2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the MIT license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
13 #include <isl_ctx_private.h>
14 #include <isl_map_private.h>
15 #include <isl_factorization.h>
18 #include <isl_union_map_private.h>
19 #include <isl_constraint_private.h>
20 #include <isl_polynomial_private.h>
21 #include <isl_point_private.h>
22 #include <isl_space_private.h>
23 #include <isl_mat_private.h>
24 #include <isl_range.h>
25 #include <isl_local_space_private.h>
26 #include <isl_aff_private.h>
27 #include <isl_val_private.h>
28 #include <isl_config.h>
30 static unsigned pos(__isl_keep isl_space *dim, enum isl_dim_type type)
33 case isl_dim_param: return 0;
34 case isl_dim_in: return dim->nparam;
35 case isl_dim_out: return dim->nparam + dim->n_in;
40 int isl_upoly_is_cst(__isl_keep struct isl_upoly *up)
48 __isl_keep struct isl_upoly_cst *isl_upoly_as_cst(__isl_keep struct isl_upoly *up)
53 isl_assert(up->ctx, up->var < 0, return NULL);
55 return (struct isl_upoly_cst *)up;
58 __isl_keep struct isl_upoly_rec *isl_upoly_as_rec(__isl_keep struct isl_upoly *up)
63 isl_assert(up->ctx, up->var >= 0, return NULL);
65 return (struct isl_upoly_rec *)up;
68 int isl_upoly_is_equal(__isl_keep struct isl_upoly *up1,
69 __isl_keep struct isl_upoly *up2)
72 struct isl_upoly_rec *rec1, *rec2;
78 if (up1->var != up2->var)
80 if (isl_upoly_is_cst(up1)) {
81 struct isl_upoly_cst *cst1, *cst2;
82 cst1 = isl_upoly_as_cst(up1);
83 cst2 = isl_upoly_as_cst(up2);
86 return isl_int_eq(cst1->n, cst2->n) &&
87 isl_int_eq(cst1->d, cst2->d);
90 rec1 = isl_upoly_as_rec(up1);
91 rec2 = isl_upoly_as_rec(up2);
95 if (rec1->n != rec2->n)
98 for (i = 0; i < rec1->n; ++i) {
99 int eq = isl_upoly_is_equal(rec1->p[i], rec2->p[i]);
107 int isl_upoly_is_zero(__isl_keep struct isl_upoly *up)
109 struct isl_upoly_cst *cst;
113 if (!isl_upoly_is_cst(up))
116 cst = isl_upoly_as_cst(up);
120 return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
123 int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
125 struct isl_upoly_cst *cst;
129 if (!isl_upoly_is_cst(up))
132 cst = isl_upoly_as_cst(up);
136 return isl_int_sgn(cst->n);
139 int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
141 struct isl_upoly_cst *cst;
145 if (!isl_upoly_is_cst(up))
148 cst = isl_upoly_as_cst(up);
152 return isl_int_is_zero(cst->n) && isl_int_is_zero(cst->d);
155 int isl_upoly_is_infty(__isl_keep struct isl_upoly *up)
157 struct isl_upoly_cst *cst;
161 if (!isl_upoly_is_cst(up))
164 cst = isl_upoly_as_cst(up);
168 return isl_int_is_pos(cst->n) && isl_int_is_zero(cst->d);
171 int isl_upoly_is_neginfty(__isl_keep struct isl_upoly *up)
173 struct isl_upoly_cst *cst;
177 if (!isl_upoly_is_cst(up))
180 cst = isl_upoly_as_cst(up);
184 return isl_int_is_neg(cst->n) && isl_int_is_zero(cst->d);
187 int isl_upoly_is_one(__isl_keep struct isl_upoly *up)
189 struct isl_upoly_cst *cst;
193 if (!isl_upoly_is_cst(up))
196 cst = isl_upoly_as_cst(up);
200 return isl_int_eq(cst->n, cst->d) && isl_int_is_pos(cst->d);
203 int isl_upoly_is_negone(__isl_keep struct isl_upoly *up)
205 struct isl_upoly_cst *cst;
209 if (!isl_upoly_is_cst(up))
212 cst = isl_upoly_as_cst(up);
216 return isl_int_is_negone(cst->n) && isl_int_is_one(cst->d);
219 __isl_give struct isl_upoly_cst *isl_upoly_cst_alloc(struct isl_ctx *ctx)
221 struct isl_upoly_cst *cst;
223 cst = isl_alloc_type(ctx, struct isl_upoly_cst);
232 isl_int_init(cst->n);
233 isl_int_init(cst->d);
238 __isl_give struct isl_upoly *isl_upoly_zero(struct isl_ctx *ctx)
240 struct isl_upoly_cst *cst;
242 cst = isl_upoly_cst_alloc(ctx);
246 isl_int_set_si(cst->n, 0);
247 isl_int_set_si(cst->d, 1);
252 __isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
254 struct isl_upoly_cst *cst;
256 cst = isl_upoly_cst_alloc(ctx);
260 isl_int_set_si(cst->n, 1);
261 isl_int_set_si(cst->d, 1);
266 __isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
268 struct isl_upoly_cst *cst;
270 cst = isl_upoly_cst_alloc(ctx);
274 isl_int_set_si(cst->n, 1);
275 isl_int_set_si(cst->d, 0);
280 __isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
282 struct isl_upoly_cst *cst;
284 cst = isl_upoly_cst_alloc(ctx);
288 isl_int_set_si(cst->n, -1);
289 isl_int_set_si(cst->d, 0);
294 __isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
296 struct isl_upoly_cst *cst;
298 cst = isl_upoly_cst_alloc(ctx);
302 isl_int_set_si(cst->n, 0);
303 isl_int_set_si(cst->d, 0);
308 __isl_give struct isl_upoly *isl_upoly_rat_cst(struct isl_ctx *ctx,
309 isl_int n, isl_int d)
311 struct isl_upoly_cst *cst;
313 cst = isl_upoly_cst_alloc(ctx);
317 isl_int_set(cst->n, n);
318 isl_int_set(cst->d, d);
323 __isl_give struct isl_upoly_rec *isl_upoly_alloc_rec(struct isl_ctx *ctx,
326 struct isl_upoly_rec *rec;
328 isl_assert(ctx, var >= 0, return NULL);
329 isl_assert(ctx, size >= 0, return NULL);
330 rec = isl_calloc(ctx, struct isl_upoly_rec,
331 sizeof(struct isl_upoly_rec) +
332 size * sizeof(struct isl_upoly *));
347 __isl_give isl_qpolynomial *isl_qpolynomial_reset_domain_space(
348 __isl_take isl_qpolynomial *qp, __isl_take isl_space *dim)
350 qp = isl_qpolynomial_cow(qp);
354 isl_space_free(qp->dim);
359 isl_qpolynomial_free(qp);
364 /* Reset the space of "qp". This function is called from isl_pw_templ.c
365 * and doesn't know if the space of an element object is represented
366 * directly or through its domain. It therefore passes along both.
368 __isl_give isl_qpolynomial *isl_qpolynomial_reset_space_and_domain(
369 __isl_take isl_qpolynomial *qp, __isl_take isl_space *space,
370 __isl_take isl_space *domain)
372 isl_space_free(space);
373 return isl_qpolynomial_reset_domain_space(qp, domain);
376 isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
378 return qp ? qp->dim->ctx : NULL;
381 __isl_give isl_space *isl_qpolynomial_get_domain_space(
382 __isl_keep isl_qpolynomial *qp)
384 return qp ? isl_space_copy(qp->dim) : NULL;
387 __isl_give isl_space *isl_qpolynomial_get_space(__isl_keep isl_qpolynomial *qp)
392 space = isl_space_copy(qp->dim);
393 space = isl_space_from_domain(space);
394 space = isl_space_add_dims(space, isl_dim_out, 1);
398 /* Externally, an isl_qpolynomial has a map space, but internally, the
399 * ls field corresponds to the domain of that space.
401 unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
402 enum isl_dim_type type)
406 if (type == isl_dim_out)
408 if (type == isl_dim_in)
410 return isl_space_dim(qp->dim, type);
413 int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
415 return qp ? isl_upoly_is_zero(qp->upoly) : -1;
418 int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
420 return qp ? isl_upoly_is_one(qp->upoly) : -1;
423 int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
425 return qp ? isl_upoly_is_nan(qp->upoly) : -1;
428 int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
430 return qp ? isl_upoly_is_infty(qp->upoly) : -1;
433 int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
435 return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
438 int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
440 return qp ? isl_upoly_sgn(qp->upoly) : 0;
443 static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
445 isl_int_clear(cst->n);
446 isl_int_clear(cst->d);
449 static void upoly_free_rec(__isl_take struct isl_upoly_rec *rec)
453 for (i = 0; i < rec->n; ++i)
454 isl_upoly_free(rec->p[i]);
457 __isl_give struct isl_upoly *isl_upoly_copy(__isl_keep struct isl_upoly *up)
466 __isl_give struct isl_upoly *isl_upoly_dup_cst(__isl_keep struct isl_upoly *up)
468 struct isl_upoly_cst *cst;
469 struct isl_upoly_cst *dup;
471 cst = isl_upoly_as_cst(up);
475 dup = isl_upoly_as_cst(isl_upoly_zero(up->ctx));
478 isl_int_set(dup->n, cst->n);
479 isl_int_set(dup->d, cst->d);
484 __isl_give struct isl_upoly *isl_upoly_dup_rec(__isl_keep struct isl_upoly *up)
487 struct isl_upoly_rec *rec;
488 struct isl_upoly_rec *dup;
490 rec = isl_upoly_as_rec(up);
494 dup = isl_upoly_alloc_rec(up->ctx, up->var, rec->n);
498 for (i = 0; i < rec->n; ++i) {
499 dup->p[i] = isl_upoly_copy(rec->p[i]);
507 isl_upoly_free(&dup->up);
511 __isl_give struct isl_upoly *isl_upoly_dup(__isl_keep struct isl_upoly *up)
516 if (isl_upoly_is_cst(up))
517 return isl_upoly_dup_cst(up);
519 return isl_upoly_dup_rec(up);
522 __isl_give struct isl_upoly *isl_upoly_cow(__isl_take struct isl_upoly *up)
530 return isl_upoly_dup(up);
533 void isl_upoly_free(__isl_take struct isl_upoly *up)
542 upoly_free_cst((struct isl_upoly_cst *)up);
544 upoly_free_rec((struct isl_upoly_rec *)up);
546 isl_ctx_deref(up->ctx);
550 static void isl_upoly_cst_reduce(__isl_keep struct isl_upoly_cst *cst)
555 isl_int_gcd(gcd, cst->n, cst->d);
556 if (!isl_int_is_zero(gcd) && !isl_int_is_one(gcd)) {
557 isl_int_divexact(cst->n, cst->n, gcd);
558 isl_int_divexact(cst->d, cst->d, gcd);
563 __isl_give struct isl_upoly *isl_upoly_sum_cst(__isl_take struct isl_upoly *up1,
564 __isl_take struct isl_upoly *up2)
566 struct isl_upoly_cst *cst1;
567 struct isl_upoly_cst *cst2;
569 up1 = isl_upoly_cow(up1);
573 cst1 = isl_upoly_as_cst(up1);
574 cst2 = isl_upoly_as_cst(up2);
576 if (isl_int_eq(cst1->d, cst2->d))
577 isl_int_add(cst1->n, cst1->n, cst2->n);
579 isl_int_mul(cst1->n, cst1->n, cst2->d);
580 isl_int_addmul(cst1->n, cst2->n, cst1->d);
581 isl_int_mul(cst1->d, cst1->d, cst2->d);
584 isl_upoly_cst_reduce(cst1);
594 static __isl_give struct isl_upoly *replace_by_zero(
595 __isl_take struct isl_upoly *up)
603 return isl_upoly_zero(ctx);
606 static __isl_give struct isl_upoly *replace_by_constant_term(
607 __isl_take struct isl_upoly *up)
609 struct isl_upoly_rec *rec;
610 struct isl_upoly *cst;
615 rec = isl_upoly_as_rec(up);
618 cst = isl_upoly_copy(rec->p[0]);
626 __isl_give struct isl_upoly *isl_upoly_sum(__isl_take struct isl_upoly *up1,
627 __isl_take struct isl_upoly *up2)
630 struct isl_upoly_rec *rec1, *rec2;
635 if (isl_upoly_is_nan(up1)) {
640 if (isl_upoly_is_nan(up2)) {
645 if (isl_upoly_is_zero(up1)) {
650 if (isl_upoly_is_zero(up2)) {
655 if (up1->var < up2->var)
656 return isl_upoly_sum(up2, up1);
658 if (up2->var < up1->var) {
659 struct isl_upoly_rec *rec;
660 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
664 up1 = isl_upoly_cow(up1);
665 rec = isl_upoly_as_rec(up1);
668 rec->p[0] = isl_upoly_sum(rec->p[0], up2);
670 up1 = replace_by_constant_term(up1);
674 if (isl_upoly_is_cst(up1))
675 return isl_upoly_sum_cst(up1, up2);
677 rec1 = isl_upoly_as_rec(up1);
678 rec2 = isl_upoly_as_rec(up2);
682 if (rec1->n < rec2->n)
683 return isl_upoly_sum(up2, up1);
685 up1 = isl_upoly_cow(up1);
686 rec1 = isl_upoly_as_rec(up1);
690 for (i = rec2->n - 1; i >= 0; --i) {
691 rec1->p[i] = isl_upoly_sum(rec1->p[i],
692 isl_upoly_copy(rec2->p[i]));
695 if (i == rec1->n - 1 && isl_upoly_is_zero(rec1->p[i])) {
696 isl_upoly_free(rec1->p[i]);
702 up1 = replace_by_zero(up1);
703 else if (rec1->n == 1)
704 up1 = replace_by_constant_term(up1);
715 __isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
716 __isl_take struct isl_upoly *up, isl_int v)
718 struct isl_upoly_cst *cst;
720 up = isl_upoly_cow(up);
724 cst = isl_upoly_as_cst(up);
726 isl_int_addmul(cst->n, cst->d, v);
731 __isl_give struct isl_upoly *isl_upoly_add_isl_int(
732 __isl_take struct isl_upoly *up, isl_int v)
734 struct isl_upoly_rec *rec;
739 if (isl_upoly_is_cst(up))
740 return isl_upoly_cst_add_isl_int(up, v);
742 up = isl_upoly_cow(up);
743 rec = isl_upoly_as_rec(up);
747 rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
757 __isl_give struct isl_upoly *isl_upoly_cst_mul_isl_int(
758 __isl_take struct isl_upoly *up, isl_int v)
760 struct isl_upoly_cst *cst;
762 if (isl_upoly_is_zero(up))
765 up = isl_upoly_cow(up);
769 cst = isl_upoly_as_cst(up);
771 isl_int_mul(cst->n, cst->n, v);
776 __isl_give struct isl_upoly *isl_upoly_mul_isl_int(
777 __isl_take struct isl_upoly *up, isl_int v)
780 struct isl_upoly_rec *rec;
785 if (isl_upoly_is_cst(up))
786 return isl_upoly_cst_mul_isl_int(up, v);
788 up = isl_upoly_cow(up);
789 rec = isl_upoly_as_rec(up);
793 for (i = 0; i < rec->n; ++i) {
794 rec->p[i] = isl_upoly_mul_isl_int(rec->p[i], v);
805 __isl_give struct isl_upoly *isl_upoly_mul_cst(__isl_take struct isl_upoly *up1,
806 __isl_take struct isl_upoly *up2)
808 struct isl_upoly_cst *cst1;
809 struct isl_upoly_cst *cst2;
811 up1 = isl_upoly_cow(up1);
815 cst1 = isl_upoly_as_cst(up1);
816 cst2 = isl_upoly_as_cst(up2);
818 isl_int_mul(cst1->n, cst1->n, cst2->n);
819 isl_int_mul(cst1->d, cst1->d, cst2->d);
821 isl_upoly_cst_reduce(cst1);
831 __isl_give struct isl_upoly *isl_upoly_mul_rec(__isl_take struct isl_upoly *up1,
832 __isl_take struct isl_upoly *up2)
834 struct isl_upoly_rec *rec1;
835 struct isl_upoly_rec *rec2;
836 struct isl_upoly_rec *res = NULL;
840 rec1 = isl_upoly_as_rec(up1);
841 rec2 = isl_upoly_as_rec(up2);
844 size = rec1->n + rec2->n - 1;
845 res = isl_upoly_alloc_rec(up1->ctx, up1->var, size);
849 for (i = 0; i < rec1->n; ++i) {
850 res->p[i] = isl_upoly_mul(isl_upoly_copy(rec2->p[0]),
851 isl_upoly_copy(rec1->p[i]));
856 for (; i < size; ++i) {
857 res->p[i] = isl_upoly_zero(up1->ctx);
862 for (i = 0; i < rec1->n; ++i) {
863 for (j = 1; j < rec2->n; ++j) {
864 struct isl_upoly *up;
865 up = isl_upoly_mul(isl_upoly_copy(rec2->p[j]),
866 isl_upoly_copy(rec1->p[i]));
867 res->p[i + j] = isl_upoly_sum(res->p[i + j], up);
880 isl_upoly_free(&res->up);
884 __isl_give struct isl_upoly *isl_upoly_mul(__isl_take struct isl_upoly *up1,
885 __isl_take struct isl_upoly *up2)
890 if (isl_upoly_is_nan(up1)) {
895 if (isl_upoly_is_nan(up2)) {
900 if (isl_upoly_is_zero(up1)) {
905 if (isl_upoly_is_zero(up2)) {
910 if (isl_upoly_is_one(up1)) {
915 if (isl_upoly_is_one(up2)) {
920 if (up1->var < up2->var)
921 return isl_upoly_mul(up2, up1);
923 if (up2->var < up1->var) {
925 struct isl_upoly_rec *rec;
926 if (isl_upoly_is_infty(up2) || isl_upoly_is_neginfty(up2)) {
927 isl_ctx *ctx = up1->ctx;
930 return isl_upoly_nan(ctx);
932 up1 = isl_upoly_cow(up1);
933 rec = isl_upoly_as_rec(up1);
937 for (i = 0; i < rec->n; ++i) {
938 rec->p[i] = isl_upoly_mul(rec->p[i],
939 isl_upoly_copy(up2));
947 if (isl_upoly_is_cst(up1))
948 return isl_upoly_mul_cst(up1, up2);
950 return isl_upoly_mul_rec(up1, up2);
957 __isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
960 struct isl_upoly *res;
968 res = isl_upoly_copy(up);
970 res = isl_upoly_one(up->ctx);
972 while (power >>= 1) {
973 up = isl_upoly_mul(up, isl_upoly_copy(up));
975 res = isl_upoly_mul(res, isl_upoly_copy(up));
982 __isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_space *dim,
983 unsigned n_div, __isl_take struct isl_upoly *up)
985 struct isl_qpolynomial *qp = NULL;
991 if (!isl_space_is_set(dim))
992 isl_die(isl_space_get_ctx(dim), isl_error_invalid,
993 "domain of polynomial should be a set", goto error);
995 total = isl_space_dim(dim, isl_dim_all);
997 qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
1002 qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
1011 isl_space_free(dim);
1013 isl_qpolynomial_free(qp);
1017 __isl_give isl_qpolynomial *isl_qpolynomial_copy(__isl_keep isl_qpolynomial *qp)
1026 __isl_give isl_qpolynomial *isl_qpolynomial_dup(__isl_keep isl_qpolynomial *qp)
1028 struct isl_qpolynomial *dup;
1033 dup = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row,
1034 isl_upoly_copy(qp->upoly));
1037 isl_mat_free(dup->div);
1038 dup->div = isl_mat_copy(qp->div);
1044 isl_qpolynomial_free(dup);
1048 __isl_give isl_qpolynomial *isl_qpolynomial_cow(__isl_take isl_qpolynomial *qp)
1056 return isl_qpolynomial_dup(qp);
1059 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp)
1067 isl_space_free(qp->dim);
1068 isl_mat_free(qp->div);
1069 isl_upoly_free(qp->upoly);
1075 __isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
1078 struct isl_upoly_rec *rec;
1079 struct isl_upoly_cst *cst;
1081 rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
1084 for (i = 0; i < 1 + power; ++i) {
1085 rec->p[i] = isl_upoly_zero(ctx);
1090 cst = isl_upoly_as_cst(rec->p[power]);
1091 isl_int_set_si(cst->n, 1);
1095 isl_upoly_free(&rec->up);
1099 /* r array maps original positions to new positions.
1101 static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
1105 struct isl_upoly_rec *rec;
1106 struct isl_upoly *base;
1107 struct isl_upoly *res;
1109 if (isl_upoly_is_cst(up))
1112 rec = isl_upoly_as_rec(up);
1116 isl_assert(up->ctx, rec->n >= 1, goto error);
1118 base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
1119 res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
1121 for (i = rec->n - 2; i >= 0; --i) {
1122 res = isl_upoly_mul(res, isl_upoly_copy(base));
1123 res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
1126 isl_upoly_free(base);
1135 static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
1140 isl_assert(div1->ctx, div1->n_row >= div2->n_row &&
1141 div1->n_col >= div2->n_col, return -1);
1143 if (div1->n_row == div2->n_row)
1144 return isl_mat_is_equal(div1, div2);
1146 n_row = div1->n_row;
1147 n_col = div1->n_col;
1148 div1->n_row = div2->n_row;
1149 div1->n_col = div2->n_col;
1151 equal = isl_mat_is_equal(div1, div2);
1153 div1->n_row = n_row;
1154 div1->n_col = n_col;
1159 static int cmp_row(__isl_keep isl_mat *div, int i, int j)
1163 li = isl_seq_last_non_zero(div->row[i], div->n_col);
1164 lj = isl_seq_last_non_zero(div->row[j], div->n_col);
1169 return isl_seq_cmp(div->row[i], div->row[j], div->n_col);
1172 struct isl_div_sort_info {
1177 static int div_sort_cmp(const void *p1, const void *p2)
1179 const struct isl_div_sort_info *i1, *i2;
1180 i1 = (const struct isl_div_sort_info *) p1;
1181 i2 = (const struct isl_div_sort_info *) p2;
1183 return cmp_row(i1->div, i1->row, i2->row);
1186 /* Sort divs and remove duplicates.
1188 static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
1193 struct isl_div_sort_info *array = NULL;
1194 int *pos = NULL, *at = NULL;
1195 int *reordering = NULL;
1200 if (qp->div->n_row <= 1)
1203 div_pos = isl_space_dim(qp->dim, isl_dim_all);
1205 array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
1207 pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1208 at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
1209 len = qp->div->n_col - 2;
1210 reordering = isl_alloc_array(qp->div->ctx, int, len);
1211 if (!array || !pos || !at || !reordering)
1214 for (i = 0; i < qp->div->n_row; ++i) {
1215 array[i].div = qp->div;
1221 qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
1224 for (i = 0; i < div_pos; ++i)
1227 for (i = 0; i < qp->div->n_row; ++i) {
1228 if (pos[array[i].row] == i)
1230 qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
1231 pos[at[i]] = pos[array[i].row];
1232 at[pos[array[i].row]] = at[i];
1233 at[i] = array[i].row;
1234 pos[array[i].row] = i;
1238 for (i = 0; i < len - div_pos; ++i) {
1240 isl_seq_eq(qp->div->row[i - skip - 1],
1241 qp->div->row[i - skip], qp->div->n_col)) {
1242 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
1243 isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
1244 2 + div_pos + i - skip);
1245 qp->div = isl_mat_drop_cols(qp->div,
1246 2 + div_pos + i - skip, 1);
1249 reordering[div_pos + array[i].row] = div_pos + i - skip;
1252 qp->upoly = reorder(qp->upoly, reordering);
1254 if (!qp->upoly || !qp->div)
1268 isl_qpolynomial_free(qp);
1272 static __isl_give struct isl_upoly *expand(__isl_take struct isl_upoly *up,
1273 int *exp, int first)
1276 struct isl_upoly_rec *rec;
1278 if (isl_upoly_is_cst(up))
1281 if (up->var < first)
1284 if (exp[up->var - first] == up->var - first)
1287 up = isl_upoly_cow(up);
1291 up->var = exp[up->var - first] + first;
1293 rec = isl_upoly_as_rec(up);
1297 for (i = 0; i < rec->n; ++i) {
1298 rec->p[i] = expand(rec->p[i], exp, first);
1309 static __isl_give isl_qpolynomial *with_merged_divs(
1310 __isl_give isl_qpolynomial *(*fn)(__isl_take isl_qpolynomial *qp1,
1311 __isl_take isl_qpolynomial *qp2),
1312 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
1316 isl_mat *div = NULL;
1318 qp1 = isl_qpolynomial_cow(qp1);
1319 qp2 = isl_qpolynomial_cow(qp2);
1324 isl_assert(qp1->div->ctx, qp1->div->n_row >= qp2->div->n_row &&
1325 qp1->div->n_col >= qp2->div->n_col, goto error);
1327 exp1 = isl_alloc_array(qp1->div->ctx, int, qp1->div->n_row);
1328 exp2 = isl_alloc_array(qp2->div->ctx, int, qp2->div->n_row);
1332 div = isl_merge_divs(qp1->div, qp2->div, exp1, exp2);
1336 isl_mat_free(qp1->div);
1337 qp1->div = isl_mat_copy(div);
1338 isl_mat_free(qp2->div);
1339 qp2->div = isl_mat_copy(div);
1341 qp1->upoly = expand(qp1->upoly, exp1, div->n_col - div->n_row - 2);
1342 qp2->upoly = expand(qp2->upoly, exp2, div->n_col - div->n_row - 2);
1344 if (!qp1->upoly || !qp2->upoly)
1351 return fn(qp1, qp2);
1356 isl_qpolynomial_free(qp1);
1357 isl_qpolynomial_free(qp2);
1361 __isl_give isl_qpolynomial *isl_qpolynomial_add(__isl_take isl_qpolynomial *qp1,
1362 __isl_take isl_qpolynomial *qp2)
1364 qp1 = isl_qpolynomial_cow(qp1);
1369 if (qp1->div->n_row < qp2->div->n_row)
1370 return isl_qpolynomial_add(qp2, qp1);
1372 isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1373 if (!compatible_divs(qp1->div, qp2->div))
1374 return with_merged_divs(isl_qpolynomial_add, qp1, qp2);
1376 qp1->upoly = isl_upoly_sum(qp1->upoly, isl_upoly_copy(qp2->upoly));
1380 isl_qpolynomial_free(qp2);
1384 isl_qpolynomial_free(qp1);
1385 isl_qpolynomial_free(qp2);
1389 __isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
1390 __isl_keep isl_set *dom,
1391 __isl_take isl_qpolynomial *qp1,
1392 __isl_take isl_qpolynomial *qp2)
1394 qp1 = isl_qpolynomial_add(qp1, qp2);
1395 qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
1399 __isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
1400 __isl_take isl_qpolynomial *qp2)
1402 return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
1405 __isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
1406 __isl_take isl_qpolynomial *qp, isl_int v)
1408 if (isl_int_is_zero(v))
1411 qp = isl_qpolynomial_cow(qp);
1415 qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
1421 isl_qpolynomial_free(qp);
1426 __isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
1431 return isl_qpolynomial_mul_isl_int(qp, qp->dim->ctx->negone);
1434 __isl_give isl_qpolynomial *isl_qpolynomial_mul_isl_int(
1435 __isl_take isl_qpolynomial *qp, isl_int v)
1437 if (isl_int_is_one(v))
1440 if (qp && isl_int_is_zero(v)) {
1441 isl_qpolynomial *zero;
1442 zero = isl_qpolynomial_zero_on_domain(isl_space_copy(qp->dim));
1443 isl_qpolynomial_free(qp);
1447 qp = isl_qpolynomial_cow(qp);
1451 qp->upoly = isl_upoly_mul_isl_int(qp->upoly, v);
1457 isl_qpolynomial_free(qp);
1461 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
1462 __isl_take isl_qpolynomial *qp, isl_int v)
1464 return isl_qpolynomial_mul_isl_int(qp, v);
1467 __isl_give isl_qpolynomial *isl_qpolynomial_mul(__isl_take isl_qpolynomial *qp1,
1468 __isl_take isl_qpolynomial *qp2)
1470 qp1 = isl_qpolynomial_cow(qp1);
1475 if (qp1->div->n_row < qp2->div->n_row)
1476 return isl_qpolynomial_mul(qp2, qp1);
1478 isl_assert(qp1->dim->ctx, isl_space_is_equal(qp1->dim, qp2->dim), goto error);
1479 if (!compatible_divs(qp1->div, qp2->div))
1480 return with_merged_divs(isl_qpolynomial_mul, qp1, qp2);
1482 qp1->upoly = isl_upoly_mul(qp1->upoly, isl_upoly_copy(qp2->upoly));
1486 isl_qpolynomial_free(qp2);
1490 isl_qpolynomial_free(qp1);
1491 isl_qpolynomial_free(qp2);
1495 __isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
1498 qp = isl_qpolynomial_cow(qp);
1503 qp->upoly = isl_upoly_pow(qp->upoly, power);
1509 isl_qpolynomial_free(qp);
1513 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
1514 __isl_take isl_pw_qpolynomial *pwqp, unsigned power)
1521 pwqp = isl_pw_qpolynomial_cow(pwqp);
1525 for (i = 0; i < pwqp->n; ++i) {
1526 pwqp->p[i].qp = isl_qpolynomial_pow(pwqp->p[i].qp, power);
1528 return isl_pw_qpolynomial_free(pwqp);
1534 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
1535 __isl_take isl_space *dim)
1539 return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1542 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
1543 __isl_take isl_space *dim)
1547 return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
1550 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
1551 __isl_take isl_space *dim)
1555 return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
1558 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
1559 __isl_take isl_space *dim)
1563 return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
1566 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
1567 __isl_take isl_space *dim)
1571 return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
1574 __isl_give isl_qpolynomial *isl_qpolynomial_cst_on_domain(
1575 __isl_take isl_space *dim,
1578 struct isl_qpolynomial *qp;
1579 struct isl_upoly_cst *cst;
1584 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
1588 cst = isl_upoly_as_cst(qp->upoly);
1589 isl_int_set(cst->n, v);
1594 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1595 isl_int *n, isl_int *d)
1597 struct isl_upoly_cst *cst;
1602 if (!isl_upoly_is_cst(qp->upoly))
1605 cst = isl_upoly_as_cst(qp->upoly);
1610 isl_int_set(*n, cst->n);
1612 isl_int_set(*d, cst->d);
1617 /* Return the constant term of "up".
1619 static __isl_give isl_val *isl_upoly_get_constant_val(
1620 __isl_keep struct isl_upoly *up)
1622 struct isl_upoly_cst *cst;
1627 while (!isl_upoly_is_cst(up)) {
1628 struct isl_upoly_rec *rec;
1630 rec = isl_upoly_as_rec(up);
1636 cst = isl_upoly_as_cst(up);
1639 return isl_val_rat_from_isl_int(cst->up.ctx, cst->n, cst->d);
1642 /* Return the constant term of "qp".
1644 __isl_give isl_val *isl_qpolynomial_get_constant_val(
1645 __isl_keep isl_qpolynomial *qp)
1650 return isl_upoly_get_constant_val(qp->upoly);
1653 int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
1656 struct isl_upoly_rec *rec;
1664 rec = isl_upoly_as_rec(up);
1671 isl_assert(up->ctx, rec->n > 1, return -1);
1673 is_cst = isl_upoly_is_cst(rec->p[1]);
1679 return isl_upoly_is_affine(rec->p[0]);
1682 int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
1687 if (qp->div->n_row > 0)
1690 return isl_upoly_is_affine(qp->upoly);
1693 static void update_coeff(__isl_keep isl_vec *aff,
1694 __isl_keep struct isl_upoly_cst *cst, int pos)
1699 if (isl_int_is_zero(cst->n))
1704 isl_int_gcd(gcd, cst->d, aff->el[0]);
1705 isl_int_divexact(f, cst->d, gcd);
1706 isl_int_divexact(gcd, aff->el[0], gcd);
1707 isl_seq_scale(aff->el, aff->el, f, aff->size);
1708 isl_int_mul(aff->el[1 + pos], gcd, cst->n);
1713 int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
1714 __isl_keep isl_vec *aff)
1716 struct isl_upoly_cst *cst;
1717 struct isl_upoly_rec *rec;
1723 struct isl_upoly_cst *cst;
1725 cst = isl_upoly_as_cst(up);
1728 update_coeff(aff, cst, 0);
1732 rec = isl_upoly_as_rec(up);
1735 isl_assert(up->ctx, rec->n == 2, return -1);
1737 cst = isl_upoly_as_cst(rec->p[1]);
1740 update_coeff(aff, cst, 1 + up->var);
1742 return isl_upoly_update_affine(rec->p[0], aff);
1745 __isl_give isl_vec *isl_qpolynomial_extract_affine(
1746 __isl_keep isl_qpolynomial *qp)
1754 d = isl_space_dim(qp->dim, isl_dim_all);
1755 aff = isl_vec_alloc(qp->div->ctx, 2 + d + qp->div->n_row);
1759 isl_seq_clr(aff->el + 1, 1 + d + qp->div->n_row);
1760 isl_int_set_si(aff->el[0], 1);
1762 if (isl_upoly_update_affine(qp->upoly, aff) < 0)
1771 int isl_qpolynomial_plain_is_equal(__isl_keep isl_qpolynomial *qp1,
1772 __isl_keep isl_qpolynomial *qp2)
1779 equal = isl_space_is_equal(qp1->dim, qp2->dim);
1780 if (equal < 0 || !equal)
1783 equal = isl_mat_is_equal(qp1->div, qp2->div);
1784 if (equal < 0 || !equal)
1787 return isl_upoly_is_equal(qp1->upoly, qp2->upoly);
1790 static void upoly_update_den(__isl_keep struct isl_upoly *up, isl_int *d)
1793 struct isl_upoly_rec *rec;
1795 if (isl_upoly_is_cst(up)) {
1796 struct isl_upoly_cst *cst;
1797 cst = isl_upoly_as_cst(up);
1800 isl_int_lcm(*d, *d, cst->d);
1804 rec = isl_upoly_as_rec(up);
1808 for (i = 0; i < rec->n; ++i)
1809 upoly_update_den(rec->p[i], d);
1812 void isl_qpolynomial_get_den(__isl_keep isl_qpolynomial *qp, isl_int *d)
1814 isl_int_set_si(*d, 1);
1817 upoly_update_den(qp->upoly, d);
1820 __isl_give isl_qpolynomial *isl_qpolynomial_var_pow_on_domain(
1821 __isl_take isl_space *dim, int pos, int power)
1823 struct isl_ctx *ctx;
1830 return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
1833 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(__isl_take isl_space *dim,
1834 enum isl_dim_type type, unsigned pos)
1839 isl_assert(dim->ctx, isl_space_dim(dim, isl_dim_in) == 0, goto error);
1840 isl_assert(dim->ctx, pos < isl_space_dim(dim, type), goto error);
1842 if (type == isl_dim_set)
1843 pos += isl_space_dim(dim, isl_dim_param);
1845 return isl_qpolynomial_var_pow_on_domain(dim, pos, 1);
1847 isl_space_free(dim);
1851 __isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
1852 unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
1855 struct isl_upoly_rec *rec;
1856 struct isl_upoly *base, *res;
1861 if (isl_upoly_is_cst(up))
1864 if (up->var < first)
1867 rec = isl_upoly_as_rec(up);
1871 isl_assert(up->ctx, rec->n >= 1, goto error);
1873 if (up->var >= first + n)
1874 base = isl_upoly_var_pow(up->ctx, up->var, 1);
1876 base = isl_upoly_copy(subs[up->var - first]);
1878 res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
1879 for (i = rec->n - 2; i >= 0; --i) {
1880 struct isl_upoly *t;
1881 t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
1882 res = isl_upoly_mul(res, isl_upoly_copy(base));
1883 res = isl_upoly_sum(res, t);
1886 isl_upoly_free(base);
1895 __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
1896 isl_int denom, unsigned len)
1899 struct isl_upoly *up;
1901 isl_assert(ctx, len >= 1, return NULL);
1903 up = isl_upoly_rat_cst(ctx, f[0], denom);
1904 for (i = 0; i < len - 1; ++i) {
1905 struct isl_upoly *t;
1906 struct isl_upoly *c;
1908 if (isl_int_is_zero(f[1 + i]))
1911 c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
1912 t = isl_upoly_var_pow(ctx, i, 1);
1913 t = isl_upoly_mul(c, t);
1914 up = isl_upoly_sum(up, t);
1920 /* Remove common factor of non-constant terms and denominator.
1922 static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
1924 isl_ctx *ctx = qp->div->ctx;
1925 unsigned total = qp->div->n_col - 2;
1927 isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
1928 isl_int_gcd(ctx->normalize_gcd,
1929 ctx->normalize_gcd, qp->div->row[div][0]);
1930 if (isl_int_is_one(ctx->normalize_gcd))
1933 isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
1934 ctx->normalize_gcd, total);
1935 isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
1936 ctx->normalize_gcd);
1937 isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
1938 ctx->normalize_gcd);
1941 /* Replace the integer division identified by "div" by the polynomial "s".
1942 * The integer division is assumed not to appear in the definition
1943 * of any other integer divisions.
1945 static __isl_give isl_qpolynomial *substitute_div(
1946 __isl_take isl_qpolynomial *qp,
1947 int div, __isl_take struct isl_upoly *s)
1956 qp = isl_qpolynomial_cow(qp);
1960 total = isl_space_dim(qp->dim, isl_dim_all);
1961 qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
1965 reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
1968 for (i = 0; i < total + div; ++i)
1970 for (i = total + div + 1; i < total + qp->div->n_row; ++i)
1971 reordering[i] = i - 1;
1972 qp->div = isl_mat_drop_rows(qp->div, div, 1);
1973 qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
1974 qp->upoly = reorder(qp->upoly, reordering);
1977 if (!qp->upoly || !qp->div)
1983 isl_qpolynomial_free(qp);
1988 /* Replace all integer divisions [e/d] that turn out to not actually be integer
1989 * divisions because d is equal to 1 by their definition, i.e., e.
1991 static __isl_give isl_qpolynomial *substitute_non_divs(
1992 __isl_take isl_qpolynomial *qp)
1996 struct isl_upoly *s;
2001 total = isl_space_dim(qp->dim, isl_dim_all);
2002 for (i = 0; qp && i < qp->div->n_row; ++i) {
2003 if (!isl_int_is_one(qp->div->row[i][0]))
2005 for (j = i + 1; j < qp->div->n_row; ++j) {
2006 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
2008 isl_seq_combine(qp->div->row[j] + 1,
2009 qp->div->ctx->one, qp->div->row[j] + 1,
2010 qp->div->row[j][2 + total + i],
2011 qp->div->row[i] + 1, 1 + total + i);
2012 isl_int_set_si(qp->div->row[j][2 + total + i], 0);
2013 normalize_div(qp, j);
2015 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
2016 qp->div->row[i][0], qp->div->n_col - 1);
2017 qp = substitute_div(qp, i, s);
2024 /* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
2025 * with d the denominator. When replacing the coefficient e of x by
2026 * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
2027 * inside the division, so we need to add floor(e/d) * x outside.
2028 * That is, we replace q by q' + floor(e/d) * x and we therefore need
2029 * to adjust the coefficient of x in each later div that depends on the
2030 * current div "div" and also in the affine expression "aff"
2031 * (if it too depends on "div").
2033 static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
2034 __isl_keep isl_vec *aff)
2038 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2041 for (i = 0; i < 1 + total + div; ++i) {
2042 if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
2043 isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
2045 isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
2046 isl_int_fdiv_r(qp->div->row[div][1 + i],
2047 qp->div->row[div][1 + i], qp->div->row[div][0]);
2048 if (!isl_int_is_zero(aff->el[1 + total + div]))
2049 isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
2050 for (j = div + 1; j < qp->div->n_row; ++j) {
2051 if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
2053 isl_int_addmul(qp->div->row[j][1 + i],
2054 v, qp->div->row[j][2 + total + div]);
2060 /* Check if the last non-zero coefficient is bigger that half of the
2061 * denominator. If so, we will invert the div to further reduce the number
2062 * of distinct divs that may appear.
2063 * If the last non-zero coefficient is exactly half the denominator,
2064 * then we continue looking for earlier coefficients that are bigger
2065 * than half the denominator.
2067 static int needs_invert(__isl_keep isl_mat *div, int row)
2072 for (i = div->n_col - 1; i >= 1; --i) {
2073 if (isl_int_is_zero(div->row[row][i]))
2075 isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
2076 cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
2077 isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
2087 /* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
2088 * We only invert the coefficients of e (and the coefficient of q in
2089 * later divs and in "aff"). After calling this function, the
2090 * coefficients of e should be reduced again.
2092 static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
2093 __isl_keep isl_vec *aff)
2095 unsigned total = qp->div->n_col - qp->div->n_row - 2;
2097 isl_seq_neg(qp->div->row[div] + 1,
2098 qp->div->row[div] + 1, qp->div->n_col - 1);
2099 isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
2100 isl_int_add(qp->div->row[div][1],
2101 qp->div->row[div][1], qp->div->row[div][0]);
2102 if (!isl_int_is_zero(aff->el[1 + total + div]))
2103 isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
2104 isl_mat_col_mul(qp->div, 2 + total + div,
2105 qp->div->ctx->negone, 2 + total + div);
2108 /* Assuming "qp" is a monomial, reduce all its divs to have coefficients
2109 * in the interval [0, d-1], with d the denominator and such that the
2110 * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
2112 * After the reduction, some divs may have become redundant or identical,
2113 * so we call substitute_non_divs and sort_divs. If these functions
2114 * eliminate divs or merge two or more divs into one, the coefficients
2115 * of the enclosing divs may have to be reduced again, so we call
2116 * ourselves recursively if the number of divs decreases.
2118 static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
2121 isl_vec *aff = NULL;
2122 struct isl_upoly *s;
2128 aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
2129 aff = isl_vec_clr(aff);
2133 isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
2135 for (i = 0; i < qp->div->n_row; ++i) {
2136 normalize_div(qp, i);
2137 reduce_div(qp, i, aff);
2138 if (needs_invert(qp->div, i)) {
2139 invert_div(qp, i, aff);
2140 reduce_div(qp, i, aff);
2144 s = isl_upoly_from_affine(qp->div->ctx, aff->el,
2145 qp->div->ctx->one, aff->size);
2146 qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
2153 n_div = qp->div->n_row;
2154 qp = substitute_non_divs(qp);
2156 if (qp && qp->div->n_row < n_div)
2157 return reduce_divs(qp);
2161 isl_qpolynomial_free(qp);
2166 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
2167 __isl_take isl_space *dim, const isl_int n, const isl_int d)
2169 struct isl_qpolynomial *qp;
2170 struct isl_upoly_cst *cst;
2175 qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
2179 cst = isl_upoly_as_cst(qp->upoly);
2180 isl_int_set(cst->n, n);
2181 isl_int_set(cst->d, d);
2186 /* Return an isl_qpolynomial that is equal to "val" on domain space "domain".
2188 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2189 __isl_take isl_space *domain, __isl_take isl_val *val)
2191 isl_qpolynomial *qp;
2192 struct isl_upoly_cst *cst;
2194 if (!domain || !val)
2197 qp = isl_qpolynomial_alloc(domain, 0, isl_upoly_zero(domain->ctx));
2201 cst = isl_upoly_as_cst(qp->upoly);
2202 isl_int_set(cst->n, val->n);
2203 isl_int_set(cst->d, val->d);
2208 isl_space_free(domain);
2213 static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
2215 struct isl_upoly_rec *rec;
2221 if (isl_upoly_is_cst(up))
2225 active[up->var] = 1;
2227 rec = isl_upoly_as_rec(up);
2228 for (i = 0; i < rec->n; ++i)
2229 if (up_set_active(rec->p[i], active, d) < 0)
2235 static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
2238 int d = isl_space_dim(qp->dim, isl_dim_all);
2243 for (i = 0; i < d; ++i)
2244 for (j = 0; j < qp->div->n_row; ++j) {
2245 if (isl_int_is_zero(qp->div->row[j][2 + i]))
2251 return up_set_active(qp->upoly, active, d);
2254 int isl_qpolynomial_involves_dims(__isl_keep isl_qpolynomial *qp,
2255 enum isl_dim_type type, unsigned first, unsigned n)
2266 isl_assert(qp->dim->ctx,
2267 first + n <= isl_qpolynomial_dim(qp, type), return -1);
2268 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2269 type == isl_dim_in, return -1);
2271 active = isl_calloc_array(qp->dim->ctx, int,
2272 isl_space_dim(qp->dim, isl_dim_all));
2273 if (set_active(qp, active) < 0)
2276 if (type == isl_dim_in)
2277 first += isl_space_dim(qp->dim, isl_dim_param);
2278 for (i = 0; i < n; ++i)
2279 if (active[first + i]) {
2292 /* Remove divs that do not appear in the quasi-polynomial, nor in any
2293 * of the divs that do appear in the quasi-polynomial.
2295 static __isl_give isl_qpolynomial *remove_redundant_divs(
2296 __isl_take isl_qpolynomial *qp)
2303 int *reordering = NULL;
2310 if (qp->div->n_row == 0)
2313 d = isl_space_dim(qp->dim, isl_dim_all);
2314 len = qp->div->n_col - 2;
2315 ctx = isl_qpolynomial_get_ctx(qp);
2316 active = isl_calloc_array(ctx, int, len);
2320 if (up_set_active(qp->upoly, active, len) < 0)
2323 for (i = qp->div->n_row - 1; i >= 0; --i) {
2324 if (!active[d + i]) {
2328 for (j = 0; j < i; ++j) {
2329 if (isl_int_is_zero(qp->div->row[i][2 + d + j]))
2341 reordering = isl_alloc_array(qp->div->ctx, int, len);
2345 for (i = 0; i < d; ++i)
2349 n_div = qp->div->n_row;
2350 for (i = 0; i < n_div; ++i) {
2351 if (!active[d + i]) {
2352 qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
2353 qp->div = isl_mat_drop_cols(qp->div,
2354 2 + d + i - skip, 1);
2357 reordering[d + i] = d + i - skip;
2360 qp->upoly = reorder(qp->upoly, reordering);
2362 if (!qp->upoly || !qp->div)
2372 isl_qpolynomial_free(qp);
2376 __isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
2377 unsigned first, unsigned n)
2380 struct isl_upoly_rec *rec;
2384 if (n == 0 || up->var < 0 || up->var < first)
2386 if (up->var < first + n) {
2387 up = replace_by_constant_term(up);
2388 return isl_upoly_drop(up, first, n);
2390 up = isl_upoly_cow(up);
2394 rec = isl_upoly_as_rec(up);
2398 for (i = 0; i < rec->n; ++i) {
2399 rec->p[i] = isl_upoly_drop(rec->p[i], first, n);
2410 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2411 __isl_take isl_qpolynomial *qp,
2412 enum isl_dim_type type, unsigned pos, const char *s)
2414 qp = isl_qpolynomial_cow(qp);
2417 qp->dim = isl_space_set_dim_name(qp->dim, type, pos, s);
2422 isl_qpolynomial_free(qp);
2426 __isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
2427 __isl_take isl_qpolynomial *qp,
2428 enum isl_dim_type type, unsigned first, unsigned n)
2432 if (type == isl_dim_out)
2433 isl_die(qp->dim->ctx, isl_error_invalid,
2434 "cannot drop output/set dimension",
2436 if (type == isl_dim_in)
2438 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2441 qp = isl_qpolynomial_cow(qp);
2445 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
2447 isl_assert(qp->dim->ctx, type == isl_dim_param ||
2448 type == isl_dim_set, goto error);
2450 qp->dim = isl_space_drop_dims(qp->dim, type, first, n);
2454 if (type == isl_dim_set)
2455 first += isl_space_dim(qp->dim, isl_dim_param);
2457 qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
2461 qp->upoly = isl_upoly_drop(qp->upoly, first, n);
2467 isl_qpolynomial_free(qp);
2471 /* Project the domain of the quasi-polynomial onto its parameter space.
2472 * The quasi-polynomial may not involve any of the domain dimensions.
2474 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
2475 __isl_take isl_qpolynomial *qp)
2481 n = isl_qpolynomial_dim(qp, isl_dim_in);
2482 involves = isl_qpolynomial_involves_dims(qp, isl_dim_in, 0, n);
2484 return isl_qpolynomial_free(qp);
2486 isl_die(isl_qpolynomial_get_ctx(qp), isl_error_invalid,
2487 "polynomial involves some of the domain dimensions",
2488 return isl_qpolynomial_free(qp));
2489 qp = isl_qpolynomial_drop_dims(qp, isl_dim_in, 0, n);
2490 space = isl_qpolynomial_get_domain_space(qp);
2491 space = isl_space_params(space);
2492 qp = isl_qpolynomial_reset_domain_space(qp, space);
2496 static __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities_lifted(
2497 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2503 struct isl_upoly *up;
2507 if (eq->n_eq == 0) {
2508 isl_basic_set_free(eq);
2512 qp = isl_qpolynomial_cow(qp);
2515 qp->div = isl_mat_cow(qp->div);
2519 total = 1 + isl_space_dim(eq->dim, isl_dim_all);
2521 isl_int_init(denom);
2522 for (i = 0; i < eq->n_eq; ++i) {
2523 j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
2524 if (j < 0 || j == 0 || j >= total)
2527 for (k = 0; k < qp->div->n_row; ++k) {
2528 if (isl_int_is_zero(qp->div->row[k][1 + j]))
2530 isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
2531 &qp->div->row[k][0]);
2532 normalize_div(qp, k);
2535 if (isl_int_is_pos(eq->eq[i][j]))
2536 isl_seq_neg(eq->eq[i], eq->eq[i], total);
2537 isl_int_abs(denom, eq->eq[i][j]);
2538 isl_int_set_si(eq->eq[i][j], 0);
2540 up = isl_upoly_from_affine(qp->dim->ctx,
2541 eq->eq[i], denom, total);
2542 qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
2545 isl_int_clear(denom);
2550 isl_basic_set_free(eq);
2552 qp = substitute_non_divs(qp);
2557 isl_basic_set_free(eq);
2558 isl_qpolynomial_free(qp);
2562 /* Exploit the equalities in "eq" to simplify the quasi-polynomial.
2564 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
2565 __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
2569 if (qp->div->n_row > 0)
2570 eq = isl_basic_set_add_dims(eq, isl_dim_set, qp->div->n_row);
2571 return isl_qpolynomial_substitute_equalities_lifted(qp, eq);
2573 isl_basic_set_free(eq);
2574 isl_qpolynomial_free(qp);
2578 static __isl_give isl_basic_set *add_div_constraints(
2579 __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
2587 bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
2590 total = isl_basic_set_total_dim(bset);
2591 for (i = 0; i < div->n_row; ++i)
2592 if (isl_basic_set_add_div_constraints_var(bset,
2593 total - div->n_row + i, div->row[i]) < 0)
2600 isl_basic_set_free(bset);
2604 /* Look for equalities among the variables shared by context and qp
2605 * and the integer divisions of qp, if any.
2606 * The equalities are then used to eliminate variables and/or integer
2607 * divisions from qp.
2609 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2610 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2616 if (qp->div->n_row > 0) {
2617 isl_basic_set *bset;
2618 context = isl_set_add_dims(context, isl_dim_set,
2620 bset = isl_basic_set_universe(isl_set_get_space(context));
2621 bset = add_div_constraints(bset, isl_mat_copy(qp->div));
2622 context = isl_set_intersect(context,
2623 isl_set_from_basic_set(bset));
2626 aff = isl_set_affine_hull(context);
2627 return isl_qpolynomial_substitute_equalities_lifted(qp, aff);
2629 isl_qpolynomial_free(qp);
2630 isl_set_free(context);
2634 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
2635 __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
2637 isl_space *space = isl_qpolynomial_get_domain_space(qp);
2638 isl_set *dom_context = isl_set_universe(space);
2639 dom_context = isl_set_intersect_params(dom_context, context);
2640 return isl_qpolynomial_gist(qp, dom_context);
2643 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
2644 __isl_take isl_qpolynomial *qp)
2650 if (isl_qpolynomial_is_zero(qp)) {
2651 isl_space *dim = isl_qpolynomial_get_space(qp);
2652 isl_qpolynomial_free(qp);
2653 return isl_pw_qpolynomial_zero(dim);
2656 dom = isl_set_universe(isl_qpolynomial_get_domain_space(qp));
2657 return isl_pw_qpolynomial_alloc(dom, qp);
2661 #define PW isl_pw_qpolynomial
2663 #define EL isl_qpolynomial
2665 #define EL_IS_ZERO is_zero
2669 #define IS_ZERO is_zero
2672 #undef DEFAULT_IS_ZERO
2673 #define DEFAULT_IS_ZERO 1
2677 #include <isl_pw_templ.c>
2680 #define UNION isl_union_pw_qpolynomial
2682 #define PART isl_pw_qpolynomial
2684 #define PARTS pw_qpolynomial
2685 #define ALIGN_DOMAIN
2687 #include <isl_union_templ.c>
2689 int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
2697 if (!isl_set_plain_is_universe(pwqp->p[0].set))
2700 return isl_qpolynomial_is_one(pwqp->p[0].qp);
2703 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2704 __isl_take isl_pw_qpolynomial *pwqp1,
2705 __isl_take isl_pw_qpolynomial *pwqp2)
2707 return isl_pw_qpolynomial_union_add_(pwqp1, pwqp2);
2710 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2711 __isl_take isl_pw_qpolynomial *pwqp1,
2712 __isl_take isl_pw_qpolynomial *pwqp2)
2715 struct isl_pw_qpolynomial *res;
2717 if (!pwqp1 || !pwqp2)
2720 isl_assert(pwqp1->dim->ctx, isl_space_is_equal(pwqp1->dim, pwqp2->dim),
2723 if (isl_pw_qpolynomial_is_zero(pwqp1)) {
2724 isl_pw_qpolynomial_free(pwqp2);
2728 if (isl_pw_qpolynomial_is_zero(pwqp2)) {
2729 isl_pw_qpolynomial_free(pwqp1);
2733 if (isl_pw_qpolynomial_is_one(pwqp1)) {
2734 isl_pw_qpolynomial_free(pwqp1);
2738 if (isl_pw_qpolynomial_is_one(pwqp2)) {
2739 isl_pw_qpolynomial_free(pwqp2);
2743 n = pwqp1->n * pwqp2->n;
2744 res = isl_pw_qpolynomial_alloc_size(isl_space_copy(pwqp1->dim), n);
2746 for (i = 0; i < pwqp1->n; ++i) {
2747 for (j = 0; j < pwqp2->n; ++j) {
2748 struct isl_set *common;
2749 struct isl_qpolynomial *prod;
2750 common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
2751 isl_set_copy(pwqp2->p[j].set));
2752 if (isl_set_plain_is_empty(common)) {
2753 isl_set_free(common);
2757 prod = isl_qpolynomial_mul(
2758 isl_qpolynomial_copy(pwqp1->p[i].qp),
2759 isl_qpolynomial_copy(pwqp2->p[j].qp));
2761 res = isl_pw_qpolynomial_add_piece(res, common, prod);
2765 isl_pw_qpolynomial_free(pwqp1);
2766 isl_pw_qpolynomial_free(pwqp2);
2770 isl_pw_qpolynomial_free(pwqp1);
2771 isl_pw_qpolynomial_free(pwqp2);
2775 __isl_give struct isl_upoly *isl_upoly_eval(
2776 __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
2779 struct isl_upoly_rec *rec;
2780 struct isl_upoly *res;
2781 struct isl_upoly *base;
2783 if (isl_upoly_is_cst(up)) {
2788 rec = isl_upoly_as_rec(up);
2792 isl_assert(up->ctx, rec->n >= 1, goto error);
2794 base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
2796 res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
2799 for (i = rec->n - 2; i >= 0; --i) {
2800 res = isl_upoly_mul(res, isl_upoly_copy(base));
2801 res = isl_upoly_sum(res,
2802 isl_upoly_eval(isl_upoly_copy(rec->p[i]),
2803 isl_vec_copy(vec)));
2806 isl_upoly_free(base);
2816 __isl_give isl_qpolynomial *isl_qpolynomial_eval(
2817 __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
2820 struct isl_upoly *up;
2825 isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, qp->dim), goto error);
2827 if (qp->div->n_row == 0)
2828 ext = isl_vec_copy(pnt->vec);
2831 unsigned dim = isl_space_dim(qp->dim, isl_dim_all);
2832 ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
2836 isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
2837 for (i = 0; i < qp->div->n_row; ++i) {
2838 isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
2839 1 + dim + i, &ext->el[1+dim+i]);
2840 isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
2841 qp->div->row[i][0]);
2845 up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
2849 dim = isl_space_copy(qp->dim);
2850 isl_qpolynomial_free(qp);
2851 isl_point_free(pnt);
2853 return isl_qpolynomial_alloc(dim, 0, up);
2855 isl_qpolynomial_free(qp);
2856 isl_point_free(pnt);
2860 int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
2861 __isl_keep struct isl_upoly_cst *cst2)
2866 isl_int_mul(t, cst1->n, cst2->d);
2867 isl_int_submul(t, cst2->n, cst1->d);
2868 cmp = isl_int_sgn(t);
2873 int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
2874 __isl_keep isl_qpolynomial *qp2)
2876 struct isl_upoly_cst *cst1, *cst2;
2880 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
2881 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
2882 if (isl_qpolynomial_is_nan(qp1))
2884 if (isl_qpolynomial_is_nan(qp2))
2886 cst1 = isl_upoly_as_cst(qp1->upoly);
2887 cst2 = isl_upoly_as_cst(qp2->upoly);
2889 return isl_upoly_cmp(cst1, cst2) <= 0;
2892 __isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
2893 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2895 struct isl_upoly_cst *cst1, *cst2;
2900 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2901 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2902 cst1 = isl_upoly_as_cst(qp1->upoly);
2903 cst2 = isl_upoly_as_cst(qp2->upoly);
2904 cmp = isl_upoly_cmp(cst1, cst2);
2907 isl_qpolynomial_free(qp2);
2909 isl_qpolynomial_free(qp1);
2914 isl_qpolynomial_free(qp1);
2915 isl_qpolynomial_free(qp2);
2919 __isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
2920 __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
2922 struct isl_upoly_cst *cst1, *cst2;
2927 isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
2928 isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
2929 cst1 = isl_upoly_as_cst(qp1->upoly);
2930 cst2 = isl_upoly_as_cst(qp2->upoly);
2931 cmp = isl_upoly_cmp(cst1, cst2);
2934 isl_qpolynomial_free(qp2);
2936 isl_qpolynomial_free(qp1);
2941 isl_qpolynomial_free(qp1);
2942 isl_qpolynomial_free(qp2);
2946 __isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
2947 __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
2948 unsigned first, unsigned n)
2956 if (type == isl_dim_out)
2957 isl_die(qp->div->ctx, isl_error_invalid,
2958 "cannot insert output/set dimensions",
2960 if (type == isl_dim_in)
2962 if (n == 0 && !isl_space_is_named_or_nested(qp->dim, type))
2965 qp = isl_qpolynomial_cow(qp);
2969 isl_assert(qp->div->ctx, first <= isl_space_dim(qp->dim, type),
2972 g_pos = pos(qp->dim, type) + first;
2974 qp->div = isl_mat_insert_zero_cols(qp->div, 2 + g_pos, n);
2978 total = qp->div->n_col - 2;
2979 if (total > g_pos) {
2981 exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
2984 for (i = 0; i < total - g_pos; ++i)
2986 qp->upoly = expand(qp->upoly, exp, g_pos);
2992 qp->dim = isl_space_insert_dims(qp->dim, type, first, n);
2998 isl_qpolynomial_free(qp);
3002 __isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
3003 __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
3007 pos = isl_qpolynomial_dim(qp, type);
3009 return isl_qpolynomial_insert_dims(qp, type, pos, n);
3012 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
3013 __isl_take isl_pw_qpolynomial *pwqp,
3014 enum isl_dim_type type, unsigned n)
3018 pos = isl_pw_qpolynomial_dim(pwqp, type);
3020 return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
3023 static int *reordering_move(isl_ctx *ctx,
3024 unsigned len, unsigned dst, unsigned src, unsigned n)
3029 reordering = isl_alloc_array(ctx, int, len);
3034 for (i = 0; i < dst; ++i)
3036 for (i = 0; i < n; ++i)
3037 reordering[src + i] = dst + i;
3038 for (i = 0; i < src - dst; ++i)
3039 reordering[dst + i] = dst + n + i;
3040 for (i = 0; i < len - src - n; ++i)
3041 reordering[src + n + i] = src + n + i;
3043 for (i = 0; i < src; ++i)
3045 for (i = 0; i < n; ++i)
3046 reordering[src + i] = dst + i;
3047 for (i = 0; i < dst - src; ++i)
3048 reordering[src + n + i] = src + i;
3049 for (i = 0; i < len - dst - n; ++i)
3050 reordering[dst + n + i] = dst + n + i;
3056 __isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
3057 __isl_take isl_qpolynomial *qp,
3058 enum isl_dim_type dst_type, unsigned dst_pos,
3059 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
3065 qp = isl_qpolynomial_cow(qp);
3069 if (dst_type == isl_dim_out || src_type == isl_dim_out)
3070 isl_die(qp->dim->ctx, isl_error_invalid,
3071 "cannot move output/set dimension",
3073 if (dst_type == isl_dim_in)
3074 dst_type = isl_dim_set;
3075 if (src_type == isl_dim_in)
3076 src_type = isl_dim_set;
3078 isl_assert(qp->dim->ctx, src_pos + n <= isl_space_dim(qp->dim, src_type),
3081 g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
3082 g_src_pos = pos(qp->dim, src_type) + src_pos;
3083 if (dst_type > src_type)
3086 qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
3093 reordering = reordering_move(qp->dim->ctx,
3094 qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
3098 qp->upoly = reorder(qp->upoly, reordering);
3103 qp->dim = isl_space_move_dims(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
3109 isl_qpolynomial_free(qp);
3113 __isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_space *dim,
3114 isl_int *f, isl_int denom)
3116 struct isl_upoly *up;
3118 dim = isl_space_domain(dim);
3122 up = isl_upoly_from_affine(dim->ctx, f, denom,
3123 1 + isl_space_dim(dim, isl_dim_all));
3125 return isl_qpolynomial_alloc(dim, 0, up);
3128 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(__isl_take isl_aff *aff)
3131 struct isl_upoly *up;
3132 isl_qpolynomial *qp;
3137 ctx = isl_aff_get_ctx(aff);
3138 up = isl_upoly_from_affine(ctx, aff->v->el + 1, aff->v->el[0],
3141 qp = isl_qpolynomial_alloc(isl_aff_get_domain_space(aff),
3142 aff->ls->div->n_row, up);
3146 isl_mat_free(qp->div);
3147 qp->div = isl_mat_copy(aff->ls->div);
3148 qp->div = isl_mat_cow(qp->div);
3153 qp = reduce_divs(qp);
3154 qp = remove_redundant_divs(qp);
3161 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3162 __isl_take isl_pw_aff *pwaff)
3165 isl_pw_qpolynomial *pwqp;
3170 pwqp = isl_pw_qpolynomial_alloc_size(isl_pw_aff_get_space(pwaff),
3173 for (i = 0; i < pwaff->n; ++i) {
3175 isl_qpolynomial *qp;
3177 dom = isl_set_copy(pwaff->p[i].set);
3178 qp = isl_qpolynomial_from_aff(isl_aff_copy(pwaff->p[i].aff));
3179 pwqp = isl_pw_qpolynomial_add_piece(pwqp, dom, qp);
3182 isl_pw_aff_free(pwaff);
3186 __isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
3187 __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
3191 aff = isl_constraint_get_bound(c, type, pos);
3192 isl_constraint_free(c);
3193 return isl_qpolynomial_from_aff(aff);
3196 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
3197 * in "qp" by subs[i].
3199 __isl_give isl_qpolynomial *isl_qpolynomial_substitute(
3200 __isl_take isl_qpolynomial *qp,
3201 enum isl_dim_type type, unsigned first, unsigned n,
3202 __isl_keep isl_qpolynomial **subs)
3205 struct isl_upoly **ups;
3210 qp = isl_qpolynomial_cow(qp);
3214 if (type == isl_dim_out)
3215 isl_die(qp->dim->ctx, isl_error_invalid,
3216 "cannot substitute output/set dimension",
3218 if (type == isl_dim_in)
3221 for (i = 0; i < n; ++i)
3225 isl_assert(qp->dim->ctx, first + n <= isl_space_dim(qp->dim, type),
3228 for (i = 0; i < n; ++i)
3229 isl_assert(qp->dim->ctx, isl_space_is_equal(qp->dim, subs[i]->dim),
3232 isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
3233 for (i = 0; i < n; ++i)
3234 isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
3236 first += pos(qp->dim, type);
3238 ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
3241 for (i = 0; i < n; ++i)
3242 ups[i] = subs[i]->upoly;
3244 qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
3253 isl_qpolynomial_free(qp);
3257 /* Extend "bset" with extra set dimensions for each integer division
3258 * in "qp" and then call "fn" with the extended bset and the polynomial
3259 * that results from replacing each of the integer divisions by the
3260 * corresponding extra set dimension.
3262 int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
3263 __isl_keep isl_basic_set *bset,
3264 int (*fn)(__isl_take isl_basic_set *bset,
3265 __isl_take isl_qpolynomial *poly, void *user), void *user)
3269 isl_qpolynomial *poly;
3273 if (qp->div->n_row == 0)
3274 return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
3277 div = isl_mat_copy(qp->div);
3278 dim = isl_space_copy(qp->dim);
3279 dim = isl_space_add_dims(dim, isl_dim_set, qp->div->n_row);
3280 poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
3281 bset = isl_basic_set_copy(bset);
3282 bset = isl_basic_set_add_dims(bset, isl_dim_set, qp->div->n_row);
3283 bset = add_div_constraints(bset, div);
3285 return fn(bset, poly, user);
3290 /* Return total degree in variables first (inclusive) up to last (exclusive).
3292 int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
3296 struct isl_upoly_rec *rec;
3300 if (isl_upoly_is_zero(up))
3302 if (isl_upoly_is_cst(up) || up->var < first)
3305 rec = isl_upoly_as_rec(up);
3309 for (i = 0; i < rec->n; ++i) {
3312 if (isl_upoly_is_zero(rec->p[i]))
3314 d = isl_upoly_degree(rec->p[i], first, last);
3324 /* Return total degree in set variables.
3326 int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
3334 ovar = isl_space_offset(poly->dim, isl_dim_set);
3335 nvar = isl_space_dim(poly->dim, isl_dim_set);
3336 return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
3339 __isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
3340 unsigned pos, int deg)
3343 struct isl_upoly_rec *rec;
3348 if (isl_upoly_is_cst(up) || up->var < pos) {
3350 return isl_upoly_copy(up);
3352 return isl_upoly_zero(up->ctx);
3355 rec = isl_upoly_as_rec(up);
3359 if (up->var == pos) {
3361 return isl_upoly_copy(rec->p[deg]);
3363 return isl_upoly_zero(up->ctx);
3366 up = isl_upoly_copy(up);
3367 up = isl_upoly_cow(up);
3368 rec = isl_upoly_as_rec(up);
3372 for (i = 0; i < rec->n; ++i) {
3373 struct isl_upoly *t;
3374 t = isl_upoly_coeff(rec->p[i], pos, deg);
3377 isl_upoly_free(rec->p[i]);
3387 /* Return coefficient of power "deg" of variable "t_pos" of type "type".
3389 __isl_give isl_qpolynomial *isl_qpolynomial_coeff(
3390 __isl_keep isl_qpolynomial *qp,
3391 enum isl_dim_type type, unsigned t_pos, int deg)
3394 struct isl_upoly *up;
3400 if (type == isl_dim_out)
3401 isl_die(qp->div->ctx, isl_error_invalid,
3402 "output/set dimension does not have a coefficient",
3404 if (type == isl_dim_in)
3407 isl_assert(qp->div->ctx, t_pos < isl_space_dim(qp->dim, type),
3410 g_pos = pos(qp->dim, type) + t_pos;
3411 up = isl_upoly_coeff(qp->upoly, g_pos, deg);
3413 c = isl_qpolynomial_alloc(isl_space_copy(qp->dim), qp->div->n_row, up);
3416 isl_mat_free(c->div);
3417 c->div = isl_mat_copy(qp->div);
3422 isl_qpolynomial_free(c);
3426 /* Homogenize the polynomial in the variables first (inclusive) up to
3427 * last (exclusive) by inserting powers of variable first.
3428 * Variable first is assumed not to appear in the input.
3430 __isl_give struct isl_upoly *isl_upoly_homogenize(
3431 __isl_take struct isl_upoly *up, int deg, int target,
3432 int first, int last)
3435 struct isl_upoly_rec *rec;
3439 if (isl_upoly_is_zero(up))
3443 if (isl_upoly_is_cst(up) || up->var < first) {
3444 struct isl_upoly *hom;
3446 hom = isl_upoly_var_pow(up->ctx, first, target - deg);
3449 rec = isl_upoly_as_rec(hom);
3450 rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
3455 up = isl_upoly_cow(up);
3456 rec = isl_upoly_as_rec(up);
3460 for (i = 0; i < rec->n; ++i) {
3461 if (isl_upoly_is_zero(rec->p[i]))
3463 rec->p[i] = isl_upoly_homogenize(rec->p[i],
3464 up->var < last ? deg + i : i, target,
3476 /* Homogenize the polynomial in the set variables by introducing
3477 * powers of an extra set variable at position 0.
3479 __isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
3480 __isl_take isl_qpolynomial *poly)
3484 int deg = isl_qpolynomial_degree(poly);
3489 poly = isl_qpolynomial_insert_dims(poly, isl_dim_in, 0, 1);
3490 poly = isl_qpolynomial_cow(poly);
3494 ovar = isl_space_offset(poly->dim, isl_dim_set);
3495 nvar = isl_space_dim(poly->dim, isl_dim_set);
3496 poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
3503 isl_qpolynomial_free(poly);
3507 __isl_give isl_term *isl_term_alloc(__isl_take isl_space *dim,
3508 __isl_take isl_mat *div)
3516 n = isl_space_dim(dim, isl_dim_all) + div->n_row;
3518 term = isl_calloc(dim->ctx, struct isl_term,
3519 sizeof(struct isl_term) + (n - 1) * sizeof(int));
3526 isl_int_init(term->n);
3527 isl_int_init(term->d);
3531 isl_space_free(dim);
3536 __isl_give isl_term *isl_term_copy(__isl_keep isl_term *term)
3545 __isl_give isl_term *isl_term_dup(__isl_keep isl_term *term)
3554 total = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3556 dup = isl_term_alloc(isl_space_copy(term->dim), isl_mat_copy(term->div));
3560 isl_int_set(dup->n, term->n);
3561 isl_int_set(dup->d, term->d);
3563 for (i = 0; i < total; ++i)
3564 dup->pow[i] = term->pow[i];
3569 __isl_give isl_term *isl_term_cow(__isl_take isl_term *term)
3577 return isl_term_dup(term);
3580 void isl_term_free(__isl_take isl_term *term)
3585 if (--term->ref > 0)
3588 isl_space_free(term->dim);
3589 isl_mat_free(term->div);
3590 isl_int_clear(term->n);
3591 isl_int_clear(term->d);
3595 unsigned isl_term_dim(__isl_keep isl_term *term, enum isl_dim_type type)
3603 case isl_dim_out: return isl_space_dim(term->dim, type);
3604 case isl_dim_div: return term->div->n_row;
3605 case isl_dim_all: return isl_space_dim(term->dim, isl_dim_all) +
3611 isl_ctx *isl_term_get_ctx(__isl_keep isl_term *term)
3613 return term ? term->dim->ctx : NULL;
3616 void isl_term_get_num(__isl_keep isl_term *term, isl_int *n)
3620 isl_int_set(*n, term->n);
3623 void isl_term_get_den(__isl_keep isl_term *term, isl_int *d)
3627 isl_int_set(*d, term->d);
3630 /* Return the coefficient of the term "term".
3632 __isl_give isl_val *isl_term_get_coefficient_val(__isl_keep isl_term *term)
3637 return isl_val_rat_from_isl_int(isl_term_get_ctx(term),
3641 int isl_term_get_exp(__isl_keep isl_term *term,
3642 enum isl_dim_type type, unsigned pos)
3647 isl_assert(term->dim->ctx, pos < isl_term_dim(term, type), return -1);
3649 if (type >= isl_dim_set)
3650 pos += isl_space_dim(term->dim, isl_dim_param);
3651 if (type >= isl_dim_div)
3652 pos += isl_space_dim(term->dim, isl_dim_set);
3654 return term->pow[pos];
3657 __isl_give isl_aff *isl_term_get_div(__isl_keep isl_term *term, unsigned pos)
3659 isl_local_space *ls;
3665 isl_assert(term->dim->ctx, pos < isl_term_dim(term, isl_dim_div),
3668 ls = isl_local_space_alloc_div(isl_space_copy(term->dim),
3669 isl_mat_copy(term->div));
3670 aff = isl_aff_alloc(ls);
3674 isl_seq_cpy(aff->v->el, term->div->row[pos], aff->v->size);
3676 aff = isl_aff_normalize(aff);
3681 __isl_give isl_term *isl_upoly_foreach_term(__isl_keep struct isl_upoly *up,
3682 int (*fn)(__isl_take isl_term *term, void *user),
3683 __isl_take isl_term *term, void *user)
3686 struct isl_upoly_rec *rec;
3691 if (isl_upoly_is_zero(up))
3694 isl_assert(up->ctx, !isl_upoly_is_nan(up), goto error);
3695 isl_assert(up->ctx, !isl_upoly_is_infty(up), goto error);
3696 isl_assert(up->ctx, !isl_upoly_is_neginfty(up), goto error);
3698 if (isl_upoly_is_cst(up)) {
3699 struct isl_upoly_cst *cst;
3700 cst = isl_upoly_as_cst(up);
3703 term = isl_term_cow(term);
3706 isl_int_set(term->n, cst->n);
3707 isl_int_set(term->d, cst->d);
3708 if (fn(isl_term_copy(term), user) < 0)
3713 rec = isl_upoly_as_rec(up);
3717 for (i = 0; i < rec->n; ++i) {
3718 term = isl_term_cow(term);
3721 term->pow[up->var] = i;
3722 term = isl_upoly_foreach_term(rec->p[i], fn, term, user);
3726 term->pow[up->var] = 0;
3730 isl_term_free(term);
3734 int isl_qpolynomial_foreach_term(__isl_keep isl_qpolynomial *qp,
3735 int (*fn)(__isl_take isl_term *term, void *user), void *user)
3742 term = isl_term_alloc(isl_space_copy(qp->dim), isl_mat_copy(qp->div));
3746 term = isl_upoly_foreach_term(qp->upoly, fn, term, user);
3748 isl_term_free(term);
3750 return term ? 0 : -1;
3753 __isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
3755 struct isl_upoly *up;
3756 isl_qpolynomial *qp;
3762 n = isl_space_dim(term->dim, isl_dim_all) + term->div->n_row;
3764 up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
3765 for (i = 0; i < n; ++i) {
3768 up = isl_upoly_mul(up,
3769 isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
3772 qp = isl_qpolynomial_alloc(isl_space_copy(term->dim), term->div->n_row, up);
3775 isl_mat_free(qp->div);
3776 qp->div = isl_mat_copy(term->div);
3780 isl_term_free(term);
3783 isl_qpolynomial_free(qp);
3784 isl_term_free(term);
3788 __isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
3789 __isl_take isl_space *dim)
3798 if (isl_space_is_equal(qp->dim, dim)) {
3799 isl_space_free(dim);
3803 qp = isl_qpolynomial_cow(qp);
3807 extra = isl_space_dim(dim, isl_dim_set) -
3808 isl_space_dim(qp->dim, isl_dim_set);
3809 total = isl_space_dim(qp->dim, isl_dim_all);
3810 if (qp->div->n_row) {
3813 exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
3816 for (i = 0; i < qp->div->n_row; ++i)
3818 qp->upoly = expand(qp->upoly, exp, total);
3823 qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
3826 for (i = 0; i < qp->div->n_row; ++i)
3827 isl_seq_clr(qp->div->row[i] + 2 + total, extra);
3829 isl_space_free(qp->dim);
3834 isl_space_free(dim);
3835 isl_qpolynomial_free(qp);
3839 /* For each parameter or variable that does not appear in qp,
3840 * first eliminate the variable from all constraints and then set it to zero.
3842 static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
3843 __isl_keep isl_qpolynomial *qp)
3854 d = isl_space_dim(set->dim, isl_dim_all);
3855 active = isl_calloc_array(set->ctx, int, d);
3856 if (set_active(qp, active) < 0)
3859 for (i = 0; i < d; ++i)
3868 nparam = isl_space_dim(set->dim, isl_dim_param);
3869 nvar = isl_space_dim(set->dim, isl_dim_set);
3870 for (i = 0; i < nparam; ++i) {
3873 set = isl_set_eliminate(set, isl_dim_param, i, 1);
3874 set = isl_set_fix_si(set, isl_dim_param, i, 0);
3876 for (i = 0; i < nvar; ++i) {
3877 if (active[nparam + i])
3879 set = isl_set_eliminate(set, isl_dim_set, i, 1);
3880 set = isl_set_fix_si(set, isl_dim_set, i, 0);
3892 struct isl_opt_data {
3893 isl_qpolynomial *qp;
3895 isl_qpolynomial *opt;
3899 static int opt_fn(__isl_take isl_point *pnt, void *user)
3901 struct isl_opt_data *data = (struct isl_opt_data *)user;
3902 isl_qpolynomial *val;
3904 val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
3908 } else if (data->max) {
3909 data->opt = isl_qpolynomial_max_cst(data->opt, val);
3911 data->opt = isl_qpolynomial_min_cst(data->opt, val);
3917 __isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
3918 __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
3920 struct isl_opt_data data = { NULL, 1, NULL, max };
3925 if (isl_upoly_is_cst(qp->upoly)) {
3930 set = fix_inactive(set, qp);
3933 if (isl_set_foreach_point(set, opt_fn, &data) < 0)
3937 isl_space *space = isl_qpolynomial_get_domain_space(qp);
3938 data.opt = isl_qpolynomial_zero_on_domain(space);
3942 isl_qpolynomial_free(qp);
3946 isl_qpolynomial_free(qp);
3947 isl_qpolynomial_free(data.opt);
3951 __isl_give isl_qpolynomial *isl_qpolynomial_morph_domain(
3952 __isl_take isl_qpolynomial *qp, __isl_take isl_morph *morph)
3957 struct isl_upoly **subs;
3958 isl_mat *mat, *diag;
3960 qp = isl_qpolynomial_cow(qp);
3965 isl_assert(ctx, isl_space_is_equal(qp->dim, morph->dom->dim), goto error);
3967 n_sub = morph->inv->n_row - 1;
3968 if (morph->inv->n_row != morph->inv->n_col)
3969 n_sub += qp->div->n_row;
3970 subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
3974 for (i = 0; 1 + i < morph->inv->n_row; ++i)
3975 subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
3976 morph->inv->row[0][0], morph->inv->n_col);
3977 if (morph->inv->n_row != morph->inv->n_col)
3978 for (i = 0; i < qp->div->n_row; ++i)
3979 subs[morph->inv->n_row - 1 + i] =
3980 isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
3982 qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
3984 for (i = 0; i < n_sub; ++i)
3985 isl_upoly_free(subs[i]);
3988 diag = isl_mat_diag(ctx, 1, morph->inv->row[0][0]);
3989 mat = isl_mat_diagonal(diag, isl_mat_copy(morph->inv));
3990 diag = isl_mat_diag(ctx, qp->div->n_row, morph->inv->row[0][0]);
3991 mat = isl_mat_diagonal(mat, diag);
3992 qp->div = isl_mat_product(qp->div, mat);
3993 isl_space_free(qp->dim);
3994 qp->dim = isl_space_copy(morph->ran->dim);
3996 if (!qp->upoly || !qp->div || !qp->dim)
3999 isl_morph_free(morph);
4003 isl_qpolynomial_free(qp);
4004 isl_morph_free(morph);
4008 static int neg_entry(void **entry, void *user)
4010 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4012 *pwqp = isl_pw_qpolynomial_neg(*pwqp);
4014 return *pwqp ? 0 : -1;
4017 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
4018 __isl_take isl_union_pw_qpolynomial *upwqp)
4020 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4024 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4025 &neg_entry, NULL) < 0)
4030 isl_union_pw_qpolynomial_free(upwqp);
4034 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4035 __isl_take isl_union_pw_qpolynomial *upwqp1,
4036 __isl_take isl_union_pw_qpolynomial *upwqp2)
4038 return match_bin_op(upwqp1, upwqp2, &isl_pw_qpolynomial_mul);
4041 /* Reorder the columns of the given div definitions according to the
4044 static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
4045 __isl_take isl_reordering *r)
4054 extra = isl_space_dim(r->dim, isl_dim_all) + div->n_row - r->len;
4055 mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
4059 for (i = 0; i < div->n_row; ++i) {
4060 isl_seq_cpy(mat->row[i], div->row[i], 2);
4061 isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
4062 for (j = 0; j < r->len; ++j)
4063 isl_int_set(mat->row[i][2 + r->pos[j]],
4064 div->row[i][2 + j]);
4067 isl_reordering_free(r);
4071 isl_reordering_free(r);
4076 /* Reorder the dimension of "qp" according to the given reordering.
4078 __isl_give isl_qpolynomial *isl_qpolynomial_realign_domain(
4079 __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
4081 qp = isl_qpolynomial_cow(qp);
4085 r = isl_reordering_extend(r, qp->div->n_row);
4089 qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
4093 qp->upoly = reorder(qp->upoly, r->pos);
4097 qp = isl_qpolynomial_reset_domain_space(qp, isl_space_copy(r->dim));
4099 isl_reordering_free(r);
4102 isl_qpolynomial_free(qp);
4103 isl_reordering_free(r);
4107 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4108 __isl_take isl_qpolynomial *qp, __isl_take isl_space *model)
4113 if (!isl_space_match(qp->dim, isl_dim_param, model, isl_dim_param)) {
4114 isl_reordering *exp;
4116 model = isl_space_drop_dims(model, isl_dim_in,
4117 0, isl_space_dim(model, isl_dim_in));
4118 model = isl_space_drop_dims(model, isl_dim_out,
4119 0, isl_space_dim(model, isl_dim_out));
4120 exp = isl_parameter_alignment_reordering(qp->dim, model);
4121 exp = isl_reordering_extend_space(exp,
4122 isl_qpolynomial_get_domain_space(qp));
4123 qp = isl_qpolynomial_realign_domain(qp, exp);
4126 isl_space_free(model);
4129 isl_space_free(model);
4130 isl_qpolynomial_free(qp);
4134 struct isl_split_periods_data {
4136 isl_pw_qpolynomial *res;
4139 /* Create a slice where the integer division "div" has the fixed value "v".
4140 * In particular, if "div" refers to floor(f/m), then create a slice
4142 * m v <= f <= m v + (m - 1)
4147 * -f + m v + (m - 1) >= 0
4149 static __isl_give isl_set *set_div_slice(__isl_take isl_space *dim,
4150 __isl_keep isl_qpolynomial *qp, int div, isl_int v)
4153 isl_basic_set *bset = NULL;
4159 total = isl_space_dim(dim, isl_dim_all);
4160 bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0, 0, 2);
4162 k = isl_basic_set_alloc_inequality(bset);
4165 isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4166 isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
4168 k = isl_basic_set_alloc_inequality(bset);
4171 isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
4172 isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
4173 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
4174 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4176 isl_space_free(dim);
4177 return isl_set_from_basic_set(bset);
4179 isl_basic_set_free(bset);
4180 isl_space_free(dim);
4184 static int split_periods(__isl_take isl_set *set,
4185 __isl_take isl_qpolynomial *qp, void *user);
4187 /* Create a slice of the domain "set" such that integer division "div"
4188 * has the fixed value "v" and add the results to data->res,
4189 * replacing the integer division by "v" in "qp".
4191 static int set_div(__isl_take isl_set *set,
4192 __isl_take isl_qpolynomial *qp, int div, isl_int v,
4193 struct isl_split_periods_data *data)
4198 struct isl_upoly *cst;
4200 slice = set_div_slice(isl_set_get_space(set), qp, div, v);
4201 set = isl_set_intersect(set, slice);
4206 total = isl_space_dim(qp->dim, isl_dim_all);
4208 for (i = div + 1; i < qp->div->n_row; ++i) {
4209 if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
4211 isl_int_addmul(qp->div->row[i][1],
4212 qp->div->row[i][2 + total + div], v);
4213 isl_int_set_si(qp->div->row[i][2 + total + div], 0);
4216 cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
4217 qp = substitute_div(qp, div, cst);
4219 return split_periods(set, qp, data);
4222 isl_qpolynomial_free(qp);
4226 /* Split the domain "set" such that integer division "div"
4227 * has a fixed value (ranging from "min" to "max") on each slice
4228 * and add the results to data->res.
4230 static int split_div(__isl_take isl_set *set,
4231 __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
4232 struct isl_split_periods_data *data)
4234 for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
4235 isl_set *set_i = isl_set_copy(set);
4236 isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
4238 if (set_div(set_i, qp_i, div, min, data) < 0)
4242 isl_qpolynomial_free(qp);
4246 isl_qpolynomial_free(qp);
4250 /* If "qp" refers to any integer division
4251 * that can only attain "max_periods" distinct values on "set"
4252 * then split the domain along those distinct values.
4253 * Add the results (or the original if no splitting occurs)
4256 static int split_periods(__isl_take isl_set *set,
4257 __isl_take isl_qpolynomial *qp, void *user)
4260 isl_pw_qpolynomial *pwqp;
4261 struct isl_split_periods_data *data;
4266 data = (struct isl_split_periods_data *)user;
4271 if (qp->div->n_row == 0) {
4272 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4273 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4279 total = isl_space_dim(qp->dim, isl_dim_all);
4280 for (i = 0; i < qp->div->n_row; ++i) {
4281 enum isl_lp_result lp_res;
4283 if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
4284 qp->div->n_row) != -1)
4287 lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
4288 set->ctx->one, &min, NULL, NULL);
4289 if (lp_res == isl_lp_error)
4291 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4293 isl_int_fdiv_q(min, min, qp->div->row[i][0]);
4295 lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
4296 set->ctx->one, &max, NULL, NULL);
4297 if (lp_res == isl_lp_error)
4299 if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
4301 isl_int_fdiv_q(max, max, qp->div->row[i][0]);
4303 isl_int_sub(max, max, min);
4304 if (isl_int_cmp_si(max, data->max_periods) < 0) {
4305 isl_int_add(max, max, min);
4310 if (i < qp->div->n_row) {
4311 r = split_div(set, qp, i, min, max, data);
4313 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4314 data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
4326 isl_qpolynomial_free(qp);
4330 /* If any quasi-polynomial in pwqp refers to any integer division
4331 * that can only attain "max_periods" distinct values on its domain
4332 * then split the domain along those distinct values.
4334 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
4335 __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
4337 struct isl_split_periods_data data;
4339 data.max_periods = max_periods;
4340 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4342 if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
4345 isl_pw_qpolynomial_free(pwqp);
4349 isl_pw_qpolynomial_free(data.res);
4350 isl_pw_qpolynomial_free(pwqp);
4354 /* Construct a piecewise quasipolynomial that is constant on the given
4355 * domain. In particular, it is
4358 * infinity if cst == -1
4360 static __isl_give isl_pw_qpolynomial *constant_on_domain(
4361 __isl_take isl_basic_set *bset, int cst)
4364 isl_qpolynomial *qp;
4369 bset = isl_basic_set_params(bset);
4370 dim = isl_basic_set_get_space(bset);
4372 qp = isl_qpolynomial_infty_on_domain(dim);
4374 qp = isl_qpolynomial_zero_on_domain(dim);
4376 qp = isl_qpolynomial_one_on_domain(dim);
4377 return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
4380 /* Factor bset, call fn on each of the factors and return the product.
4382 * If no factors can be found, simply call fn on the input.
4383 * Otherwise, construct the factors based on the factorizer,
4384 * call fn on each factor and compute the product.
4386 static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
4387 __isl_take isl_basic_set *bset,
4388 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4394 isl_qpolynomial *qp;
4395 isl_pw_qpolynomial *pwqp;
4399 f = isl_basic_set_factorizer(bset);
4402 if (f->n_group == 0) {
4403 isl_factorizer_free(f);
4407 nparam = isl_basic_set_dim(bset, isl_dim_param);
4408 nvar = isl_basic_set_dim(bset, isl_dim_set);
4410 dim = isl_basic_set_get_space(bset);
4411 dim = isl_space_domain(dim);
4412 set = isl_set_universe(isl_space_copy(dim));
4413 qp = isl_qpolynomial_one_on_domain(dim);
4414 pwqp = isl_pw_qpolynomial_alloc(set, qp);
4416 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
4418 for (i = 0, n = 0; i < f->n_group; ++i) {
4419 isl_basic_set *bset_i;
4420 isl_pw_qpolynomial *pwqp_i;
4422 bset_i = isl_basic_set_copy(bset);
4423 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4424 nparam + n + f->len[i], nvar - n - f->len[i]);
4425 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
4427 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
4428 n + f->len[i], nvar - n - f->len[i]);
4429 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
4431 pwqp_i = fn(bset_i);
4432 pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
4437 isl_basic_set_free(bset);
4438 isl_factorizer_free(f);
4442 isl_basic_set_free(bset);
4446 /* Factor bset, call fn on each of the factors and return the product.
4447 * The function is assumed to evaluate to zero on empty domains,
4448 * to one on zero-dimensional domains and to infinity on unbounded domains
4449 * and will not be called explicitly on zero-dimensional or unbounded domains.
4451 * We first check for some special cases and remove all equalities.
4452 * Then we hand over control to compressed_multiplicative_call.
4454 __isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
4455 __isl_take isl_basic_set *bset,
4456 __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
4460 isl_pw_qpolynomial *pwqp;
4465 if (isl_basic_set_plain_is_empty(bset))
4466 return constant_on_domain(bset, 0);
4468 if (isl_basic_set_dim(bset, isl_dim_set) == 0)
4469 return constant_on_domain(bset, 1);
4471 bounded = isl_basic_set_is_bounded(bset);
4475 return constant_on_domain(bset, -1);
4477 if (bset->n_eq == 0)
4478 return compressed_multiplicative_call(bset, fn);
4480 morph = isl_basic_set_full_compression(bset);
4481 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
4483 pwqp = compressed_multiplicative_call(bset, fn);
4485 morph = isl_morph_dom_params(morph);
4486 morph = isl_morph_ran_params(morph);
4487 morph = isl_morph_inverse(morph);
4489 pwqp = isl_pw_qpolynomial_morph_domain(pwqp, morph);
4493 isl_basic_set_free(bset);
4497 /* Drop all floors in "qp", turning each integer division [a/m] into
4498 * a rational division a/m. If "down" is set, then the integer division
4499 * is replaces by (a-(m-1))/m instead.
4501 static __isl_give isl_qpolynomial *qp_drop_floors(
4502 __isl_take isl_qpolynomial *qp, int down)
4505 struct isl_upoly *s;
4509 if (qp->div->n_row == 0)
4512 qp = isl_qpolynomial_cow(qp);
4516 for (i = qp->div->n_row - 1; i >= 0; --i) {
4518 isl_int_sub(qp->div->row[i][1],
4519 qp->div->row[i][1], qp->div->row[i][0]);
4520 isl_int_add_ui(qp->div->row[i][1],
4521 qp->div->row[i][1], 1);
4523 s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
4524 qp->div->row[i][0], qp->div->n_col - 1);
4525 qp = substitute_div(qp, i, s);
4533 /* Drop all floors in "pwqp", turning each integer division [a/m] into
4534 * a rational division a/m.
4536 static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
4537 __isl_take isl_pw_qpolynomial *pwqp)
4544 if (isl_pw_qpolynomial_is_zero(pwqp))
4547 pwqp = isl_pw_qpolynomial_cow(pwqp);
4551 for (i = 0; i < pwqp->n; ++i) {
4552 pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
4559 isl_pw_qpolynomial_free(pwqp);
4563 /* Adjust all the integer divisions in "qp" such that they are at least
4564 * one over the given orthant (identified by "signs"). This ensures
4565 * that they will still be non-negative even after subtracting (m-1)/m.
4567 * In particular, f is replaced by f' + v, changing f = [a/m]
4568 * to f' = [(a - m v)/m].
4569 * If the constant term k in a is smaller than m,
4570 * the constant term of v is set to floor(k/m) - 1.
4571 * For any other term, if the coefficient c and the variable x have
4572 * the same sign, then no changes are needed.
4573 * Otherwise, if the variable is positive (and c is negative),
4574 * then the coefficient of x in v is set to floor(c/m).
4575 * If the variable is negative (and c is positive),
4576 * then the coefficient of x in v is set to ceil(c/m).
4578 static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
4584 struct isl_upoly *s;
4586 qp = isl_qpolynomial_cow(qp);
4589 qp->div = isl_mat_cow(qp->div);
4593 total = isl_space_dim(qp->dim, isl_dim_all);
4594 v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
4596 for (i = 0; i < qp->div->n_row; ++i) {
4597 isl_int *row = qp->div->row[i];
4601 if (isl_int_lt(row[1], row[0])) {
4602 isl_int_fdiv_q(v->el[0], row[1], row[0]);
4603 isl_int_sub_ui(v->el[0], v->el[0], 1);
4604 isl_int_submul(row[1], row[0], v->el[0]);
4606 for (j = 0; j < total; ++j) {
4607 if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
4610 isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
4612 isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
4613 isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
4615 for (j = 0; j < i; ++j) {
4616 if (isl_int_sgn(row[2 + total + j]) >= 0)
4618 isl_int_fdiv_q(v->el[1 + total + j],
4619 row[2 + total + j], row[0]);
4620 isl_int_submul(row[2 + total + j],
4621 row[0], v->el[1 + total + j]);
4623 for (j = i + 1; j < qp->div->n_row; ++j) {
4624 if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
4626 isl_seq_combine(qp->div->row[j] + 1,
4627 qp->div->ctx->one, qp->div->row[j] + 1,
4628 qp->div->row[j][2 + total + i], v->el, v->size);
4630 isl_int_set_si(v->el[1 + total + i], 1);
4631 s = isl_upoly_from_affine(qp->dim->ctx, v->el,
4632 qp->div->ctx->one, v->size);
4633 qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
4643 isl_qpolynomial_free(qp);
4647 struct isl_to_poly_data {
4649 isl_pw_qpolynomial *res;
4650 isl_qpolynomial *qp;
4653 /* Appoximate data->qp by a polynomial on the orthant identified by "signs".
4654 * We first make all integer divisions positive and then split the
4655 * quasipolynomials into terms with sign data->sign (the direction
4656 * of the requested approximation) and terms with the opposite sign.
4657 * In the first set of terms, each integer division [a/m] is
4658 * overapproximated by a/m, while in the second it is underapproximated
4661 static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
4664 struct isl_to_poly_data *data = user;
4665 isl_pw_qpolynomial *t;
4666 isl_qpolynomial *qp, *up, *down;
4668 qp = isl_qpolynomial_copy(data->qp);
4669 qp = make_divs_pos(qp, signs);
4671 up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
4672 up = qp_drop_floors(up, 0);
4673 down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
4674 down = qp_drop_floors(down, 1);
4676 isl_qpolynomial_free(qp);
4677 qp = isl_qpolynomial_add(up, down);
4679 t = isl_pw_qpolynomial_alloc(orthant, qp);
4680 data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
4685 /* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
4686 * the polynomial will be an overapproximation. If "sign" is negative,
4687 * it will be an underapproximation. If "sign" is zero, the approximation
4688 * will lie somewhere in between.
4690 * In particular, is sign == 0, we simply drop the floors, turning
4691 * the integer divisions into rational divisions.
4692 * Otherwise, we split the domains into orthants, make all integer divisions
4693 * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
4694 * depending on the requested sign and the sign of the term in which
4695 * the integer division appears.
4697 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4698 __isl_take isl_pw_qpolynomial *pwqp, int sign)
4701 struct isl_to_poly_data data;
4704 return pwqp_drop_floors(pwqp);
4710 data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_space(pwqp));
4712 for (i = 0; i < pwqp->n; ++i) {
4713 if (pwqp->p[i].qp->div->n_row == 0) {
4714 isl_pw_qpolynomial *t;
4715 t = isl_pw_qpolynomial_alloc(
4716 isl_set_copy(pwqp->p[i].set),
4717 isl_qpolynomial_copy(pwqp->p[i].qp));
4718 data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
4721 data.qp = pwqp->p[i].qp;
4722 if (isl_set_foreach_orthant(pwqp->p[i].set,
4723 &to_polynomial_on_orthant, &data) < 0)
4727 isl_pw_qpolynomial_free(pwqp);
4731 isl_pw_qpolynomial_free(pwqp);
4732 isl_pw_qpolynomial_free(data.res);
4736 static int poly_entry(void **entry, void *user)
4739 isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
4741 *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
4743 return *pwqp ? 0 : -1;
4746 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
4747 __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
4749 upwqp = isl_union_pw_qpolynomial_cow(upwqp);
4753 if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
4754 &poly_entry, &sign) < 0)
4759 isl_union_pw_qpolynomial_free(upwqp);
4763 __isl_give isl_basic_map *isl_basic_map_from_qpolynomial(
4764 __isl_take isl_qpolynomial *qp)
4768 isl_vec *aff = NULL;
4769 isl_basic_map *bmap = NULL;
4775 if (!isl_upoly_is_affine(qp->upoly))
4776 isl_die(qp->dim->ctx, isl_error_invalid,
4777 "input quasi-polynomial not affine", goto error);
4778 aff = isl_qpolynomial_extract_affine(qp);
4781 dim = isl_qpolynomial_get_space(qp);
4782 pos = 1 + isl_space_offset(dim, isl_dim_out);
4783 n_div = qp->div->n_row;
4784 bmap = isl_basic_map_alloc_space(dim, n_div, 1, 2 * n_div);
4786 for (i = 0; i < n_div; ++i) {
4787 k = isl_basic_map_alloc_div(bmap);
4790 isl_seq_cpy(bmap->div[k], qp->div->row[i], qp->div->n_col);
4791 isl_int_set_si(bmap->div[k][qp->div->n_col], 0);
4792 if (isl_basic_map_add_div_constraints(bmap, k) < 0)
4795 k = isl_basic_map_alloc_equality(bmap);
4798 isl_int_neg(bmap->eq[k][pos], aff->el[0]);
4799 isl_seq_cpy(bmap->eq[k], aff->el + 1, pos);
4800 isl_seq_cpy(bmap->eq[k] + pos + 1, aff->el + 1 + pos, n_div);
4803 isl_qpolynomial_free(qp);
4804 bmap = isl_basic_map_finalize(bmap);
4808 isl_qpolynomial_free(qp);
4809 isl_basic_map_free(bmap);