#include <isl_polynomial_private.h>
#include <isl_point_private.h>
-#include <isl_dim_private.h>
+#include <isl_dim.h>
#include <isl_map_private.h>
+#include <isl_lp.h>
+#include <isl_seq.h>
+
+static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
+ enum isl_fold type, __isl_take isl_dim *dim, int n)
+{
+ isl_qpolynomial_fold *fold;
+
+ if (!dim)
+ goto error;
+
+ isl_assert(dim->ctx, n >= 0, goto error);
+ fold = isl_calloc(dim->ctx, struct isl_qpolynomial_fold,
+ sizeof(struct isl_qpolynomial_fold) +
+ (n - 1) * sizeof(struct isl_qpolynomial *));
+ if (!fold)
+ goto error;
+
+ fold->ref = 1;
+ fold->size = n;
+ fold->n = 0;
+ fold->type = type;
+ fold->dim = dim;
+
+ return fold;
+error:
+ isl_dim_free(dim);
+ return NULL;
+}
int isl_qpolynomial_fold_involves_dims(__isl_keep isl_qpolynomial_fold *fold,
enum isl_dim_type type, unsigned first, unsigned n)
return NULL;
}
-#undef PW
-#define PW isl_pw_qpolynomial_fold
-#undef EL
-#define EL isl_qpolynomial_fold
-#undef IS_ZERO
-#define IS_ZERO is_empty
-#undef FIELD
-#define FIELD fold
-#undef ADD
-#define ADD fold
+static int isl_qpolynomial_cst_sign(__isl_keep isl_qpolynomial *qp)
+{
+ struct isl_upoly_cst *cst;
-#include <isl_pw_templ.c>
+ cst = isl_upoly_as_cst(qp->upoly);
+ if (!cst)
+ return 0;
-static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
- enum isl_fold type, __isl_take isl_dim *dim, int n)
+ return isl_int_sgn(cst->n) < 0 ? -1 : 1;
+}
+
+static int isl_qpolynomial_aff_sign(__isl_keep isl_set *set,
+ __isl_keep isl_qpolynomial *qp)
{
- isl_qpolynomial_fold *fold;
+ enum isl_lp_result res;
+ isl_vec *aff;
+ isl_int opt;
+ int sgn = 0;
- if (!dim)
+ aff = isl_qpolynomial_extract_affine(qp);
+ if (!aff)
+ return 0;
+
+ isl_int_init(opt);
+
+ res = isl_set_solve_lp(set, 0, aff->el + 1, aff->el[0],
+ &opt, NULL, NULL);
+ if (res == isl_lp_error)
+ goto done;
+ if (res == isl_lp_empty ||
+ (res == isl_lp_ok && !isl_int_is_neg(opt))) {
+ sgn = 1;
+ goto done;
+ }
+
+ res = isl_set_solve_lp(set, 1, aff->el + 1, aff->el[0],
+ &opt, NULL, NULL);
+ if (res == isl_lp_ok && !isl_int_is_pos(opt))
+ sgn = -1;
+
+done:
+ isl_int_clear(opt);
+ isl_vec_free(aff);
+ return sgn;
+}
+
+/* Determine, if possible, the sign of the quasipolynomial "qp" on
+ * the domain "set".
+ *
+ * If qp is a constant, then the problem is trivial.
+ * If qp is linear, then we check if the minimum of the corresponding
+ * affine constraint is non-negative or if the maximum is non-positive.
+ *
+ * Otherwise, we check if the outermost variable "v" has a lower bound "l"
+ * in "set". If so, we write qp(v,v') as
+ *
+ * q(v,v') * (v - l) + r(v')
+ *
+ * if q(v,v') and r(v') have the same known sign, then the original
+ * quasipolynomial has the same sign as well.
+ *
+ * Return
+ * -1 if qp <= 0
+ * 1 if qp >= 0
+ * 0 if unknown
+ */
+static int isl_qpolynomial_sign(__isl_keep isl_set *set,
+ __isl_keep isl_qpolynomial *qp)
+{
+ int d;
+ int i;
+ int is;
+ struct isl_upoly_rec *rec;
+ isl_vec *v;
+ isl_int l;
+ enum isl_lp_result res;
+ int sgn = 0;
+
+ is = isl_qpolynomial_is_cst(qp, NULL, NULL);
+ if (is < 0)
+ return 0;
+ if (is)
+ return isl_qpolynomial_cst_sign(qp);
+
+ is = isl_qpolynomial_is_affine(qp);
+ if (is < 0)
+ return 0;
+ if (is)
+ return isl_qpolynomial_aff_sign(set, qp);
+
+ if (qp->div->n_row > 0)
+ return 0;
+
+ rec = isl_upoly_as_rec(qp->upoly);
+ if (!rec)
+ return 0;
+
+ d = isl_dim_total(qp->dim);
+ v = isl_vec_alloc(set->ctx, 2 + d);
+ if (!v)
+ return 0;
+
+ isl_seq_clr(v->el + 1, 1 + d);
+ isl_int_set_si(v->el[0], 1);
+ isl_int_set_si(v->el[2 + qp->upoly->var], 1);
+
+ isl_int_init(l);
+
+ res = isl_set_solve_lp(set, 0, v->el + 1, v->el[0], &l, NULL, NULL);
+ if (res == isl_lp_ok) {
+ isl_qpolynomial *min;
+ isl_qpolynomial *base;
+ isl_qpolynomial *r, *q;
+ isl_qpolynomial *t;
+
+ min = isl_qpolynomial_cst(isl_dim_copy(qp->dim), l);
+ base = isl_qpolynomial_pow(isl_dim_copy(qp->dim),
+ qp->upoly->var, 1);
+
+ r = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), 0,
+ isl_upoly_copy(rec->p[rec->n - 1]));
+ q = isl_qpolynomial_copy(r);
+
+ for (i = rec->n - 2; i >= 0; --i) {
+ r = isl_qpolynomial_mul(r, isl_qpolynomial_copy(min));
+ t = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), 0,
+ isl_upoly_copy(rec->p[i]));
+ r = isl_qpolynomial_add(r, t);
+ if (i == 0)
+ break;
+ q = isl_qpolynomial_mul(q, isl_qpolynomial_copy(base));
+ q = isl_qpolynomial_add(q, isl_qpolynomial_copy(r));
+ }
+
+ if (isl_qpolynomial_is_zero(q))
+ sgn = isl_qpolynomial_sign(set, r);
+ else if (isl_qpolynomial_is_zero(r))
+ sgn = isl_qpolynomial_sign(set, q);
+ else {
+ int sgn_q, sgn_r;
+ sgn_r = isl_qpolynomial_sign(set, r);
+ sgn_q = isl_qpolynomial_sign(set, q);
+ if (sgn_r == sgn_q)
+ sgn = sgn_r;
+ }
+
+ isl_qpolynomial_free(min);
+ isl_qpolynomial_free(base);
+ isl_qpolynomial_free(q);
+ isl_qpolynomial_free(r);
+ }
+
+ isl_int_clear(l);
+
+ isl_vec_free(v);
+
+ return sgn;
+}
+
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold_on_domain(
+ __isl_keep isl_set *set,
+ __isl_take isl_qpolynomial_fold *fold1,
+ __isl_take isl_qpolynomial_fold *fold2)
+{
+ int i, j;
+ int n1;
+ struct isl_qpolynomial_fold *res = NULL;
+ int better;
+
+ if (!fold1 || !fold2)
goto error;
- isl_assert(dim->ctx, n >= 0, goto error);
- fold = isl_alloc(dim->ctx, struct isl_qpolynomial_fold,
- sizeof(struct isl_qpolynomial_fold) +
- (n - 1) * sizeof(struct isl_qpolynomial *));
- if (!fold)
+ isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
+ isl_assert(fold1->dim->ctx, isl_dim_equal(fold1->dim, fold2->dim),
+ goto error);
+
+ better = fold1->type == isl_fold_max ? -1 : 1;
+
+ if (isl_qpolynomial_fold_is_empty(fold1)) {
+ isl_qpolynomial_fold_free(fold1);
+ return fold2;
+ }
+
+ if (isl_qpolynomial_fold_is_empty(fold2)) {
+ isl_qpolynomial_fold_free(fold2);
+ return fold1;
+ }
+
+ res = qpolynomial_fold_alloc(fold1->type, isl_dim_copy(fold1->dim),
+ fold1->n + fold2->n);
+ if (!res)
goto error;
- fold->ref = 1;
- fold->size = n;
- fold->n = 0;
- fold->type = type;
- fold->dim = dim;
+ for (i = 0; i < fold1->n; ++i) {
+ res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
+ if (!res->qp[res->n])
+ goto error;
+ res->n++;
+ }
+ n1 = res->n;
- return fold;
+ for (i = 0; i < fold2->n; ++i) {
+ for (j = n1 - 1; j >= 0; --j) {
+ isl_qpolynomial *d;
+ int sgn;
+ d = isl_qpolynomial_sub(
+ isl_qpolynomial_copy(res->qp[j]),
+ isl_qpolynomial_copy(fold2->qp[i]));
+ sgn = isl_qpolynomial_sign(set, d);
+ isl_qpolynomial_free(d);
+ if (sgn == 0)
+ continue;
+ if (sgn != better)
+ break;
+ isl_qpolynomial_free(res->qp[j]);
+ if (j != n1 - 1)
+ res->qp[j] = res->qp[n1 - 1];
+ n1--;
+ if (n1 != res->n - 1)
+ res->qp[n1] = res->qp[res->n - 1];
+ res->n--;
+ }
+ if (j >= 0)
+ continue;
+ res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
+ if (!res->qp[res->n])
+ goto error;
+ res->n++;
+ }
+
+ isl_qpolynomial_fold_free(fold1);
+ isl_qpolynomial_fold_free(fold2);
+
+ return res;
error:
- isl_dim_free(dim);
+ isl_qpolynomial_fold_free(res);
+ isl_qpolynomial_fold_free(fold1);
+ isl_qpolynomial_fold_free(fold2);
return NULL;
}
+#undef PW
+#define PW isl_pw_qpolynomial_fold
+#undef EL
+#define EL isl_qpolynomial_fold
+#undef IS_ZERO
+#define IS_ZERO is_empty
+#undef FIELD
+#define FIELD fold
+#undef ADD
+#define ADD(d,e1,e2) isl_qpolynomial_fold_fold_on_domain(d,e1,e2)
+
+#include <isl_pw_templ.c>
+
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_empty(enum isl_fold type,
__isl_take isl_dim *dim)
{
if (!dup)
return NULL;
+ dup->n = fold->n;
for (i = 0; i < fold->n; ++i) {
dup->qp[i] = isl_qpolynomial_copy(fold->qp[i]);
if (!dup->qp[i])
isl_point_free(pnt);
return NULL;
}
+
+size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold *pwf)
+{
+ int i;
+ size_t n = 0;
+
+ for (i = 0; i < pwf->n; ++i)
+ n += pwf->p[i].fold->n;
+
+ return n;
+}
+
+__isl_give isl_qpolynomial *isl_qpolynomial_fold_opt_on_domain(
+ __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *set, int max)
+{
+ int i;
+ isl_qpolynomial *opt;
+
+ if (!set || !fold)
+ goto error;
+
+ if (fold->n == 0) {
+ isl_dim *dim = isl_dim_copy(fold->dim);
+ isl_set_free(set);
+ isl_qpolynomial_fold_free(fold);
+ return isl_qpolynomial_zero(dim);
+ }
+
+ opt = isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold->qp[0]),
+ isl_set_copy(set), max);
+ for (i = 1; i < fold->n; ++i) {
+ isl_qpolynomial *opt_i;
+ opt_i = isl_qpolynomial_opt_on_domain(
+ isl_qpolynomial_copy(fold->qp[i]),
+ isl_set_copy(set), max);
+ if (max)
+ opt = isl_qpolynomial_max_cst(opt, opt_i);
+ else
+ opt = isl_qpolynomial_min_cst(opt, opt_i);
+ }
+
+ isl_set_free(set);
+ isl_qpolynomial_fold_free(fold);
+
+ return opt;
+error:
+ isl_set_free(set);
+ isl_qpolynomial_fold_free(fold);
+ return NULL;
+}
+
+/* Check whether for each quasi-polynomial in "fold2" there is
+ * a quasi-polynomial in "fold1" that dominates it on "set".
+ */
+static int qpolynomial_fold_covers_on_domain(__isl_keep isl_set *set,
+ __isl_keep isl_qpolynomial_fold *fold1,
+ __isl_keep isl_qpolynomial_fold *fold2)
+{
+ int i, j;
+ int covers;
+
+ if (!set || !fold1 || !fold2)
+ return -1;
+
+ covers = fold1->type == isl_fold_max ? 1 : -1;
+
+ for (i = 0; i < fold2->n; ++i) {
+ for (j = 0; j < fold1->n; ++j) {
+ isl_qpolynomial *d;
+ int sgn;
+
+ d = isl_qpolynomial_sub(
+ isl_qpolynomial_copy(fold1->qp[j]),
+ isl_qpolynomial_copy(fold2->qp[i]));
+ sgn = isl_qpolynomial_sign(set, d);
+ isl_qpolynomial_free(d);
+ if (sgn == covers)
+ break;
+ }
+ if (j >= fold1->n)
+ return 0;
+ }
+
+ return 1;
+}
+
+/* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
+ * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
+ * that of pwf2.
+ */
+int isl_pw_qpolynomial_fold_covers(__isl_keep isl_pw_qpolynomial_fold *pwf1,
+ __isl_keep isl_pw_qpolynomial_fold *pwf2)
+{
+ int i, j;
+ isl_set *dom1, *dom2;
+ int is_subset;
+
+ if (!pwf1 || !pwf2)
+ return -1;
+
+ if (pwf2->n == 0)
+ return 1;
+ if (pwf1->n == 0)
+ return 0;
+
+ dom1 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1));
+ dom2 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2));
+ is_subset = isl_set_is_subset(dom2, dom1);
+ isl_set_free(dom1);
+ isl_set_free(dom2);
+
+ if (is_subset < 0 || !is_subset)
+ return is_subset;
+
+ for (i = 0; i < pwf2->n; ++i) {
+ for (j = 0; j < pwf1->n; ++j) {
+ int is_empty;
+ isl_set *common;
+ int covers;
+
+ common = isl_set_intersect(isl_set_copy(pwf1->p[j].set),
+ isl_set_copy(pwf2->p[i].set));
+ is_empty = isl_set_is_empty(common);
+ if (is_empty < 0 || is_empty) {
+ isl_set_free(common);
+ if (is_empty < 0)
+ return -1;
+ continue;
+ }
+ covers = qpolynomial_fold_covers_on_domain(common,
+ pwf1->p[j].fold, pwf2->p[i].fold);
+ isl_set_free(common);
+ if (covers < 0 || !covers)
+ return covers;
+ }
+ }
+
+ return 1;
+}
+
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_morph(
+ __isl_take isl_qpolynomial_fold *fold, __isl_take isl_morph *morph)
+{
+ int i;
+ isl_ctx *ctx;
+
+ if (!fold || !morph)
+ goto error;
+
+ ctx = fold->dim->ctx;
+ isl_assert(ctx, isl_dim_equal(fold->dim, morph->dom->dim), goto error);
+
+ fold = isl_qpolynomial_fold_cow(fold);
+ if (!fold)
+ goto error;
+
+ isl_dim_free(fold->dim);
+ fold->dim = isl_dim_copy(morph->ran->dim);
+ if (!fold->dim)
+ goto error;
+
+ for (i = 0; i < fold->n; ++i) {
+ fold->qp[i] = isl_qpolynomial_morph(fold->qp[i],
+ isl_morph_copy(morph));
+ if (!fold->qp[i])
+ goto error;
+ }
+
+ isl_morph_free(morph);
+
+ return fold;
+error:
+ isl_qpolynomial_fold_free(fold);
+ isl_morph_free(morph);
+ return NULL;
+}
+
+enum isl_fold isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold *fold)
+{
+ if (!fold)
+ return isl_fold_list;
+ return fold->type;
+}
+
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_lift(
+ __isl_take isl_qpolynomial_fold *fold, __isl_take isl_dim *dim)
+{
+ int i;
+ isl_ctx *ctx;
+
+ if (!fold || !dim)
+ goto error;
+
+ if (isl_dim_equal(fold->dim, dim)) {
+ isl_dim_free(dim);
+ return fold;
+ }
+
+ fold = isl_qpolynomial_fold_cow(fold);
+ if (!fold)
+ goto error;
+
+ isl_dim_free(fold->dim);
+ fold->dim = isl_dim_copy(dim);
+ if (!fold->dim)
+ goto error;
+
+ for (i = 0; i < fold->n; ++i) {
+ fold->qp[i] = isl_qpolynomial_lift(fold->qp[i],
+ isl_dim_copy(dim));
+ if (!fold->qp[i])
+ goto error;
+ }
+
+ isl_dim_free(dim);
+
+ return fold;
+error:
+ isl_qpolynomial_fold_free(fold);
+ isl_dim_free(dim);
+ return NULL;
+}
+
+int isl_qpolynomial_fold_foreach_qpolynomial(
+ __isl_keep isl_qpolynomial_fold *fold,
+ int (*fn)(__isl_take isl_qpolynomial *qp, void *user), void *user)
+{
+ int i;
+
+ if (!fold)
+ return -1;
+
+ for (i = 0; i < fold->n; ++i)
+ if (fn(isl_qpolynomial_copy(fold->qp[i]), user) < 0)
+ return -1;
+
+ return 0;
+}
+
+__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_move_dims(
+ __isl_take isl_qpolynomial_fold *fold,
+ enum isl_dim_type dst_type, unsigned dst_pos,
+ enum isl_dim_type src_type, unsigned src_pos, unsigned n)
+{
+ int i;
+
+ if (n == 0)
+ return fold;
+
+ fold = isl_qpolynomial_fold_cow(fold);
+ if (!fold)
+ return NULL;
+
+ fold->dim = isl_dim_move(fold->dim, dst_type, dst_pos,
+ src_type, src_pos, n);
+ if (!fold->dim)
+ goto error;
+
+ for (i = 0; i < fold->n; ++i) {
+ fold->qp[i] = isl_qpolynomial_move_dims(fold->qp[i],
+ dst_type, dst_pos, src_type, src_pos, n);
+ if (!fold->qp[i])
+ goto error;
+ }
+
+ return fold;
+error:
+ isl_qpolynomial_fold_free(fold);
+ return NULL;
+}
projects / platform / upstream / isl.git / blobdiff