363 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
2364 isl_int_gcd(ctx->normalize_gcd,
2365 ctx->normalize_gcd, qp->div->row[div][0]);
2366 if (isl_int_is_one(ctx->normalize_gcd))
2367 return;
2368
2369 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
2370 ctx->normalize_gcd, total);
2371 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
2372 ctx->normalize_gcd);
2373 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
2374 ctx->normalize_gcd);
2375 }
2376
2377 /* Replace the integer division identified by "div" by the polynomial "s".
2378 * The integer division is assumed not to appear in the definition
2379 * of any other integer divisions.
2380 */
2381 static __isl_give isl_qpolynomial *substitute_div(
2382 __isl_take isl_qpolynomial *qp, int div, __isl_take isl_poly *s)
2383 {
2384 int i;
2385 isl_size div_pos;
2386 int *reordering;
2387 isl_ctx *ctx;
2388
2389 if (!qp || !s)
2390 goto error;
2391
2392 qp = isl_qpolynomial_cow(qp);
2393 if (!qp)
2394 goto error;
2395
2396 div_pos = isl_qpolynomial_domain_var_offset(qp, isl_dim_div);
2397 if (div_pos < 0)
2398 goto error;
2399 qp->poly = isl_poly_subs(qp->poly, div_pos + div, 1, &s);
2400 if (!qp->poly)
2401 goto error;
2402
2403 ctx = isl_qpolynomial_get_ctx(qp);
2404 reordering = isl_alloc_array(ctx, int, div_pos + qp->div->n_row);
2405 if (!reordering)
2406 goto error;
2407 for (i = 0; i < div_pos + div; ++i)
2408 reordering[i] = i;
2409 for (i = div_pos + div + 1; i < div_pos + qp->div->n_row; ++i)
2410 reordering[i] = i - 1;
2411 qp->div = isl_mat_drop_rows(qp->div, div, 1);
2412 qp->div = isl_mat_drop_cols(qp->div, 2 + div_pos + div, 1);
2413 qp->poly = reorder(qp->poly, reordering);
2414 free(reordering);
2415
2416 if (!qp->poly || !qp->div)
2417 goto error;
2418
2419 isl_poly_free(s);
2420 return qp;
2421 error:
2422 isl_qpolynomial_free(qp);
2423 isl_poly_free(s);
2424 return NULL;
2425 }
2426
2427 /* Replace all integer divisions [e/d] that turn out to not actually be integer
2428 * divisions because d is equal to 1 by their definition, i.e., e.
2429 */
2430 static __isl_give isl_qpolynomial *substitute_non_divs(
2431 __isl_take isl_qpolynomial *qp)
2432 {
2433 int i, j;
2434 isl_size div_pos;
2435 isl_poly *s;
2436
2437 div_pos = isl_qpolynomial_domain_var_offset(qp, isl_dim_div);
2438 if (div_pos < 0)
2439 return isl_qpolynomial_free(qp);
2440
2441 for (i = 0; qp && i < qp->div->n_row; ++i) {
2442 if (!isl_int_is_one(qp->div->row[i][0]))
2443 continue;
2444 for (j = i + 1; j < qp->div->n_row; ++j) {
2445 if (isl_int_is_zero(qp->div->row[j][2 + div_pos + i]))
2446 continue;
2447 isl_seq_combine(qp->div->row[j] + 1,
2448 qp->div->ctx->one, qp->div->row[j] + 1,
2449 qp->div->row[j][2 + div_pos + i],
2450 qp->div->row[i] + 1, 1 + div_pos + i);
2451 isl_int_set_si(qp->div->row[j][2 + div_pos + i], 0);
2452 normalize_div(qp, j);
2453 }
2454 s = isl_poly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
2455 qp->div->row[i][0], qp->div->n_col - 1);
2456 qp = substitute_div(qp, i, s);
2457 --i;
2458 }
2459
2460 return qp;
2461 }
2462
2463 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2464 * with d the denominator. When replacing the coefficient e of x by
2465 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2466 * inside the division, so we need to add floor(e/d) * x outside.
2467 * That is, we replace q by q' + floor(e/d) * x and we therefore need
2468 * to adjust the coefficient of x in each later div that depends on the
2469 * current div "div" and also in the affine expressions in the rows of "mat"
2470 * (if they too depend on "div").
2471 */
2472 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
2473 __isl_keep isl_mat **mat)
2474 {
2475 int i, j;
2476 isl_int v;
2477 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2478
2479 isl_int_init(v);
2480 for (i = 0; i < 1 + total + div; ++i) {
2481 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
2482 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
2483 continue;
2484 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
2485 isl_int_fdiv_r(qp->div->row[div][1 + i],
2486 qp->div->row[div][1 + i], qp->div->row[div][0]);
2487 *mat = isl_mat_col_addmul(*mat, i, v, 1 + total + div);
2488 for (j = div + 1; j < qp->div->n_row; ++j) {
2489 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
2490 continue;
2491 isl_int_addmul(qp->div->row[j][1 + i],
2492 v, qp->div->row[j][2 + total + div]);
2493 }
2494 }
2495 isl_int_clear(v);
2496 }
2497
2498 /* Check if the last non-zero coefficient is bigger that half of the
2499 * denominator. If so, we will invert the div to further reduce the number
2500 * of distinct divs that may appear.
2501 * If the last non-zero coefficient is exactly half the denominator,
2502 * then we continue looking for earlier coefficients that are bigger
2503 * than half the denominator.
2504 */
2505 static int needs_invert(__isl_keep isl_mat *div, int row)
2506 {
2507 int i;
2508 int cmp;
2509
2510 for (i = div->n_col - 1; i >= 1; --i) {
2511 if (isl_int_is_zero(div->row[row][i]))
2512 continue;
2513 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
2514 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
2515 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
2516 if (cmp)
2517 return cmp > 0;
2518 if (i == 1)
2519 return 1;
2520 }
2521
2522 return 0;
2523 }
2524
2525 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2526 * We only invert the coefficients of e (and the coefficient of q in
2527 * later divs and in the rows of "mat"). After calling this function, the
2528 * coefficients of e should be reduced again.
2529 */
2530 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
2531 __isl_keep isl_mat **mat)
2532 {
2533 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2534
2535 isl_seq_neg(qp->div->row[div] + 1,
2536 qp->div->row[div] + 1, qp->div->n_col - 1);
2537 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2538 isl_int_add(qp->div->row[div][1],
2539 qp->div->row[div][1], qp->div->row[div][0]);
2540 *mat = isl_mat_col_neg(*mat, 1 + total + div);
2541 isl_mat_col_mul(qp->div, 2 + total + div,
2542 qp->div->ctx->negone, 2 + total + div);
2543 }
2544
2545 /* Reduce all divs of "qp" to have coefficients
2546 * in the interval [0, d-1], with d the denominator and such that the
2547 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2548 * The modifications to the integer divisions need to be reflected
2549 * in the factors of the polynomial that refer to the original
2550 * integer divisions. To this end, the modifications are collected
2551 * as a set of affine expressions and then plugged into the polynomial.
2552 *
2553 * After the reduction, some divs may have become redundant or identical,
2554 * so we call substitute_non_divs and sort_divs. If these functions
2555 * eliminate divs or merge two or more divs into one, the coefficients
2556 * of the enclosing divs may have to be reduced again, so we call
2557 * ourselves recursively if the number of divs decreases.
2558 */
2559 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2560 {
2561 int i;
2562 isl_ctx *ctx;
2563 isl_mat *mat;
2564 isl_poly **s;
2565 unsigned o_div;
2566 isl_size n_div, total, new_n_div;
2567
2568 total = isl_qpolynomial_domain_dim(qp, isl_dim_all);
2569 n_div = isl_qpolynomial_domain_dim(qp, isl_dim_div);
2570 o_div = isl_qpolynomial_domain_offset(qp, isl_dim_div);
2571 if (total < 0 || n_div < 0)
2572 return isl_qpolynomial_free(qp);
2573 ctx = isl_qpolynomial_get_ctx(qp);
2574 mat = isl_mat_zero(ctx, n_div, 1 + total);
2575
2576 for (i = 0; i < n_div; ++i)
2577 mat = isl_mat_set_element_si(mat, i, o_div + i, 1);
2578
2579 for (i = 0; i < qp->div->n_row; ++i) {
2580 normalize_div(qp, i);
2581 reduce_div(qp, i, &mat);
2582 if (needs_invert(qp->div, i)) {
2583 invert_div(qp, i, &mat);
2584 reduce_div(qp, i, &mat);
2585 }
2586 }
2587 if (!mat)
2588 goto error;
2589
2590 s = isl_alloc_array(ctx, struct isl_poly *, n_div);
2591 if (n_div && !s)
2592 goto error;
2593 for (i = 0; i < n_div; ++i)
2594 s[i] = isl_poly_from_affine(ctx, mat->row[i], ctx->one,
2595 1 + total);
2596 qp->poly = isl_poly_subs(qp->poly, o_div - 1, n_div, s);
2597 for (i = 0; i < n_div; ++i)
2598 isl_poly_free(s[i]);
2599 free(s);
2600 if (!qp->poly)
2601 goto error;
2602
2603 isl_mat_free(mat);
2604
2605 qp = substitute_non_divs(qp);
2606 qp = sort_divs(qp);
2607 new_n_div = isl_qpolynomial_domain_dim(qp, isl_dim_div);
2608 if (new_n_div < 0)
2609 return isl_qpolynomial_free(qp);
2610 if (new_n_div < n_div)
2611 return reduce_divs(qp);
2612
2613 return qp;
2614 error:
2615 isl_qpolynomial_free(qp);
2616 isl_mat_free(mat);
2617 return NULL;
2618 }
2619
2620 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
2621 __isl_take isl_space *domain, const isl_int n, const isl_int d)
2622 {
2623 struct isl_qpolynomial *qp;
2624 isl_poly_cst *cst;
2625
2626 qp = isl_qpolynomial_zero_on_domain(domain);
2627 if (!qp)
2628 return NULL;
2629
2630 cst = isl_poly_as_cst(qp->poly);
2631 isl_int_set(cst->n, n);
2632 isl_int_set(cst->d, d);
2633
2634 return qp;
2635 }
2636
2637 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2638 */
2639 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2640 __isl_take isl_space *domain, __isl_take isl_val *val)
2641 {
2642 isl_qpolynomial *qp;
2643 isl_poly_cst *cst;
2644
2645 qp = isl_qpolynomial_zero_on_domain(domain);
2646 if (!qp || !val)
2647 goto error;
2648
2649 cst = isl_poly_as_cst(qp->poly);
2650 isl_int_set(cst->n, val->n);
2651 isl_int_set(cst->d, val->d);
2652
2653 isl_val_free(val);
2654 return qp;
2655 error:
2656 isl_val_free(val);
2657 isl_qpolynomial_free(qp);
2658 return NULL;
2659 }
2660
2661 static isl_stat poly_set_active(__isl_keep isl_poly *poly, int *active, int d)
2662 {
2663 isl_bool is_cst;
2664 isl_poly_rec *rec;
2665 int i;
2666
2667 is_cst = isl_poly_is_cst(poly);
2668 if (is_cst < 0)
2669 return isl_stat_error;
2670 if (is_cst)
2671 return isl_stat_ok;
2672
2673 if (poly->var < d)
2674 active[poly->var] = 1;
2675
2676 rec = isl_poly_as_rec(poly);
2677 for (i = 0; i < rec->n; ++i)
2678 if (poly_set_active(rec->p[i], active, d) < 0)
2679 return isl_stat_error;
2680
2681 return isl_stat_ok;
2682 }
2683
2684 static isl_stat set_active(__isl_keep isl_qpolynomial *qp, int *active)
2685 {
2686 int i, j;
2687 isl_size d;
2688 isl_space *space;
2689
2690 space = isl_qpolynomial_peek_domain_space(qp);
2691 d = isl_space_dim(space, isl_dim_all);
2692 if (d < 0 || !active)
2693 return isl_stat_error;
2694
2695 for (i = 0; i < d; ++i)
2696 for (j = 0; j < qp->div->n_row; ++j) {
2697 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2698 continue;
2699 active[i] = 1;
2700 break;
2701 }
2702
2703 return poly_set_active(qp->poly, active, d);
2704 }
2705
2706 #undef TYPE
2707 #define TYPE isl_qpolynomial
2708 static
2709 #include "check_type_range_templ.c"
2710
2711 isl_bool isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2712 enum isl_dim_type type, unsigned first, unsigned n)
2713 {
2714 int i;
2715 int *active = NULL;
2716 isl_bool involves = isl_bool_false;
2717 isl_size offset;
2718 isl_size d;
2719 isl_space *space;
2720
2721 if (!qp)
2722 return isl_bool_error;
2723 if (n == 0)
2724 return isl_bool_false;
2725
2726 if (isl_qpolynomial_check_range(qp, type, first, n) < 0)
2727 return isl_bool_error;
2728 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2729 type == isl_dim_in, return isl_bool_error);
2730
2731 space = isl_qpolynomial_peek_domain_space(qp);
2732 d = isl_space_dim(space, isl_dim_all);
2733 if (d < 0)
2734 return isl_bool_error;
2735 active = isl_calloc_array(qp->dim->ctx, int, d);
2736 if (set_active(qp, active) < 0)
2737 goto error;
2738
2739 offset = isl_qpolynomial_domain_var_offset(qp, domain_type(type));
2740 if (offset < 0)
2741 goto error;
2742 first += offset;
2743 for (i = 0; i < n; ++i)
2744 if (active[first + i]) {
2745 involves = isl_bool_true;
2746 break;
2747 }
2748
2749 free(active);
2750
2751 return involves;
2752 error:
2753 free(active);
2754 return isl_bool_error;
2755 }
2756
2757 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2758 * of the divs that do appear in the quasi-polynomial.
2759 */
2760 static __isl_give isl_qpolynomial *remove_redundant_divs(
2761 __isl_take isl_qpolynomial *qp)
2762 {
2763 int i, j;
2764 isl_size div_pos;
2765 int len;
2766 int skip;
2767 int *active = NULL;
2768 int *reordering = NULL;
2769 int redundant = 0;
2770 int n_div;
2771 isl_ctx *ctx;
2772
2773 if (!qp)
2774 return NULL;
2775 if (qp->div->n_row == 0)
2776 return qp;
2777
2778 div_pos = isl_qpolynomial_domain_var_offset(qp, isl_dim_div);
2779 if (div_pos < 0)
2780 return isl_qpolynomial_free(qp);
2781 len = qp->div->n_col - 2;
2782 ctx = isl_qpolynomial_get_ctx(qp);
2783 active = isl_calloc_array(ctx, int, len);
2784 if (!active)
2785 goto error;
2786
2787 if (poly_set_active(qp->poly, active, len) < 0)
2788 goto error;
2789
2790 for (i = qp->div->n_row - 1; i >= 0; --i) {
2791 if (!active[div_pos + i]) {
2792 redundant = 1;
2793 continue;
2794 }
2795 for (j = 0; j < i; ++j) {
2796 if (isl_int_is_zero(qp->div->row[i][2 + div_pos + j]))
2797 continue;
2798 active[div_pos + j] = 1;
2799 break;
2800 }
2801 }
2802
2803 if (!redundant) {
2804 free(active);
2805 return qp;
2806 }
2807
2808 reordering = isl_alloc_array(qp->div->ctx, int, len);
2809 if (!reordering)
2810 goto error;
2811
2812 for (i = 0; i < div_pos; ++i)
2813 reordering[i] = i;
2814
2815 skip = 0;
2816 n_div = qp->div->n_row;
2817 for (i = 0; i < n_div; ++i) {
2818 if (!active[div_pos + i]) {
2819 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2820 qp->div = isl_mat_drop_cols(qp->div,
2821 2 + div_pos + i - skip, 1);
2822 skip++;
2823 }
2824 reordering[div_pos + i] = div_pos + i - skip;
2825 }
2826
2827 qp->poly = reorder(qp->poly, reordering);
2828
2829 if (!qp->poly || !qp->div)
2830 goto error;
2831
2832 free(active);
2833 free(reordering);
2834
2835 return qp;
2836 error:
2837 free(active);
2838 free(reordering);
2839 isl_qpolynomial_free(qp);
2840 return NULL;
2841 }
2842
2843 __isl_give isl_poly *isl_poly_drop(__isl_take isl_poly *poly,
2844 unsigned first, unsigned n)
2845 {
2846 int i;
2847 isl_poly_rec *rec;
2848
2849 if (!poly)
2850 return NULL;
2851 if (n == 0 || poly->var < 0 || poly->var < first)
2852 return poly;
2853 if (poly->var < first + n) {
2854 poly = replace_by_constant_term(poly);
2855 return isl_poly_drop(poly, first, n);
2856 }
2857 poly = isl_poly_cow(poly);
2858 if (!poly)
2859 return NULL;
2860 poly->var -= n;
2861 rec = isl_poly_as_rec(poly);
2862 if (!rec)
2863 goto error;
2864
2865 for (i = 0; i < rec->n; ++i) {
2866 rec->p[i] = isl_poly_drop(rec->p[i], first, n);
2867 if (!rec->p[i])
2868 goto error;
2869 }
2870
2871 return poly;
2872 error:
2873 isl_poly_free(poly);
2874 return NULL;
2875 }
2876
2877 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2878 __isl_take isl_qpolynomial *qp,
2879 enum isl_dim_type type, unsigned pos, const char *s)
2880 {
2881 qp = isl_qpolynomial_cow(qp);
2882 if (!qp)
2883 return NULL;
2884 if (type == isl_dim_out)
2885 isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
2886 "cannot set name of output/set dimension",
2887 return isl_qpolynomial_free(qp));
2888 type = domain_type(type);
2889 qp->dim = isl_space_set_dim_name(qp->dim, type, pos, s);
2890 if (!qp->dim)
2891 goto error;
2892 return qp;
2893 error:
2894 isl_qpolynomial_free(qp);
2895 return NULL;
2896 }
2897
2898 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2899 __isl_take isl_qpolynomial *qp,
2900 enum isl_dim_type type, unsigned first, unsigned n)
2901 {
2902 isl_size offset;
2903
2904 if (!qp)
2905 return NULL;
2906 if (type == isl_dim_out)
2907 isl_die(qp->dim->ctx, isl_error_invalid,
2908 "cannot drop output/set dimension",
2909 goto error);
2910 if (isl_qpolynomial_check_range(qp, type, first, n) < 0)
2911 return isl_qpolynomial_free(qp);
2912 type = domain_type(type);
2913 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2914 return qp;
2915
2916 qp = isl_qpolynomial_cow(qp);
2917 if (!qp)
2918 return NULL;
2919
2920 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2921 type == isl_dim_set, goto error);
2922
2923 qp->dim = isl_space_drop_dims(qp->dim, type, first, n);
2924 if (!qp->dim)
2925 goto error;
2926
2927 offset = isl_qpolynomial_domain_var_offset(qp, type);
2928 if (offset < 0)
2929 goto error;
2930 first += offset;
2931
2932 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2933 if (!qp->div)
2934 goto error;
2935
2936 qp->poly = isl_poly_drop(qp->poly, first, n);
2937 if (!qp->poly)
2938 goto error;
2939
2940 return qp;
2941 error:
2942 isl_qpolynomial_free(qp);
2943 return NULL;
2944 }
2945
2946 /* Project the domain of the quasi-polynomial onto its parameter space.
2947 * The quasi-polynomial may not involve any of the domain dimensions.
2948 */
2949 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
2950 __isl_take isl_qpolynomial *qp)
2951 {
2952 isl_space *space;
2953 isl_size n;
2954 isl_bool involves;
2955
2956 n = isl_qpolynomial_dim(qp, isl_dim_in);
2957 if (n < 0)
2958 return isl_qpolynomial_free(qp);
2959 involves = isl_qpolynomial_involves_dims(qp, isl_dim_in, 0, n);
2960 if (involves < 0)
2961 return isl_qpolynomial_free(qp);
2962 if (involves)
2963 isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
2964 "polynomial involves some of the domain dimensions",
2965 return isl_qpolynomial_free(qp));
2966 qp = isl_qpolynomial_drop_dims(qp, isl_dim_in, 0, n);
2967 space = isl_qpolynomial_get_domain_space(qp);
2968 space = isl_space_params(space);
2969 qp = isl_qpolynomial_reset_domain_space(qp, space);
2970 return qp;
2971 }
2972
2973 static __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities_lifted(
2974 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2975 {
2976 int i, j, k;
2977 isl_int denom;
2978 unsigned total;
2979 unsigned n_div;
2980 isl_poly *poly;
2981
2982 if (!eq)
2983 goto error;
2984 if (eq->n_eq == 0) {
2985 isl_basic_set_free(eq);
2986 return qp;
2987 }
2988
2989 qp = isl_qpolynomial_cow(qp);
2990 if (!qp)
2991 goto error;
2992 qp->div = isl_mat_cow(qp->div);
2993 if (!qp->div)
2994 goto error;
2995
2996 total = isl_basic_set_offset(eq, isl_dim_div);
2997 n_div = eq->n_div;
2998 isl_int_init(denom);
2999 for (i = 0; i < eq->n_eq; ++i) {
3000 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
3001 if (j < 0 || j == 0 || j >= total)
3002 continue;
3003
3004 for (k = 0; k < qp->div->n_row; ++k) {
3005 if (isl_int_is_zero(qp->div->row[k][1 + j]))
3006 continue;
3007 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
3008 &qp->div->row[k][0]);
3009 normalize_div(qp, k);
3010 }
3011
3012 if (isl_int_is_pos(eq->eq[i][j]))
3013 isl_seq_neg(eq->eq[i], eq->eq[i], total);
3014 isl_int_abs(denom, eq->eq[i][j]);
3015 isl_int_set_si(eq->eq[i][j], 0);
3016
3017 poly = isl_poly_from_affine(qp->dim->ctx,
3018 eq->eq[i], denom, total);
3019 qp->poly = isl_poly_subs(qp->poly, j - 1, 1, &poly);
3020 isl_poly_free(poly);
3021 }
3022 isl_int_clear(denom);
3023
3024 if (!qp->poly)
3025 goto error;
3026
3027 isl_basic_set_free(eq);
3028
3029 qp = substitute_non_divs(qp);
3030 qp = sort_divs(qp);
3031
3032 return qp;
3033 error:
3034 isl_basic_set_free(eq);
3035 isl_qpolynomial_free(qp);
3036 return NULL;
3037 }
3038
3039 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
3040 */
3041 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
3042 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
3043 {
3044 if (!qp || !eq)
3045 goto error;
3046 if (qp->div->n_row > 0)
3047 eq = isl_basic_set_add_dims(eq, isl_dim_set, qp->div->n_row);
3048 return isl_qpolynomial_substitute_equalities_lifted(qp, eq);
3049 error:
3050 isl_basic_set_free(eq);
3051 isl_qpolynomial_free(qp);
3052 return NULL;
3053 }
3054
3055 /* Look for equalities among the variables shared by context and qp
3056 * and the integer divisions of qp, if any.
3057 * The equalities are then used to eliminate variables and/or integer
3058 * divisions from qp.
3059 */
3060 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3061 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
3062 {
3063 isl_local_space *ls;
3064 isl_basic_set *aff;
3065
3066 ls = isl_qpolynomial_get_domain_local_space(qp);
3067 context = isl_local_space_lift_set(ls, context);
3068
3069 aff = isl_set_affine_hull(context);
3070 return isl_qpolynomial_substitute_equalities_lifted(qp, aff);
3071 }
3072
3073 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3074 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
3075 {
3076 isl_space *space = isl_qpolynomial_get_domain_space(qp);
3077 isl_set *dom_context = isl_set_universe(space);
3078 dom_context = isl_set_intersect_params(dom_context, context);
3079 return isl_qpolynomial_gist(qp, dom_context);
3080 }
3081
3082 /* Return a zero isl_qpolynomial in the given space.
3083 *
3084 * This is a helper function for isl_pw_*_as_* that ensures a uniform
3085 * interface over all piecewise types.
3086 */
3087 static __isl_give isl_qpolynomial *isl_qpolynomial_zero_in_space(
3088 __isl_take isl_space *space)
3089 {
3090 return isl_qpolynomial_zero_on_domain(isl_space_domain(space));
3091 }
3092
3093 #define isl_qpolynomial_involves_nan isl_qpolynomial_is_nan
3094
3095 #undef PW
3096 #define PW isl_pw_qpolynomial
3097 #undef BASE
3098 #define BASE qpolynomial
3099 #undef EL_IS_ZERO
3100 #define EL_IS_ZERO is_zero
3101 #undef ZERO
3102 #define ZERO zero
3103 #undef IS_ZERO
3104 #define IS_ZERO is_zero
3105 #undef FIELD
3106 #define FIELD qp
3107 #undef DEFAULT_IS_ZERO
3108 #define DEFAULT_IS_ZERO 1
3109
3110 #include <isl_pw_templ.c>
3111 #include <isl_pw_un_op_templ.c>
3112 #include <isl_pw_add_disjoint_templ.c>
3113 #include <isl_pw_eval.c>
3114 #include <isl_pw_fix_templ.c>
3115 #include <isl_pw_from_range_templ.c>
3116 #include <isl_pw_insert_dims_templ.c>
3117 #include <isl_pw_lift_templ.c>
3118 #include <isl_pw_morph_templ.c>
3119 #include <isl_pw_move_dims_templ.c>
3120 #include <isl_pw_neg_templ.c>
3121 #include <isl_pw_opt_templ.c>
3122 #include <isl_pw_split_dims_templ.c>
3123 #include <isl_pw_sub_templ.c>
3124
3125 #undef BASE
3126 #define BASE pw_qpolynomial
3127
3128 #include <isl_union_single.c>
3129 #include <isl_union_eval.c>
3130 #include <isl_union_neg.c>
3131 #include <isl_union_sub_templ.c>
3132
3133 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
3134 {
3135 if (!pwqp)
3136 return -1;
3137
3138 if (pwqp->n != -1)
3139 return 0;
3140
3141 if (!isl_set_plain_is_universe(pwqp->p[0].set))
3142 return 0;
3143
3144 return isl_qpolynomial_is_one(pwqp->p[0].qp);
3145 }
3146
3147 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3148 __isl_take isl_pw_qpolynomial *pwqp1,
3149 __isl_take isl_pw_qpolynomial *pwqp2)
3150 {
3151 return isl_pw_qpolynomial_union_add_(pwqp1, pwqp2);
3152 }
3153
3154 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3155 __isl_take isl_pw_qpolynomial *pwqp1,
3156 __isl_take isl_pw_qpolynomial *pwqp2)
3157 {
3158 int i, j, n;
3159 struct isl_pw_qpolynomial *res;
3160
3161 if (!pwqp1 || !pwqp2)
3162 goto error;
3163
3164 isl_assert(pwqp1->dim->ctx, isl_space_is_equal(pwqp1->dim, pwqp2->dim),
3165 goto error);
3166
3167 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
3168 isl_pw_qpolynomial_free(pwqp2);
3169 return pwqp1;
3170 }
3171
3172 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
3173 isl_pw_qpolynomial_free(pwqp1);
3174 return pwqp2;
3175 }
3176
3177 if (isl_pw_qpolynomial_is_one(pwqp1)) {
3178 isl_pw_qpolynomial_free(pwqp1);
3179 return pwqp2;
3180 }
3181
3182 if (isl_pw_qpolynomial_is_one(pwqp2)) {
3183 isl_pw_qpolynomial_free(pwqp2);
3184 return pwqp1;
3185 }
3186
3187 n = pwqp1->n * pwqp2->n;
3188 res = isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1->dim), n);
3189
3190 for (i = 0; i < pwqp1->n; ++i) {
3191 for (j = 0; j < pwqp2->n; ++j) {
3192 struct isl_set *common;
3193 struct isl_qpolynomial *prod;
3194 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
3195 isl_set_copy(pwqp2->p[j].set));
3196 if (isl_set_plain_is_empty(common)) {
3197 isl_set_free(common);
3198 continue;
3199 }
3200
3201 prod = isl_qpolynomial_mul(
3202 isl_qpolynomial_copy(pwqp1->p[i].qp),
3203 isl_qpolynomial_copy(pwqp2->p[j].qp));
3204
3205 res = isl_pw_qpolynomial_add_piece(res, common, prod);
3206 }
3207 }
3208
3209 isl_pw_qpolynomial_free(pwqp1);
3210 isl_pw_qpolynomial_free(pwqp2);
3211
3212 return res;
3213 error:
3214 isl_pw_qpolynomial_free(pwqp1);
3215 isl_pw_qpolynomial_free(pwqp2);
3216 return NULL;
3217 }
3218
3219 __isl_give isl_val *isl_poly_eval(__isl_take isl_poly *poly,
3220 __isl_take isl_vec *vec)
3221 {
3222 int i;
3223 isl_bool is_cst;
3224 isl_poly_rec *rec;
3225 isl_val *res;
3226 isl_val *base;
3227
3228 is_cst = isl_poly_is_cst(poly);
3229 if (is_cst < 0)
3230 goto error;
3231 if (is_cst) {
3232 isl_vec_free(vec);
3233 res = isl_poly_get_constant_val(poly);
3234 isl_poly_free(poly);
3235 return res;
3236 }
3237
3238 rec = isl_poly_as_rec(poly);
3239 if (!rec || !vec)
3240 goto error;
3241
3242 isl_assert(poly->ctx, rec->n >= 1, goto error);
3243
3244 base = isl_val_rat_from_isl_int(poly->ctx,
3245 vec->el[1 + poly->var], vec->el[0]);
3246
3247 res = isl_poly_eval(isl_poly_copy(rec->p[rec->n - 1]),
3248 isl_vec_copy(vec));
3249
3250 for (i = rec->n - 2; i >= 0; --i) {
3251 res = isl_val_mul(res, isl_val_copy(base));
3252 res = isl_val_add(res, isl_poly_eval(isl_poly_copy(rec->p[i]),
3253 isl_vec_copy(vec)));
3254 }
3255
3256 isl_val_free(base);
3257 isl_poly_free(poly);
3258 isl_vec_free(vec);
3259 return res;
3260 error:
3261 isl_poly_free(poly);
3262 isl_vec_free(vec);
3263 return NULL;
3264 }
3265
3266 /* Evaluate "qp" in the void point "pnt".
3267 * In particular, return the value NaN.
3268 */
3269 static __isl_give isl_val *eval_void(__isl_take isl_qpolynomial *qp,
3270 __isl_take isl_point *pnt)
3271 {
3272 isl_ctx *ctx;
3273
3274 ctx = isl_point_get_ctx(pnt);
3275 isl_qpolynomial_free(qp);
3276 isl_point_free(pnt);
3277 return isl_val_nan(ctx);
3278 }
3279
3280 __isl_give isl_val *isl_qpolynomial_eval(__isl_take isl_qpolynomial *qp,
3281 __isl_take isl_point *pnt)
3282 {
3283 isl_bool is_void;
3284 isl_vec *ext;
3285 isl_val *v;
3286
3287 if (!qp || !pnt)
3288 goto error;
3289 isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, qp->dim), goto error);
3290 is_void = isl_point_is_void(pnt);
3291 if (is_void < 0)
3292 goto error;
3293 if (is_void)
3294 return eval_void(qp, pnt);
3295
3296 ext = isl_local_extend_point_vec(qp->div, isl_vec_copy(pnt->vec));
3297
3298 v = isl_poly_eval(isl_poly_copy(qp->poly), ext);
3299
3300 isl_qpolynomial_free(qp);
3301 isl_point_free(pnt);
3302
3303 return v;
3304 error:
3305 isl_qpolynomial_free(qp);
3306 isl_point_free(pnt);
3307 return NULL;
3308 }
3309
3310 int isl_poly_cmp(__isl_keep isl_poly_cst *cst1, __isl_keep isl_poly_cst *cst2)
3311 {
3312 int cmp;
3313 isl_int t;
3314 isl_int_init(t);
3315 isl_int_mul(t, cst1->n, cst2->d);
3316 isl_int_submul(t, cst2->n, cst1->d);
3317 cmp = isl_int_sgn(t);
3318 isl_int_clear(t);
3319 return cmp;
3320 }
3321
3322 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
3323 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
3324 unsigned first, unsigned n)
3325 {
3326 unsigned total;
3327 unsigned g_pos;
3328 int *exp;
3329
3330 if (!qp)
3331 return NULL;
3332 if (type == isl_dim_out)
3333 isl_die(qp->div->ctx, isl_error_invalid,
3334 "cannot insert output/set dimensions",
3335 goto error);
3336 if (isl_qpolynomial_check_range(qp, type, first, 0) < 0)
3337 return isl_qpolynomial_free(qp);
3338 type = domain_type(type);
3339 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
3340 return qp;
3341
3342 qp = isl_qpolynomial_cow(qp);
3343 if (!qp)
3344 return NULL;
3345
3346 g_pos = pos(qp->dim, type) + first;
3347
3348 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
3349 if (!qp->div)
3350 goto error;
3351
3352 total = qp->div->n_col - 2;
3353 if (total > g_pos) {
3354 int i;
3355 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
3356 if (!exp)
3357 goto error;
3358 for (i = 0; i < total - g_pos; ++i)
3359 exp[i] = i + n;
3360 qp->poly = expand(qp->poly, exp, g_pos);
3361 free(exp);
3362 if (!qp->poly)
3363 goto error;
3364 }
3365
3366 qp->dim = isl_space_insert_dims(qp->dim, type, first, n);
3367 if (!qp->dim)
3368 goto error;
3369
3370 return qp;
3371 error:
3372 isl_qpolynomial_free(qp);
3373 return NULL;
3374 }
3375
3376 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
3377 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
3378 {
3379 isl_size pos;
3380
3381 pos = isl_qpolynomial_dim(qp, type);
3382 if (pos < 0)
3383 return isl_qpolynomial_free(qp);
3384
3385 return isl_qpolynomial_insert_dims(qp, type, pos, n);
3386 }
3387
3388 static int *reordering_move(isl_ctx *ctx,
3389 unsigned len, unsigned dst, unsigned src, unsigned n)
3390 {
3391 int i;
3392 int *reordering;
3393
3394 reordering = isl_alloc_array(ctx, int, len);
3395 if (!reordering)
3396 return NULL;
3397
3398 if (dst <= src) {
3399 for (i = 0; i < dst; ++i)
3400 reordering[i] = i;
3401 for (i = 0; i < n; ++i)
3402 reordering[src + i] = dst + i;
3403 for (i = 0; i < src - dst; ++i)
3404 reordering[dst + i] = dst + n + i;
3405 for (i = 0; i < len - src - n; ++i)
3406 reordering[src + n + i] = src + n + i;
3407 } else {
3408 for (i = 0; i < src; ++i)
3409 reordering[i] = i;
3410 for (i = 0; i < n; ++i)
3411 reordering[src + i] = dst + i;
3412 for (i = 0; i < dst - src; ++i)
3413 reordering[src + n + i] = src + i;
3414 for (i = 0; i < len - dst - n; ++i)
3415 reordering[dst + n + i] = dst + n + i;
3416 }
3417
3418 return reordering;
3419 }
3420
3421 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
3422 __isl_take isl_qpolynomial *qp,
3423 enum isl_dim_type dst_type, unsigned dst_pos,
3424 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3425 {
3426 unsigned g_dst_pos;
3427 unsigned g_src_pos;
3428 int *reordering;
3429
3430 if (!qp)
3431 return NULL;
3432
3433 if (dst_type == isl_dim_out || src_type == isl_dim_out)
3434 isl_die(qp->dim->ctx, isl_error_invalid,
3435 "cannot move output/set dimension",
3436 goto error);
3437 if (isl_qpolynomial_check_range(qp, src_type, src_pos, n) < 0)
3438 return isl_qpolynomial_free(qp);
3439 if (dst_type == isl_dim_in)
3440 dst_type = isl_dim_set;
3441 if (src_type == isl_dim_in)
3442 src_type = isl_dim_set;
3443
3444 if (n == 0 &&
3445 !isl_space_is_named_or_nested(qp->dim, src_type) &&
3446 !isl_space_is_named_or_nested(qp->dim, dst_type))
3447 return qp;
3448
3449 qp = isl_qpolynomial_cow(qp);
3450 if (!qp)
3451 return NULL;
3452
3453 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
3454 g_src_pos = pos(qp->dim, src_type) + src_pos;
3455 if (dst_type > src_type)
3456 g_dst_pos -= n;
3457
3458 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
3459 if (!qp->div)
3460 goto error;
3461 qp = sort_divs(qp);
3462 if (!qp)
3463 goto error;
3464
3465 reordering = reordering_move(qp->dim->ctx,
3466 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
3467 if (!reordering)
3468 goto error;
3469
3470 qp->poly = reorder(qp->poly, reordering);
3471 free(reordering);
3472 if (!qp->poly)
3473 goto error;
3474
3475 qp->dim = isl_space_move_dims(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
3476 if (!qp->dim)
3477 goto error;
3478
3479 return qp;
3480 error:
3481 isl_qpolynomial_free(qp);
3482 return NULL;
3483 }
3484
3485 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(
3486 __isl_take isl_space *space, isl_int *f, isl_int denom)
3487 {
3488 isl_size d;
3489 isl_poly *poly;
3490
3491 space = isl_space_domain(space);
3492 if (!space)
3493 return NULL;
3494
3495 d = isl_space_dim(space, isl_dim_all);
3496 poly = d < 0 ? NULL : isl_poly_from_affine(space->ctx, f, denom, 1 + d);
3497
3498 return isl_qpolynomial_alloc(space, 0, poly);
3499 }
3500
3501 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
3502 {
3503 isl_ctx *ctx;
3504 isl_poly *poly;
3505 isl_qpolynomial *qp;
3506
3507 if (!aff)
3508 return NULL;
3509
3510 ctx = isl_aff_get_ctx(aff);
3511 poly = isl_poly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
3512 aff->v->size - 1);
3513
3514 qp = isl_qpolynomial_alloc(isl_aff_get_domain_space(aff),
3515 aff->ls->div->n_row, poly);
3516 if (!qp)
3517 goto error;
3518
3519 isl_mat_free(qp->div);
3520 qp->div = isl_mat_copy(aff->ls->div);
3521 qp->div = isl_mat_cow(qp->div);
3522 if (!qp->div)
3523 goto error;
3524
3525 isl_aff_free(aff);
3526 qp = reduce_divs(qp);
3527 qp = remove_redundant_divs(qp);
3528 return qp;
3529 error:
3530 isl_aff_free(aff);
3531 return isl_qpolynomial_free(qp);
3532 }
3533
3534 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3535 __isl_take isl_pw_aff *pwaff)
3536 {
3537 int i;
3538 isl_pw_qpolynomial *pwqp;
3539
3540 if (!pwaff)
3541 return NULL;
3542
3543 pwqp = isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff),
3544 pwaff->n);
3545
3546 for (i = 0; i < pwaff->n; ++i) {
3547 isl_set *dom;
3548 isl_qpolynomial *qp;
3549
3550 dom = isl_set_copy(pwaff->p[i].set);
3551 qp = isl_qpolynomial_from_aff(isl_aff_copy(pwaff->p[i].aff));
3552 pwqp = isl_pw_qpolynomial_add_piece(pwqp, dom, qp);
3553 }
3554
3555 isl_pw_aff_free(pwaff);
3556 return pwqp;
3557 }
3558
3559 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
3560 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3561 {
3562 isl_aff *aff;
3563
3564 aff = isl_constraint_get_bound(c, type, pos);
3565 isl_constraint_free(c);
3566 return isl_qpolynomial_from_aff(aff);
3567 }
3568
3569 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3570 * in "qp" by subs[i].
3571 */
3572 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3573 __isl_take isl_qpolynomial *qp,
3574 enum isl_dim_type type, unsigned first, unsigned n,
3575 __isl_keep isl_qpolynomial **subs)
3576 {
3577 int i;
3578 isl_poly **polys;
3579
3580 if (n == 0)
3581 return qp;
3582
3583 qp = isl_qpolynomial_cow(qp);
3584 if (!qp)
3585 return NULL;
3586
3587 if (type == isl_dim_out)
3588 isl_die(qp->dim->ctx, isl_error_invalid,
3589 "cannot substitute output/set dimension",
3590 goto error);
3591 if (isl_qpolynomial_check_range(qp, type, first, n) < 0)
3592 return isl_qpolynomial_free(qp);
3593 type = domain_type(type);
3594
3595 for (i = 0; i < n; ++i)
3596 if (!subs[i])
3597 goto error;
3598
3599 for (i = 0; i < n; ++i)
3600 if (isl_qpolynomial_check_equal_space(qp, subs[i]) < 0)
3601 goto error;
3602
3603 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3604 for (i = 0; i < n; ++i)
3605 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3606
3607 first += pos(qp->dim, type);
3608
3609 polys = isl_alloc_array(qp->dim->ctx, struct isl_poly *, n);
3610 if (!polys)
3611 goto error;
3612 for (i = 0; i < n; ++i)
3613 polys[i] = subs[i]->poly;
3614
3615 qp->poly = isl_poly_subs(qp->poly, first, n, polys);
3616
3617 free(polys);
3618
3619 if (!qp->poly)
3620 goto error;
3621
3622 return qp;
3623 error:
3624 isl_qpolynomial_free(qp);
3625 return NULL;
3626 }
3627
3628 /* Extend "bset" with extra set dimensions for each integer division
3629 * in "qp" and then call "fn" with the extended bset and the polynomial
3630 * that results from replacing each of the integer divisions by the
3631 * corresponding extra set dimension.
3632 */
3633 isl_stat isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3634 __isl_keep isl_basic_set *bset,
3635 isl_stat (*fn)(__isl_take isl_basic_set *bset,
3636 __isl_take isl_qpolynomial *poly, void *user), void *user)
3637 {
3638 isl_space *space;
3639 isl_local_space *ls;
3640 isl_qpolynomial *poly;
3641
3642 if (!qp || !bset)
3643 return isl_stat_error;
3644 if (qp->div->n_row == 0)
3645 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3646 user);
3647
3648 space = isl_space_copy(qp->dim);
3649 space = isl_space_add_dims(space, isl_dim_set, qp->div->n_row);
3650 poly = isl_qpolynomial_alloc(space, 0, isl_poly_copy(qp->poly));
3651 bset = isl_basic_set_copy(bset);
3652 ls = isl_qpolynomial_get_domain_local_space(qp);
3653 bset = isl_local_space_lift_basic_set(ls, bset);
3654
3655 return fn(bset, poly, user);
3656 }
3657
3658 /* Return total degree in variables first (inclusive) up to last (exclusive).
3659 */
3660 int isl_poly_degree(__isl_keep isl_poly *poly, int first, int last)
3661 {
3662 int deg = -1;
3663 int i;
3664 isl_bool is_zero, is_cst;
3665 isl_poly_rec *rec;
3666
3667 is_zero = isl_poly_is_zero(poly);
3668 if (is_zero < 0)
3669 return -2;
3670 if (is_zero)
3671 return -1;
3672 is_cst = isl_poly_is_cst(poly);
3673 if (is_cst < 0)
3674 return -2;
3675 if (is_cst || poly->var < first)
3676 return 0;
3677
3678 rec = isl_poly_as_rec(poly);
3679 if (!rec)
3680 return -2;
3681
3682 for (i = 0; i < rec->n; ++i) {
3683 int d;
3684
3685 is_zero = isl_poly_is_zero(rec->p[i]);
3686 if (is_zero < 0)
3687 return -2;
3688 if (is_zero)
3689 continue;
3690 d = isl_poly_degree(rec->p[i], first, last);
3691 if (poly->var < last)
3692 d += i;
3693 if (d > deg)
3694 deg = d;
3695 }
3696
3697 return deg;
3698 }
3699
3700 /* Return total degree in set variables.
3701 */
3702 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3703 {
3704 unsigned ovar;
3705 isl_size nvar;
3706
3707 if (!poly)
3708 return -2;
3709
3710 ovar = isl_space_offset(poly->dim, isl_dim_set);
3711 nvar = isl_space_dim(poly->dim, isl_dim_set);
3712 if (nvar < 0)
3713 return -2;
3714 return isl_poly_degree(poly->poly, ovar, ovar + nvar);
3715 }
3716
3717 __isl_give isl_poly *isl_poly_coeff(__isl_keep isl_poly *poly,
3718 unsigned pos, int deg)
3719 {
3720 int i;
3721 isl_bool is_cst;
3722 isl_poly_rec *rec;
3723
3724 is_cst = isl_poly_is_cst(poly);
3725 if (is_cst < 0)
3726 return NULL;
3727 if (is_cst || poly->var < pos) {
3728 if (deg == 0)
3729 return isl_poly_copy(poly);
3730 else
3731 return isl_poly_zero(poly->ctx);
3732 }
3733
3734 rec = isl_poly_as_rec(poly);
3735 if (!rec)
3736 return NULL;
3737
3738 if (poly->var == pos) {
3739 if (deg < rec->n)
3740 return isl_poly_copy(rec->p[deg]);
3741 else
3742 return isl_poly_zero(poly->ctx);
3743 }
3744
3745 poly = isl_poly_copy(poly);
3746 poly = isl_poly_cow(poly);
3747 rec = isl_poly_as_rec(poly);
3748 if (!rec)
3749 goto error;
3750
3751 for (i = 0; i < rec->n; ++i) {
3752 isl_poly *t;
3753 t = isl_poly_coeff(rec->p[i], pos, deg);
3754 if (!t)
3755 goto error;
3756 isl_poly_free(rec->p[i]);
3757 rec->p[i] = t;
3758 }
3759
3760 return poly;
3761 error:
3762 isl_poly_free(poly);
3763 return NULL;
3764 }
3765
3766 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3767 */
3768 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3769 __isl_keep isl_qpolynomial *qp,
3770 enum isl_dim_type type, unsigned t_pos, int deg)
3771 {
3772 unsigned g_pos;
3773 isl_poly *poly;
3774 isl_qpolynomial *c;
3775
3776 if (!qp)
3777 return NULL;
3778
3779 if (type == isl_dim_out)
3780 isl_die(qp->div->ctx, isl_error_invalid,
3781 "output/set dimension does not have a coefficient",
3782 return NULL);
3783 if (isl_qpolynomial_check_range(qp, type, t_pos, 1) < 0)
3784 return NULL;
3785 type = domain_type(type);
3786
3787 g_pos = pos(qp->dim, type) + t_pos;
3788 poly = isl_poly_coeff(qp->poly, g_pos, deg);
3789
3790 c = isl_qpolynomial_alloc(isl_space_copy(qp->dim),
3791 qp->div->n_row, poly);
3792 if (!c)
3793 return NULL;
3794 isl_mat_free(c->div);
3795 c->div = isl_mat_copy(qp->div);
3796 if (!c->div)
3797 goto error;
3798 return c;
3799 error:
3800 isl_qpolynomial_free(c);
3801 return NULL;
3802 }
3803
3804 /* Homogenize the polynomial in the variables first (inclusive) up to
3805 * last (exclusive) by inserting powers of variable first.
3806 * Variable first is assumed not to appear in the input.
3807 */
3808 __isl_give isl_poly *isl_poly_homogenize(__isl_take isl_poly *poly, int deg,
3809 int target, int first, int last)
3810 {
3811 int i;
3812 isl_bool is_zero, is_cst;
3813 isl_poly_rec *rec;
3814
3815 is_zero = isl_poly_is_zero(poly);
3816 if (is_zero < 0)
3817 return isl_poly_free(poly);
3818 if (is_zero)
3819 return poly;
3820 if (deg == target)
3821 return poly;
3822 is_cst = isl_poly_is_cst(poly);
3823 if (is_cst < 0)
3824 return isl_poly_free(poly);
3825 if (is_cst || poly->var < first) {
3826 isl_poly *hom;
3827
3828 hom = isl_poly_var_pow(poly->ctx, first, target - deg);
3829 if (!hom)
3830 goto error;
3831 rec = isl_poly_as_rec(hom);
3832 rec->p[target - deg] = isl_poly_mul(rec->p[target - deg], poly);
3833
3834 return hom;
3835 }
3836
3837 poly = isl_poly_cow(poly);
3838 rec = isl_poly_as_rec(poly);
3839 if (!rec)
3840 goto error;
3841
3842 for (i = 0; i < rec->n; ++i) {
3843 is_zero = isl_poly_is_zero(rec->p[i]);
3844 if (is_zero < 0)
3845 return isl_poly_free(poly);
3846 if (is_zero)
3847 continue;
3848 rec->p[i] = isl_poly_homogenize(rec->p[i],
3849 poly->var < last ? deg + i : i, target,
3850 first, last);
3851 if (!rec->p[i])
3852 goto error;
3853 }
3854
3855 return poly;
3856 error:
3857 isl_poly_free(poly);
3858 return NULL;
3859 }
3860
3861 /* Homogenize the polynomial in the set variables by introducing
3862 * powers of an extra set variable at position 0.
3863 */
3864 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3865 __isl_take isl_qpolynomial *poly)
3866 {
3867 unsigned ovar;
3868 isl_size nvar;
3869 int deg = isl_qpolynomial_degree(poly);
3870
3871 if (deg < -1)
3872 goto error;
3873
3874 poly = isl_qpolynomial_insert_dims(poly, isl_dim_in, 0, 1);
3875 poly = isl_qpolynomial_cow(poly);
3876 if (!poly)
3877 goto error;
3878
3879 ovar = isl_space_offset(poly->dim, isl_dim_set);
3880 nvar = isl_space_dim(poly->dim, isl_dim_set);
3881 if (nvar < 0)
3882 return isl_qpolynomial_free(poly);
3883 poly->poly = isl_poly_homogenize(poly->poly, 0, deg, ovar, ovar + nvar);
3884 if (!poly->poly)
3885 goto error;
3886
3887 return poly;
3888 error:
3889 isl_qpolynomial_free(poly);
3890 return NULL;
3891 }
3892
3893 __isl_give isl_term *isl_term_alloc(__isl_take isl_space *space,
3894 __isl_take isl_mat *div)
3895 {
3896 isl_term *term;
3897 isl_size d;
3898 int n;
3899
3900 d = isl_space_dim(space, isl_dim_all);
3901 if (d < 0 || !div)
3902 goto error;
3903
3904 n = d + div->n_row;
3905
3906 term = isl_calloc(space->ctx, struct isl_term,
3907 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3908 if (!term)
3909 goto error;
3910
3911 term->ref = 1;
3912 term->dim = space;
3913 term->div = div;
3914 isl_int_init(term->n);
3915 isl_int_init(term->d);
3916
3917 return term;
3918 error:
3919 isl_space_free(space);
3920 isl_mat_free(div);
3921 return NULL;
3922 }
3923
3924 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3925 {
3926 if (!term)
3927 return NULL;
3928
3929 term->ref++;
3930 return term;
3931 }
3932
3933 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3934 {
3935 int i;
3936 isl_term *dup;
3937 isl_size total;
3938
3939 total = isl_term_dim(term, isl_dim_all);
3940 if (total < 0)
3941 return NULL;
3942
3943 dup = isl_term_alloc(isl_space_copy(term->dim), isl_mat_copy(term->div));
3944 if (!dup)
3945 return NULL;
3946
3947 isl_int_set(dup->n, term->n);
3948 isl_int_set(dup->d, term->d);
3949
3950 for (i = 0; i < total; ++i)
3951 dup->pow[i] = term->pow[i];
3952
3953 return dup;
3954 }
3955
3956 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3957 {
3958 if (!term)
3959 return NULL;
3960
3961 if (term->ref == 1)
3962 return term;
3963 term->ref--;
3964 return isl_term_dup(term);
3965 }
3966
3967 __isl_null isl_term *isl_term_free(__isl_take isl_term *term)
3968 {
3969 if (!term)
3970 return NULL;
3971
3972 if (--term->ref > 0)
3973 return NULL;
3974
3975 isl_space_free(term->dim);
3976 isl_mat_free(term->div);
3977 isl_int_clear(term->n);
3978 isl_int_clear(term->d);
3979 free(term);
3980
3981 return NULL;
3982 }
3983
3984 isl_size isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3985 {
3986 isl_size dim;
3987
3988 if (!term)
3989 return isl_size_error;
3990
3991 switch (type) {
3992 case isl_dim_param:
3993 case isl_dim_in:
3994 case isl_dim_out: return isl_space_dim(term->dim, type);
3995 case isl_dim_div: return term->div->n_row;
3996 case isl_dim_all: dim = isl_space_dim(term->dim, isl_dim_all);
3997 if (dim < 0)
3998 return isl_size_error;
3999 return dim + term->div->n_row;
4000 default: return isl_size_error;
4001 }
4002 }
4003
4004 /* Return the space of "term".
4005 */
4006 static __isl_keep isl_space *isl_term_peek_space(__isl_keep isl_term *term)
4007 {
4008 return term ? term->dim : NULL;
4009 }
4010
4011 /* Return the offset of the first variable of type "type" within
4012 * the variables of "term".
4013 */
4014 static isl_size isl_term_offset(__isl_keep isl_term *term,
4015 enum isl_dim_type type)
4016 {
4017 isl_space *space;
4018
4019 space = isl_term_peek_space(term);
4020 if (!space)
4021 return isl_size_error;
4022
4023 switch (type) {
4024 case isl_dim_param:
4025 case isl_dim_set: return isl_space_offset(space, type);
4026 case isl_dim_div: return isl_space_dim(space, isl_dim_all);
4027 default:
4028 isl_die(isl_term_get_ctx(term), isl_error_invalid,
4029 "invalid dimension type", return isl_size_error);
4030 }
4031 }
4032
4033 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
4034 {
4035 return term ? term->dim->ctx : NULL;
4036 }
4037
4038 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
4039 {
4040 if (!term)
4041 return;
4042 isl_int_set(*n, term->n);
4043 }
4044
4045 /* Return the coefficient of the term "term".
4046 */
4047 __isl_give isl_val *isl_term_get_coefficient_val(__isl_keep isl_term *term)
4048 {
4049 if (!term)
4050 return NULL;
4051
4052 return isl_val_rat_from_isl_int(isl_term_get_ctx(term),
4053 term->n, term->d);
4054 }
4055
4056 #undef TYPE
4057 #define TYPE isl_term
4058 static
4059 #include "check_type_range_templ.c"
4060
4061 isl_size isl_term_get_exp(__isl_keep isl_term *term,
4062 enum isl_dim_type type, unsigned pos)
4063 {
4064 isl_size offset;
4065
4066 if (isl_term_check_range(term, type, pos, 1) < 0)
4067 return isl_size_error;
4068 offset = isl_term_offset(term, type);
4069 if (offset < 0)
4070 return isl_size_error;
4071
4072 return term->pow[offset + pos];
4073 }
4074
4075 __isl_give isl_aff *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
4076 {
4077 isl_local_space *ls;
4078 isl_aff *aff;
4079
4080 if (isl_term_check_range(term, isl_dim_div, pos, 1) < 0)
4081 return NULL;
4082
4083 ls = isl_local_space_alloc_div(isl_space_copy(term->dim),
4084 isl_mat_copy(term->div));
4085 aff = isl_aff_alloc(ls);
4086 if (!aff)
4087 return NULL;
4088
4089 isl_seq_cpy(aff->v->el, term->div->row[pos], aff->v->size);
4090
4091 aff = isl_aff_normalize(aff);
4092
4093 return aff;
4094 }
4095
4096 __isl_give isl_term *isl_poly_foreach_term(__isl_keep isl_poly *poly,
4097 isl_stat (*fn)(__isl_take isl_term *term, void *user),
4098 __isl_take isl_term *term, void *user)
4099 {
4100 int i;
4101 isl_bool is_zero, is_bad, is_cst;
4102 isl_poly_rec *rec;
4103
4104 is_zero = isl_poly_is_zero(poly);
4105 if (is_zero < 0 || !term)
4106 goto error;
4107
4108 if (is_zero)
4109 return term;
4110
4111 is_cst = isl_poly_is_cst(poly);
4112 is_bad = isl_poly_is_nan(poly);
4113 if (is_bad >= 0 && !is_bad)
4114 is_bad = isl_poly_is_infty(poly);
4115 if (is_bad >= 0 && !is_bad)
4116 is_bad = isl_poly_is_neginfty(poly);
4117 if (is_cst < 0 || is_bad < 0)
4118 return isl_term_free(term);
4119 if (is_bad)
4120 isl_die(isl_term_get_ctx(term), isl_error_invalid,
4121 "cannot handle NaN/infty polynomial",
4122 return isl_term_free(term));
4123
4124 if (is_cst) {
4125 isl_poly_cst *cst;
4126 cst = isl_poly_as_cst(poly);
4127 if (!cst)
4128 goto error;
4129 term = isl_term_cow(term);
4130 if (!term)
4131 goto error;
4132 isl_int_set(term->n, cst->n);
4133 isl_int_set(term->d, cst->d);
4134 if (fn(isl_term_copy(term), user) < 0)
4135 goto error;
4136 return term;
4137 }
4138
4139 rec = isl_poly_as_rec(poly);
4140 if (!rec)
4141 goto error;
4142
4143 for (i = 0; i < rec->n; ++i) {
4144 term = isl_term_cow(term);
4145 if (!term)
4146 goto error;
4147 term->pow[poly->var] = i;
4148 term = isl_poly_foreach_term(rec->p[i], fn, term, user);
4149 if (!term)
4150 goto error;
4151 }
4152 term = isl_term_cow(term);
4153 if (!term)
4154 return NULL;
4155 term->pow[poly->var] = 0;
4156
4157 return term;
4158 error:
4159 isl_term_free(term);
4160 return NULL;
4161 }
4162
4163 isl_stat isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
4164 isl_stat (*fn)(__isl_take isl_term *term, void *user), void *user)
4165 {
4166 isl_term *term;
4167
4168 if (!qp)
4169 return isl_stat_error;
4170
4171 term = isl_term_alloc(isl_space_copy(qp->dim), isl_mat_copy(qp->div));
4172 if (!term)
4173 return isl_stat_error;
4174
4175 term = isl_poly_foreach_term(qp->poly, fn, term, user);
4176
4177 isl_term_free(term);
4178
4179 return term ? isl_stat_ok : isl_stat_error;
4180 }
4181
4182 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
4183 {
4184 isl_poly *poly;
4185 isl_qpolynomial *qp;
4186 int i;
4187 isl_size n;
4188
4189 n = isl_term_dim(term, isl_dim_all);
4190 if (n < 0)
4191 term = isl_term_free(term);
4192 if (!term)
4193 return NULL;
4194
4195 poly = isl_poly_rat_cst(term->dim->ctx, term->n, term->d);
4196 for (i = 0; i < n; ++i) {
4197 if (!term->pow[i])
4198 continue;
4199 poly = isl_poly_mul(poly,
4200 isl_poly_var_pow(term->dim->ctx, i, term->pow[i]));
4201 }
4202
4203 qp = isl_qpolynomial_alloc(isl_space_copy(term->dim),
4204 term->div->n_row, poly);
4205 if (!qp)
4206 goto error;
4207 isl_mat_free(qp->div);
4208 qp->div = isl_mat_copy(term->div);
4209 if (!qp->div)
4210 goto error;
4211
4212 isl_term_free(term);
4213 return qp;
4214 error:
4215 isl_qpolynomial_free(qp);
4216 isl_term_free(term);
4217 return NULL;
4218 }
4219
4220 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
4221 __isl_take isl_space *space)
4222 {
4223 int i;
4224 int extra;
4225 isl_size total, d_set, d_qp;
4226
4227 if (!qp || !space)
4228 goto error;
4229
4230 if (isl_space_is_equal(qp->dim, space)) {
4231 isl_space_free(space);
4232 return qp;
4233 }
4234
4235 qp = isl_qpolynomial_cow(qp);
4236 if (!qp)
4237 goto error;
4238
4239 d_set = isl_space_dim(space, isl_dim_set);
4240 d_qp = isl_qpolynomial_domain_dim(qp, isl_dim_set);
4241 extra = d_set - d_qp;
4242 total = isl_space_dim(qp->dim, isl_dim_all);
4243 if (d_set < 0 || d_qp < 0 || total < 0)
4244 goto error;
4245 if (qp->div->n_row) {
4246 int *exp;
4247
4248 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
4249 if (!exp)
4250 goto error;
4251 for (i = 0; i < qp->div->n_row; ++i)
4252 exp[i] = extra + i;
4253 qp->poly = expand(qp->poly, exp, total);
4254 free(exp);
4255 if (!qp->poly)
4256 goto error;
4257 }
4258 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
4259 if (!qp->div)
4260 goto error;
4261 for (i = 0; i < qp->div->n_row; ++i)
4262 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
4263
4264 isl_space_free(qp->dim);
4265 qp->dim = space;
4266
4267 return qp;
4268 error:
4269 isl_space_free(space);
4270 isl_qpolynomial_free(qp);
4271 return NULL;
4272 }
4273
4274 /* For each parameter or variable that does not appear in qp,
4275 * first eliminate the variable from all constraints and then set it to zero.
4276 */
4277 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
4278 __isl_keep isl_qpolynomial *qp)
4279 {
4280 int *active = NULL;
4281 int i;
4282 isl_size d;
4283 isl_size nparam;
4284 isl_size nvar;
4285
4286 d = isl_set_dim(set, isl_dim_all);
4287 if (d < 0 || !qp)
4288 goto error;
4289
4290 active = isl_calloc_array(set->ctx, int, d);
4291 if (set_active(qp, active) < 0)
4292 goto error;
4293
4294 for (i = 0; i < d; ++i)
4295 if (!active[i])
4296 break;
4297
4298 if (i == d) {
4299 free(active);
4300 return set;
4301 }
4302
4303 nparam = isl_set_dim(set, isl_dim_param);
4304 nvar = isl_set_dim(set, isl_dim_set);
4305 if (nparam < 0 || nvar < 0)
4306 goto error;
4307 for (i = 0; i < nparam; ++i) {
4308 if (active[i])
4309 continue;
4310 set = isl_set_eliminate(set, isl_dim_param, i, 1);
4311 set = isl_set_fix_si(set, isl_dim_param, i, 0);
4312 }
4313 for (i = 0; i < nvar; ++i) {
4314 if (active[nparam + i])
4315 continue;
4316 set = isl_set_eliminate(set, isl_dim_set, i, 1);
4317 set = isl_set_fix_si(set, isl_dim_set, i, 0);
4318 }
4319
4320 free(active);
4321
4322 return set;
4323 error:
4324 free(active);
4325 isl_set_free(set);
4326 return NULL;
4327 }
4328
4329 struct isl_opt_data {
4330 isl_qpolynomial *qp;
4331 int first;
4332 isl_val *opt;
4333 int max;
4334 };
4335
4336 static isl_stat opt_fn(__isl_take isl_point *pnt, void *user)
4337 {
4338 struct isl_opt_data *data = (struct isl_opt_data *)user;
4339 isl_val *val;
4340
4341 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
4342 if (data->first) {
4343 data->first = 0;
4344 data->opt = val;
4345 } else if (data->max) {
4346 data->opt = isl_val_max(data->opt, val);
4347 } else {
4348 data->opt = isl_val_min(data->opt, val);
4349 }
4350
4351 return isl_stat_ok;
4352 }
4353
4354 __isl_give isl_val *isl_qpolynomial_opt_on_domain(
4355 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
4356 {
4357 struct isl_opt_data data = { NULL, 1, NULL, max };
4358 isl_bool is_cst;
4359
4360 if (!set || !qp)
4361 goto error;
4362
4363 is_cst = isl_poly_is_cst(qp->poly);
4364 if (is_cst < 0)
4365 goto error;
4366 if (is_cst) {
4367 isl_set_free(set);
4368 data.opt = isl_qpolynomial_get_constant_val(qp);
4369 isl_qpolynomial_free(qp);
4370 return data.opt;
4371 }
4372
4373 set = fix_inactive(set, qp);
4374
4375 data.qp = qp;
4376 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
4377 goto error;
4378
4379 if (data.first)
4380 data.opt = isl_val_zero(isl_set_get_ctx(set));
4381
4382 isl_set_free(set);
4383 isl_qpolynomial_free(qp);
4384 return data.opt;
4385 error:
4386 isl_set_free(set);
4387 isl_qpolynomial_free(qp);
4388 isl_val_free(data.opt);
4389 return NULL;
4390 }
4391
4392 __isl_give isl_qpolynomial *isl_qpolynomial_morph_domain(
4393 __isl_take isl_qpolynomial *qp, __isl_take isl_morph *morph)
4394 {
4395 int i;
4396 int n_sub;
4397 isl_ctx *ctx;
4398 isl_space *space;
4399 isl_poly **subs;
4400 isl_mat *mat, *diag;
4401
4402 qp = isl_qpolynomial_cow(qp);
4403
4404 space = isl_qpolynomial_peek_domain_space(qp);
4405 if (isl_morph_check_applies(morph, space) < 0)
4406 goto error;
4407
4408 ctx = isl_qpolynomial_get_ctx(qp);
4409 n_sub = morph->inv->n_row - 1;
4410 if (morph->inv->n_row != morph->inv->n_col)
4411 n_sub += qp->div->n_row;
4412 subs = isl_calloc_array(ctx, struct isl_poly *, n_sub);
4413 if (n_sub && !subs)
4414 goto error;
4415
4416 for (i = 0; 1 + i < morph->inv->n_row; ++i)
4417 subs[i] = isl_poly_from_affine(ctx, morph->inv->row[1 + i],
4418 morph->inv->row[0][0], morph->inv->n_col);
4419 if (morph->inv->n_row != morph->inv->n_col)
4420 for (i = 0; i < qp->div->n_row; ++i)
4421 subs[morph->inv->n_row - 1 + i] =
4422 isl_poly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
4423
4424 qp->poly = isl_poly_subs(qp->poly, 0, n_sub, subs);
4425
4426 for (i = 0; i < n_sub; ++i)
4427 isl_poly_free(subs[i]);
4428 free(subs);
4429
4430 diag = isl_mat_diag(ctx, 1, morph->inv->row[0][0]);
4431 mat = isl_mat_diagonal(diag, isl_mat_copy(morph->inv));
4432 diag = isl_mat_diag(ctx, qp->div->n_row, morph->inv->row[0][0]);
4433 mat = isl_mat_diagonal(mat, diag);
4434 qp->div = isl_mat_product(qp->div, mat);
4435 isl_space_free(qp->dim);
4436 qp->dim = isl_space_copy(morph->ran->dim);
4437
4438 if (!qp->poly || !qp->div || !qp->dim)
4439 goto error;
4440
4441 isl_morph_free(morph);
4442
4443 return qp;
4444 error:
4445 isl_qpolynomial_free(qp);
4446 isl_morph_free(morph);
4447 return NULL;
4448 }
4449
4450 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4451 __isl_take isl_union_pw_qpolynomial *upwqp1,
4452 __isl_take isl_union_pw_qpolynomial *upwqp2)
4453 {
4454 return isl_union_pw_qpolynomial_match_bin_op(upwqp1, upwqp2,
4455 &isl_pw_qpolynomial_mul);
4456 }
4457
4458 /* Reorder the dimension of "qp" according to the given reordering.
4459 */
4460 __isl_give isl_qpolynomial *isl_qpolynomial_realign_domain(
4461 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
4462 {
4463 isl_space *space;
4464
4465 qp = isl_qpolynomial_cow(qp);
4466 if (!qp)
4467 goto error;
4468
4469 r = isl_reordering_extend(r, qp->div->n_row);
4470 if (!r)
4471 goto error;
4472
4473 qp->div = isl_local_reorder(qp->div, isl_reordering_copy(r));
4474 if (!qp->div)
4475 goto error;
4476
4477 qp->poly = reorder(qp->poly, r->pos);
4478 if (!qp->poly)
4479 goto error;
4480
4481 space = isl_reordering_get_space(r);
4482 qp = isl_qpolynomial_reset_domain_space(qp, space);
4483
4484 isl_reordering_free(r);
4485 return qp;
4486 error:
4487 isl_qpolynomial_free(qp);
4488 isl_reordering_free(r);
4489 return NULL;
4490 }
4491
4492 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4493 __isl_take isl_qpolynomial *qp, __isl_take isl_space *model)
4494 {
4495 isl_space *domain_space;
4496 isl_bool equal_params;
4497
4498 domain_space = isl_qpolynomial_peek_domain_space(qp);
4499 equal_params = isl_space_has_equal_params(domain_space, model);
4500 if (equal_params < 0)
4501 goto error;
4502 if (!equal_params) {
4503 isl_reordering *exp;
4504
4505 exp = isl_parameter_alignment_reordering(domain_space, model);
4506 qp = isl_qpolynomial_realign_domain(qp, exp);
4507 }
4508
4509 isl_space_free(model);
4510 return qp;
4511 error:
4512 isl_space_free(model);
4513 isl_qpolynomial_free(qp);
4514 return NULL;
4515 }
4516
4517 struct isl_split_periods_data {
4518 int max_periods;
4519 isl_pw_qpolynomial *res;
4520 };
4521
4522 /* Create a slice where the integer division "div" has the fixed value "v".
4523 * In particular, if "div" refers to floor(f/m), then create a slice
4524 *
4525 * m v <= f <= m v + (m - 1)
4526 *
4527 * or
4528 *
4529 * f - m v >= 0
4530 * -f + m v + (m - 1) >= 0
4531 */
4532 static __isl_give isl_set *set_div_slice(__isl_take isl_space *space,
4533 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4534 {
4535 isl_size total;
4536 isl_basic_set *bset = NULL;
4537 int k;
4538
4539 total = isl_space_dim(space, isl_dim_all);
4540 if (total < 0 || !qp)
4541 goto error;
4542
4543 bset = isl_basic_set_alloc_space(isl_space_copy(space), 0, 0, 2);
4544
4545 k = isl_basic_set_alloc_inequality(bset);
4546 if (k < 0)
4547 goto error;
4548 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4549 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4550
4551 k = isl_basic_set_alloc_inequality(bset);
4552 if (k < 0)
4553 goto error;
4554 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4555 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4556 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4557 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4558
4559 isl_space_free(space);
4560 return isl_set_from_basic_set(bset);
4561 error:
4562 isl_basic_set_free(bset);
4563 isl_space_free(space);
4564 return NULL;
4565 }
4566
4567 static isl_stat split_periods(__isl_take isl_set *set,
4568 __isl_take isl_qpolynomial *qp, void *user);
4569
4570 /* Create a slice of the domain "set" such that integer division "div"
4571 * has the fixed value "v" and add the results to data->res,
4572 * replacing the integer division by "v" in "qp".
4573 */
4574 static isl_stat set_div(__isl_take isl_set *set,
4575 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4576 struct isl_split_periods_data *data)
4577 {
4578 int i;
4579 isl_size div_pos;
4580 isl_set *slice;
4581 isl_poly *cst;
4582
4583 slice = set_div_slice(isl_set_get_space(set), qp, div, v);
4584 set = isl_set_intersect(set, slice);
4585
4586 div_pos = isl_qpolynomial_domain_var_offset(qp, isl_dim_div);
4587 if (div_pos < 0)
4588 goto error;
4589
4590 for (i = div + 1; i < qp->div->n_row; ++i) {
4591 if (isl_int_is_zero(qp->div->row[i][2 + div_pos + div]))
4592 continue;
4593 isl_int_addmul(qp->div->row[i][1],
4594 qp->div->row[i][2 + div_pos + div], v);
4595 isl_int_set_si(qp->div->row[i][2 + div_pos + div], 0);
4596 }
4597
4598 cst = isl_poly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4599 qp = substitute_div(qp, div, cst);
4600
4601 return split_periods(set, qp, data);
4602 error:
4603 isl_set_free(set);
4604 isl_qpolynomial_free(qp);
4605 return isl_stat_error;
4606 }
4607
4608 /* Split the domain "set" such that integer division "div"
4609 * has a fixed value (ranging from "min" to "max") on each slice
4610 * and add the results to data->res.
4611 */
4612 static isl_stat split_div(__isl_take isl_set *set,
4613 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4614 struct isl_split_periods_data *data)
4615 {
4616 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4617 isl_set *set_i = isl_set_copy(set);
4618 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4619
4620 if (set_div(set_i, qp_i, div, min, data) < 0)
4621 goto error;
4622 }
4623 isl_set_free(set);
4624 isl_qpolynomial_free(qp);
4625 return isl_stat_ok;
4626 error:
4627 isl_set_free(set);
4628 isl_qpolynomial_free(qp);
4629 return isl_stat_error;
4630 }
4631
4632 /* If "qp" refers to any integer division
4633 * that can only attain "max_periods" distinct values on "set"
4634 * then split the domain along those distinct values.
4635 * Add the results (or the original if no splitting occurs)
4636 * to data->res.
4637 */
4638 static isl_stat split_periods(__isl_take isl_set *set,
4639 __isl_take isl_qpolynomial *qp, void *user)
4640 {
4641 int i;
4642 isl_pw_qpolynomial *pwqp;
4643 struct isl_split_periods_data *data;
4644 isl_int min, max;
4645 isl_size div_pos;
4646 isl_stat r = isl_stat_ok;
4647
4648 data = (struct isl_split_periods_data *)user;
4649
4650 if (!set || !qp)
4651 goto error;
4652
4653 if (qp->div->n_row == 0) {
4654 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4655 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4656 return isl_stat_ok;
4657 }
4658
4659 div_pos = isl_qpolynomial_domain_var_offset(qp, isl_dim_div);
4660 if (div_pos < 0)
4661 goto error;
4662
4663 isl_int_init(min);
4664 isl_int_init(max);
4665 for (i = 0; i < qp->div->n_row; ++i) {
4666 enum isl_lp_result lp_res;
4667
4668 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + div_pos,
4669 qp->div->n_row) != -1)
4670 continue;
4671
4672 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4673 set->ctx->one, &min, NULL, NULL);
4674 if (lp_res == isl_lp_error)
4675 goto error2;
4676 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4677 continue;
4678 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4679
4680 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4681 set->ctx->one, &max, NULL, NULL);
4682 if (lp_res == isl_lp_error)
4683 goto error2;
4684 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4685 continue;
4686 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4687
4688 isl_int_sub(max, max, min);
4689 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4690 isl_int_add(max, max, min);
4691 break;
4692 }
4693 }
4694
4695 if (i < qp->div->n_row) {
4696 r = split_div(set, qp, i, min, max, data);
4697 } else {
4698 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4699 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4700 }
4701
4702 isl_int_clear(max);
4703 isl_int_clear(min);
4704
4705 return r;
4706 error2:
4707 isl_int_clear(max);
4708 isl_int_clear(min);
4709 error:
4710 isl_set_free(set);
4711 isl_qpolynomial_free(qp);
4712 return isl_stat_error;
4713 }
4714
4715 /* If any quasi-polynomial in pwqp refers to any integer division
4716 * that can only attain "max_periods" distinct values on its domain
4717 * then split the domain along those distinct values.
4718 */
4719 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4720 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4721 {
4722 struct isl_split_periods_data data;
4723
4724 data.max_periods = max_periods;
4725 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4726
4727 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4728 goto error;
4729
4730 isl_pw_qpolynomial_free(pwqp);
4731
4732 return data.res;
4733 error:
4734 isl_pw_qpolynomial_free(data.res);
4735 isl_pw_qpolynomial_free(pwqp);
4736 return NULL;
4737 }
4738
4739 /* Construct a piecewise quasipolynomial that is constant on the given
4740 * domain. In particular, it is
4741 * 0 if cst == 0
4742 * 1 if cst == 1
4743 * infinity if cst == -1
4744 *
4745 * If cst == -1, then explicitly check whether the domain is empty and,
4746 * if so, return 0 instead.
4747 */
4748 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4749 __isl_take isl_basic_set *bset, int cst)
4750 {
4751 isl_space *space;
4752 isl_qpolynomial *qp;
4753
4754 if (cst < 0 && isl_basic_set_is_empty(bset) == isl_bool_true)
4755 cst = 0;
4756 if (!bset)
4757 return NULL;
4758
4759 bset = isl_basic_set_params(bset);
4760 space = isl_basic_set_get_space(bset);
4761 if (cst < 0)
4762 qp = isl_qpolynomial_infty_on_domain(space);
4763 else if (cst == 0)
4764 qp = isl_qpolynomial_zero_on_domain(space);
4765 else
4766 qp = isl_qpolynomial_one_on_domain(space);
4767 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4768 }
4769
4770 /* Internal data structure for multiplicative_call_factor_pw_qpolynomial.
4771 * "fn" is the function that is called on each factor.
4772 * "pwpq" collects the results.
4773 */
4774 struct isl_multiplicative_call_data_pw_qpolynomial {
4775 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset);
4776 isl_pw_qpolynomial *pwqp;
4777 };
4778
4779 /* Call "fn" on "bset" and return the result,
4780 * but first check if "bset" has any redundant constraints or
4781 * implicit equality constraints.
4782 * If so, there may be further opportunities for detecting factors or
4783 * removing equality constraints, so recursively call
4784 * the top-level isl_basic_set_multiplicative_call.
4785 */
4786 static __isl_give isl_pw_qpolynomial *multiplicative_call_base(
4787 __isl_take isl_basic_set *bset,
4788 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4789 {
4790 isl_size n1, n2, n_eq;
4791
4792 n1 = isl_basic_set_n_constraint(bset);
4793 if (n1 < 0)
4794 bset = isl_basic_set_free(bset);
4795 bset = isl_basic_set_remove_redundancies(bset);
4796 bset = isl_basic_set_detect_equalities(bset);
4797 n2 = isl_basic_set_n_constraint(bset);
4798 n_eq = isl_basic_set_n_equality(bset);
4799 if (n2 < 0 || n_eq < 0)
4800 bset = isl_basic_set_free(bset);
4801 else if (n2 < n1 || n_eq > 0)
4802 return isl_basic_set_multiplicative_call(bset, fn);
4803 return fn(bset);
4804 }
4805
4806 /* isl_factorizer_every_factor_basic_set callback that applies
4807 * data->fn to the factor "bset" and multiplies in the result
4808 * in data->pwqp.
4809 */
4810 static isl_bool multiplicative_call_factor_pw_qpolynomial(
4811 __isl_keep isl_basic_set *bset, void *user)
4812 {
4813 struct isl_multiplicative_call_data_pw_qpolynomial *data = user;
4814 isl_pw_qpolynomial *res;
4815
4816 bset = isl_basic_set_copy(bset);
4817 res = multiplicative_call_base(bset, data->fn);
4818 data->pwqp = isl_pw_qpolynomial_mul(data->pwqp, res);
4819 if (!data->pwqp)
4820 return isl_bool_error;
4821
4822 return isl_bool_true;
4823 }
4824
4825 /* Factor bset, call fn on each of the factors and return the product.
4826 *
4827 * If no factors can be found, simply call fn on the input.
4828 * Otherwise, construct the factors based on the factorizer,
4829 * call fn on each factor and compute the product.
4830 */
4831 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4832 __isl_take isl_basic_set *bset,
4833 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4834 {
4835 struct isl_multiplicative_call_data_pw_qpolynomial data = { fn };
4836 isl_space *space;
4837 isl_set *set;
4838 isl_factorizer *f;
4839 isl_qpolynomial *qp;
4840 isl_bool every;
4841
4842 f = isl_basic_set_factorizer(bset);
4843 if (!f)
4844 goto error;
4845 if (f->n_group == 0) {
4846 isl_factorizer_free(f);
4847 return multiplicative_call_base(bset, fn);
4848 }
4849
4850 space = isl_basic_set_get_space(bset);
4851 space = isl_space_params(space);
4852 set = isl_set_universe(isl_space_copy(space));
4853 qp = isl_qpolynomial_one_on_domain(space);
4854 data.pwqp = isl_pw_qpolynomial_alloc(set, qp);
4855
4856 every = isl_factorizer_every_factor_basic_set(f,
4857 &multiplicative_call_factor_pw_qpolynomial, &data);
4858 if (every < 0)
4859 data.pwqp = isl_pw_qpolynomial_free(data.pwqp);
4860
4861 isl_basic_set_free(bset);
4862 isl_factorizer_free(f);
4863
4864 return data.pwqp;
4865 error:
4866 isl_basic_set_free(bset);
4867 return NULL;
4868 }
4869
4870 /* Factor bset, call fn on each of the factors and return the product.
4871 * The function is assumed to evaluate to zero on empty domains,
4872 * to one on zero-dimensional domains and to infinity on unbounded domains
4873 * and will not be called explicitly on zero-dimensional or unbounded domains.
4874 *
4875 * We first check for some special cases and remove all equalities.
4876 * Then we hand over control to compressed_multiplicative_call.
4877 */
4878 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4879 __isl_take isl_basic_set *bset,
4880 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4881 {
4882 isl_bool bounded;
4883 isl_size dim;
4884 isl_morph *morph;
4885 isl_pw_qpolynomial *pwqp;
4886
4887 if (!bset)
4888 return NULL;
4889
4890 if (isl_basic_set_plain_is_empty(bset))
4891 return constant_on_domain(bset, 0);
4892
4893 dim = isl_basic_set_dim(bset, isl_dim_set);
4894 if (dim < 0)
4895 goto error;
4896 if (dim == 0)
4897 return constant_on_domain(bset, 1);
4898
4899 bounded = isl_basic_set_is_bounded(bset);
4900 if (bounded < 0)
4901 goto error;
4902 if (!bounded)
4903 return constant_on_domain(bset, -1);
4904
4905 if (bset->n_eq == 0)
4906 return compressed_multiplicative_call(bset, fn);
4907
4908 morph = isl_basic_set_full_compression(bset);
4909 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4910
4911 pwqp = compressed_multiplicative_call(bset, fn);
4912
4913 morph = isl_morph_dom_params(morph);
4914 morph = isl_morph_ran_params(morph);
4915 morph = isl_morph_inverse(morph);
4916
4917 pwqp = isl_pw_qpolynomial_morph_domain(pwqp, morph);
4918
4919 return pwqp;
4920 error:
4921 isl_basic_set_free(bset);
4922 return NULL;
4923 }
4924
4925 /* Drop all floors in "qp", turning each integer division [a/m] into
4926 * a rational division a/m. If "down" is set, then the integer division
4927 * is replaced by (a-(m-1))/m instead.
4928 */
4929 static __isl_give isl_qpolynomial *qp_drop_floors(
4930 __isl_take isl_qpolynomial *qp, int down)
4931 {
4932 int i;
4933 isl_poly *s;
4934
4935 if (!qp)
4936 return NULL;
4937 if (qp->div->n_row == 0)
4938 return qp;
4939
4940 qp = isl_qpolynomial_cow(qp);
4941 if (!qp)
4942 return NULL;
4943
4944 for (i = qp->div->n_row - 1; i >= 0; --i) {
4945 if (down) {
4946 isl_int_sub(qp->div->row[i][1],
4947 qp->div->row[i][1], qp->div->row[i][0]);
4948 isl_int_add_ui(qp->div->row[i][1],
4949 qp->div->row[i][1], 1);
4950 }
4951 s = isl_poly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4952 qp->div->row[i][0], qp->div->n_col - 1);
4953 qp = substitute_div(qp, i, s);
4954 if (!qp)
4955 return NULL;
4956 }
4957
4958 return qp;
4959 }
4960
4961 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4962 * a rational division a/m.
4963 */
4964 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4965 __isl_take isl_pw_qpolynomial *pwqp)
4966 {
4967 int i;
4968
4969 if (!pwqp)
4970 return NULL;
4971
4972 if (isl_pw_qpolynomial_is_zero(pwqp))
4973 return pwqp;
4974
4975 pwqp = isl_pw_qpolynomial_cow(pwqp);
4976 if (!pwqp)
4977 return NULL;
4978
4979 for (i = 0; i < pwqp->n; ++i) {
4980 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4981 if (!pwqp->p[i].qp)
4982 goto error;
4983 }
4984
4985 return pwqp;
4986 error:
4987 isl_pw_qpolynomial_free(pwqp);
4988 return NULL;
4989 }
4990
4991 /* Adjust all the integer divisions in "qp" such that they are at least
4992 * one over the given orthant (identified by "signs"). This ensures
4993 * that they will still be non-negative even after subtracting (m-1)/m.
4994 *
4995 * In particular, f is replaced by f' + v, changing f = [a/m]
4996 * to f' = [(a - m v)/m].
4997 * If the constant term k in a is smaller than m,
4998 * the constant term of v is set to floor(k/m) - 1.
4999 * For any other term, if the coefficient c and the variable x have
5000 * the same sign, then no changes are needed.
5001 * Otherwise, if the variable is positive (and c is negative),
5002 * then the coefficient of x in v is set to floor(c/m).
5003 * If the variable is negative (and c is positive),
5004 * then the coefficient of x in v is set to ceil(c/m).
5005 */
5006 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
5007 int *signs)
5008 {
5009 int i, j;
5010 isl_size div_pos;
5011 isl_vec *v = NULL;
5012 isl_poly *s;
5013
5014 qp = isl_qpolynomial_cow(qp);
5015 div_pos = isl_qpolynomial_domain_var_offset(qp, isl_dim_div);
5016 if (div_pos < 0)
5017 return isl_qpolynomial_free(qp);
5018 qp->div = isl_mat_cow(qp->div);
5019 if (!qp->div)
5020 goto error;
5021
5022 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
5023
5024 for (i = 0; i < qp->div->n_row; ++i) {
5025 isl_int *row = qp->div->row[i];
5026 v = isl_vec_clr(v);
5027 if (!v)
5028 goto error;
5029 if (isl_int_lt(row[1], row[0])) {
5030 isl_int_fdiv_q(v->el[0], row[1], row[0]);
5031 isl_int_sub_ui(v->el[0], v->el[0], 1);
5032 isl_int_submul(row[1], row[0], v->el[0]);
5033 }
5034 for (j = 0; j < div_pos; ++j) {
5035 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
5036 continue;
5037 if (signs[j] < 0)
5038 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
5039 else
5040 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
5041 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
5042 }
5043 for (j = 0; j < i; ++j) {
5044 if (isl_int_sgn(row[2 + div_pos + j]) >= 0)
5045 continue;
5046 isl_int_fdiv_q(v->el[1 + div_pos + j],
5047 row[2 + div_pos + j], row[0]);
5048 isl_int_submul(row[2 + div_pos + j],
5049 row[0], v->el[1 + div_pos + j]);
5050 }
5051 for (j = i + 1; j < qp->div->n_row; ++j) {
5052 if (isl_int_is_zero(qp->div->row[j][2 + div_pos + i]))
5053 continue;
5054 isl_seq_combine(qp->div->row[j] + 1,
5055 qp->div->ctx->one, qp->div->row[j] + 1,
5056 qp->div->row[j][2 + div_pos + i], v->el,
5057 v->size);
5058 }
5059 isl_int_set_si(v->el[1 + div_pos + i], 1);
5060 s = isl_poly_from_affine(qp->dim->ctx, v->el,
5061 qp->div->ctx->one, v->size);
5062 qp->poly = isl_poly_subs(qp->poly, div_pos + i, 1, &s);
5063 isl_poly_free(s);
5064 if (!qp->poly)
5065 goto error;
5066 }
5067
5068 isl_vec_free(v);
5069 return qp;
5070 error:
5071 isl_vec_free(v);
5072 isl_qpolynomial_free(qp);
5073 return NULL;
5074 }
5075
5076 struct isl_to_poly_data {
5077 int sign;
5078 isl_pw_qpolynomial *res;
5079 isl_qpolynomial *qp;
5080 };
5081
5082 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
5083 * We first make all integer divisions positive and then split the
5084 * quasipolynomials into terms with sign data->sign (the direction
5085 * of the requested approximation) and terms with the opposite sign.
5086 * In the first set of terms, each integer division [a/m] is
5087 * overapproximated by a/m, while in the second it is underapproximated
5088 * by (a-(m-1))/m.
5089 */
5090 static isl_stat to_polynomial_on_orthant(__isl_take isl_set *orthant,
5091 int *signs, void *user)
5092 {
5093 struct isl_to_poly_data *data = user;
5094 isl_pw_qpolynomial *t;
5095 isl_qpolynomial *qp, *up, *down;
5096
5097 qp = isl_qpolynomial_copy(data->qp);
5098 qp = make_divs_pos(qp, signs);
5099
5100 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
5101 up = qp_drop_floors(up, 0);
5102 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
5103 down = qp_drop_floors(down, 1);
5104
5105 isl_qpolynomial_free(qp);
5106 qp = isl_qpolynomial_add(up, down);
5107
5108 t = isl_pw_qpolynomial_alloc(orthant, qp);
5109 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
5110
5111 return isl_stat_ok;
5112 }
5113
5114 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
5115 * the polynomial will be an overapproximation. If "sign" is negative,
5116 * it will be an underapproximation. If "sign" is zero, the approximation
5117 * will lie somewhere in between.
5118 *
5119 * In particular, is sign == 0, we simply drop the floors, turning
5120 * the integer divisions into rational divisions.
5121 * Otherwise, we split the domains into orthants, make all integer divisions
5122 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
5123 * depending on the requested sign and the sign of the term in which
5124 * the integer division appears.
5125 */
5126 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5127 __isl_take isl_pw_qpolynomial *pwqp, int sign)
5128 {
5129 int i;
5130 struct isl_to_poly_data data;
5131
5132 if (sign == 0)
5133 return pwqp_drop_floors(pwqp);
5134
5135 if (!pwqp)
5136 return NULL;
5137
5138 data.sign = sign;
5139 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
5140
5141 for (i = 0; i < pwqp->n; ++i) {
5142 if (pwqp->p[i].qp->div->n_row == 0) {
5143 isl_pw_qpolynomial *t;
5144 t = isl_pw_qpolynomial_alloc(
5145 isl_set_copy(pwqp->p[i].set),
5146 isl_qpolynomial_copy(pwqp->p[i].qp));
5147 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
5148 continue;
5149 }
5150 data.qp = pwqp->p[i].qp;
5151 if (isl_set_foreach_orthant(pwqp->p[i].set,
5152 &to_polynomial_on_orthant, &data) < 0)
5153 goto error;
5154 }
5155
5156 isl_pw_qpolynomial_free(pwqp);
5157
5158 return data.res;
5159 error:
5160 isl_pw_qpolynomial_free(pwqp);
5161 isl_pw_qpolynomial_free(data.res);
5162 return NULL;
5163 }
5164
5165 static __isl_give isl_pw_qpolynomial *poly_entry(
5166 __isl_take isl_pw_qpolynomial *pwqp, void *user)
5167 {
5168 int *sign = user;
5169
5170 return isl_pw_qpolynomial_to_polynomial(pwqp, *sign);
5171 }
5172
5173 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
5174 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
5175 {
5176 return isl_union_pw_qpolynomial_transform_inplace(upwqp,
5177 &poly_entry, &sign);
5178 }
5179
5180 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
5181 __isl_take isl_qpolynomial *qp)
5182 {
5183 int i, k;
5184 isl_space *space;
5185 isl_vec *aff = NULL;
5186 isl_basic_map *bmap = NULL;
5187 isl_bool is_affine;
5188 unsigned pos;
5189 unsigned n_div;
5190
5191 if (!qp)
5192 return NULL;
5193 is_affine = isl_poly_is_affine(qp->poly);
5194 if (is_affine < 0)
5195 goto error;
5196 if (!is_affine)
5197 isl_die(qp->dim->ctx, isl_error_invalid,
5198 "input quasi-polynomial not affine", goto error);
5199 aff = isl_qpolynomial_extract_affine(qp);
5200 if (!aff)
5201 goto error;
5202 space = isl_qpolynomial_get_space(qp);
5203 pos = 1 + isl_space_offset(space, isl_dim_out);
5204 n_div = qp->div->n_row;
5205 bmap = isl_basic_map_alloc_space(space, n_div, 1, 2 * n_div);
5206
5207 for (i = 0; i < n_div; ++i) {
5208 k = isl_basic_map_alloc_div(bmap);
5209 if (k < 0)
5210 goto error;
5211 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
5212 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
5213 bmap = isl_basic_map_add_div_constraints(bmap, k);
5214 }
5215 k = isl_basic_map_alloc_equality(bmap);
5216 if (k < 0)
5217 goto error;
5218 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
5219 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
5220 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
5221
5222 isl_vec_free(aff);
5223 isl_qpolynomial_free(qp);
5224 bmap = isl_basic_map_finalize(bmap);
5225 return bmap;
5226 error:
5227 isl_vec_free(aff);
5228 isl_qpolynomial_free(qp);
5229 isl_basic_map_free(bmap);
5230 return NULL;
5231 }
Integer set library