+/*
+ * Copyright 2010 INRIA Saclay
+ *
+ * Use of this software is governed by the GNU LGPLv2.1 license
+ *
+ * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
+ * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
+ * 91893 Orsay, France
+ */
+
#include <stdlib.h>
-#include <isl_seq.h>
+#include <isl_factorization.h>
+#include <isl/lp.h>
+#include <isl/seq.h>
+#include <isl_union_map_private.h>
#include <isl_polynomial_private.h>
#include <isl_point_private.h>
#include <isl_dim_private.h>
#include <isl_map_private.h>
-#include <isl_map_private.h>
+#include <isl_mat_private.h>
+#include <isl_range.h>
static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
{
case isl_dim_param: return 0;
case isl_dim_in: return dim->nparam;
case isl_dim_out: return dim->nparam + dim->n_in;
+ default: return 0;
}
}
return isl_int_is_zero(cst->n) && isl_int_is_pos(cst->d);
}
+int isl_upoly_sgn(__isl_keep struct isl_upoly *up)
+{
+ struct isl_upoly_cst *cst;
+
+ if (!up)
+ return 0;
+ if (!isl_upoly_is_cst(up))
+ return 0;
+
+ cst = isl_upoly_as_cst(up);
+ if (!cst)
+ return 0;
+
+ return isl_int_sgn(cst->n);
+}
+
int isl_upoly_is_nan(__isl_keep struct isl_upoly *up)
{
struct isl_upoly_cst *cst;
return &cst->up;
}
+__isl_give struct isl_upoly *isl_upoly_one(struct isl_ctx *ctx)
+{
+ struct isl_upoly_cst *cst;
+
+ cst = isl_upoly_cst_alloc(ctx);
+ if (!cst)
+ return NULL;
+
+ isl_int_set_si(cst->n, 1);
+ isl_int_set_si(cst->d, 1);
+
+ return &cst->up;
+}
+
__isl_give struct isl_upoly *isl_upoly_infty(struct isl_ctx *ctx)
{
struct isl_upoly_cst *cst;
return &cst->up;
}
+__isl_give struct isl_upoly *isl_upoly_neginfty(struct isl_ctx *ctx)
+{
+ struct isl_upoly_cst *cst;
+
+ cst = isl_upoly_cst_alloc(ctx);
+ if (!cst)
+ return NULL;
+
+ isl_int_set_si(cst->n, -1);
+ isl_int_set_si(cst->d, 0);
+
+ return &cst->up;
+}
+
__isl_give struct isl_upoly *isl_upoly_nan(struct isl_ctx *ctx)
{
struct isl_upoly_cst *cst;
isl_assert(ctx, var >= 0, return NULL);
isl_assert(ctx, size >= 0, return NULL);
- rec = isl_calloc(dim->ctx, struct isl_upoly_rec,
+ rec = isl_calloc(ctx, struct isl_upoly_rec,
sizeof(struct isl_upoly_rec) +
(size - 1) * sizeof(struct isl_upoly *));
if (!rec)
rec->size = size;
return rec;
+}
+
+__isl_give isl_qpolynomial *isl_qpolynomial_reset_dim(
+ __isl_take isl_qpolynomial *qp, __isl_take isl_dim *dim)
+{
+ qp = isl_qpolynomial_cow(qp);
+ if (!qp || !dim)
+ goto error;
+
+ isl_dim_free(qp->dim);
+ qp->dim = dim;
+
+ return qp;
error:
- isl_upoly_free(&rec->up);
+ isl_qpolynomial_free(qp);
+ isl_dim_free(dim);
return NULL;
}
-int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
+isl_ctx *isl_qpolynomial_get_ctx(__isl_keep isl_qpolynomial *qp)
{
- struct isl_upoly_cst *cst;
+ return qp ? qp->dim->ctx : NULL;
+}
- if (!qp)
- return -1;
+__isl_give isl_dim *isl_qpolynomial_get_dim(__isl_keep isl_qpolynomial *qp)
+{
+ return qp ? isl_dim_copy(qp->dim) : NULL;
+}
+
+unsigned isl_qpolynomial_dim(__isl_keep isl_qpolynomial *qp,
+ enum isl_dim_type type)
+{
+ return qp ? isl_dim_size(qp->dim, type) : 0;
+}
- return isl_upoly_is_zero(qp->upoly);
+int isl_qpolynomial_is_zero(__isl_keep isl_qpolynomial *qp)
+{
+ return qp ? isl_upoly_is_zero(qp->upoly) : -1;
}
int isl_qpolynomial_is_one(__isl_keep isl_qpolynomial *qp)
{
- struct isl_upoly_cst *cst;
+ return qp ? isl_upoly_is_one(qp->upoly) : -1;
+}
- if (!qp)
- return -1;
+int isl_qpolynomial_is_nan(__isl_keep isl_qpolynomial *qp)
+{
+ return qp ? isl_upoly_is_nan(qp->upoly) : -1;
+}
+
+int isl_qpolynomial_is_infty(__isl_keep isl_qpolynomial *qp)
+{
+ return qp ? isl_upoly_is_infty(qp->upoly) : -1;
+}
+
+int isl_qpolynomial_is_neginfty(__isl_keep isl_qpolynomial *qp)
+{
+ return qp ? isl_upoly_is_neginfty(qp->upoly) : -1;
+}
- return isl_upoly_is_one(qp->upoly);
+int isl_qpolynomial_sgn(__isl_keep isl_qpolynomial *qp)
+{
+ return qp ? isl_upoly_sgn(qp->upoly) : 0;
}
static void upoly_free_cst(__isl_take struct isl_upoly_cst *cst)
return NULL;
}
+__isl_give struct isl_upoly *isl_upoly_cst_add_isl_int(
+ __isl_take struct isl_upoly *up, isl_int v)
+{
+ struct isl_upoly_cst *cst;
+
+ up = isl_upoly_cow(up);
+ if (!up)
+ return NULL;
+
+ cst = isl_upoly_as_cst(up);
+
+ isl_int_addmul(cst->n, cst->d, v);
+
+ return up;
+}
+
+__isl_give struct isl_upoly *isl_upoly_add_isl_int(
+ __isl_take struct isl_upoly *up, isl_int v)
+{
+ struct isl_upoly_rec *rec;
+
+ if (!up)
+ return NULL;
+
+ if (isl_upoly_is_cst(up))
+ return isl_upoly_cst_add_isl_int(up, v);
+
+ up = isl_upoly_cow(up);
+ rec = isl_upoly_as_rec(up);
+ if (!rec)
+ goto error;
+
+ rec->p[0] = isl_upoly_add_isl_int(rec->p[0], v);
+ if (!rec->p[0])
+ goto error;
+
+ return up;
+error:
+ isl_upoly_free(up);
+ return NULL;
+}
+
__isl_give struct isl_upoly *isl_upoly_neg_cst(__isl_take struct isl_upoly *up)
{
struct isl_upoly_cst *cst;
return NULL;
}
+__isl_give struct isl_upoly *isl_upoly_pow(__isl_take struct isl_upoly *up,
+ unsigned power)
+{
+ struct isl_upoly *res;
+
+ if (!up)
+ return NULL;
+ if (power == 1)
+ return up;
+
+ if (power % 2)
+ res = isl_upoly_copy(up);
+ else
+ res = isl_upoly_one(up->ctx);
+
+ while (power >>= 1) {
+ up = isl_upoly_mul(up, isl_upoly_copy(up));
+ if (power % 2)
+ res = isl_upoly_mul(res, isl_upoly_copy(up));
+ }
+
+ isl_upoly_free(up);
+ return res;
+}
+
__isl_give isl_qpolynomial *isl_qpolynomial_alloc(__isl_take isl_dim *dim,
- unsigned n_div)
+ unsigned n_div, __isl_take struct isl_upoly *up)
{
- struct isl_qpolynomial *qp;
+ struct isl_qpolynomial *qp = NULL;
unsigned total;
- if (!dim)
- return NULL;
+ if (!dim || !up)
+ goto error;
total = isl_dim_total(dim);
qp = isl_calloc_type(dim->ctx, struct isl_qpolynomial);
if (!qp)
- return NULL;
+ goto error;
qp->ref = 1;
qp->div = isl_mat_alloc(dim->ctx, n_div, 1 + 1 + total + n_div);
goto error;
qp->dim = dim;
+ qp->upoly = up;
return qp;
error:
isl_dim_free(dim);
+ isl_upoly_free(up);
isl_qpolynomial_free(qp);
return NULL;
}
if (!qp)
return NULL;
- dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row);
+ dup = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row,
+ isl_upoly_copy(qp->upoly));
if (!dup)
return NULL;
isl_mat_free(dup->div);
dup->div = isl_mat_copy(qp->div);
if (!dup->div)
goto error;
- dup->upoly = isl_upoly_copy(qp->upoly);
- if (!dup->upoly)
- goto error;
return dup;
error:
free(qp);
}
+__isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
+{
+ int i;
+ struct isl_upoly *up;
+ struct isl_upoly_rec *rec;
+ struct isl_upoly_cst *cst;
+
+ rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
+ if (!rec)
+ return NULL;
+ for (i = 0; i < 1 + power; ++i) {
+ rec->p[i] = isl_upoly_zero(ctx);
+ if (!rec->p[i])
+ goto error;
+ rec->n++;
+ }
+ cst = isl_upoly_as_cst(rec->p[power]);
+ isl_int_set_si(cst->n, 1);
+
+ return &rec->up;
+error:
+ isl_upoly_free(&rec->up);
+ return NULL;
+}
+
+/* r array maps original positions to new positions.
+ */
+static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
+ int *r)
+{
+ int i;
+ struct isl_upoly_rec *rec;
+ struct isl_upoly *base;
+ struct isl_upoly *res;
+
+ if (isl_upoly_is_cst(up))
+ return up;
+
+ rec = isl_upoly_as_rec(up);
+ if (!rec)
+ goto error;
+
+ isl_assert(up->ctx, rec->n >= 1, goto error);
+
+ base = isl_upoly_var_pow(up->ctx, r[up->var], 1);
+ res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
+
+ for (i = rec->n - 2; i >= 0; --i) {
+ res = isl_upoly_mul(res, isl_upoly_copy(base));
+ res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
+ }
+
+ isl_upoly_free(base);
+ isl_upoly_free(up);
+
+ return res;
+error:
+ isl_upoly_free(up);
+ return NULL;
+}
+
static int compatible_divs(__isl_keep isl_mat *div1, __isl_keep isl_mat *div2)
{
int n_row, n_col;
return cmp_row(i1->div, i1->row, i2->row);
}
-static __isl_give isl_mat *sort_divs(__isl_take isl_mat *div)
+/* Sort divs and remove duplicates.
+ */
+static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
{
int i;
+ int skip;
+ int len;
struct isl_div_sort_info *array = NULL;
- int *pos = NULL;
+ int *pos = NULL, *at = NULL;
+ int *reordering = NULL;
+ unsigned div_pos;
- if (!div)
+ if (!qp)
return NULL;
- if (div->n_row <= 1)
- return div;
+ if (qp->div->n_row <= 1)
+ return qp;
- array = isl_alloc_array(div->ctx, struct isl_div_sort_info, div->n_row);
- pos = isl_alloc_array(div->ctx, int, div->n_row);
- if (!array || !pos)
+ div_pos = isl_dim_total(qp->dim);
+
+ array = isl_alloc_array(qp->div->ctx, struct isl_div_sort_info,
+ qp->div->n_row);
+ pos = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
+ at = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
+ len = qp->div->n_col - 2;
+ reordering = isl_alloc_array(qp->div->ctx, int, len);
+ if (!array || !pos || !at || !reordering)
goto error;
- for (i = 0; i < div->n_row; ++i) {
- array[i].div = div;
+ for (i = 0; i < qp->div->n_row; ++i) {
+ array[i].div = qp->div;
array[i].row = i;
pos[i] = i;
+ at[i] = i;
}
- qsort(array, div->n_row, sizeof(struct isl_div_sort_info),
+ qsort(array, qp->div->n_row, sizeof(struct isl_div_sort_info),
div_sort_cmp);
- for (i = 0; i < div->n_row; ++i) {
- int t;
+ for (i = 0; i < div_pos; ++i)
+ reordering[i] = i;
+
+ for (i = 0; i < qp->div->n_row; ++i) {
if (pos[array[i].row] == i)
continue;
- div = isl_mat_cow(div);
- div = isl_mat_swap_rows(div, i, pos[array[i].row]);
- t = pos[array[i].row];
- pos[array[i].row] = pos[i];
- pos[i] = t;
+ qp->div = isl_mat_swap_rows(qp->div, i, pos[array[i].row]);
+ pos[at[i]] = pos[array[i].row];
+ at[pos[array[i].row]] = at[i];
+ at[i] = array[i].row;
+ pos[array[i].row] = i;
+ }
+
+ skip = 0;
+ for (i = 0; i < len - div_pos; ++i) {
+ if (i > 0 &&
+ isl_seq_eq(qp->div->row[i - skip - 1],
+ qp->div->row[i - skip], qp->div->n_col)) {
+ qp->div = isl_mat_drop_rows(qp->div, i - skip, 1);
+ isl_mat_col_add(qp->div, 2 + div_pos + i - skip - 1,
+ 2 + div_pos + i - skip);
+ qp->div = isl_mat_drop_cols(qp->div,
+ 2 + div_pos + i - skip, 1);
+ skip++;
+ }
+ reordering[div_pos + array[i].row] = div_pos + i - skip;
}
+ qp->upoly = reorder(qp->upoly, reordering);
+
+ if (!qp->upoly || !qp->div)
+ goto error;
+
+ free(at);
+ free(pos);
free(array);
+ free(reordering);
- return div;
+ return qp;
error:
+ free(at);
free(pos);
free(array);
- isl_mat_free(div);
+ free(reordering);
+ isl_qpolynomial_free(qp);
return NULL;
}
return NULL;
}
+__isl_give isl_qpolynomial *isl_qpolynomial_add_on_domain(
+ __isl_keep isl_set *dom,
+ __isl_take isl_qpolynomial *qp1,
+ __isl_take isl_qpolynomial *qp2)
+{
+ qp1 = isl_qpolynomial_add(qp1, qp2);
+ qp1 = isl_qpolynomial_gist(qp1, isl_set_copy(dom));
+ return qp1;
+}
+
__isl_give isl_qpolynomial *isl_qpolynomial_sub(__isl_take isl_qpolynomial *qp1,
__isl_take isl_qpolynomial *qp2)
{
return isl_qpolynomial_add(qp1, isl_qpolynomial_neg(qp2));
}
+__isl_give isl_qpolynomial *isl_qpolynomial_add_isl_int(
+ __isl_take isl_qpolynomial *qp, isl_int v)
+{
+ if (isl_int_is_zero(v))
+ return qp;
+
+ qp = isl_qpolynomial_cow(qp);
+ if (!qp)
+ return NULL;
+
+ qp->upoly = isl_upoly_add_isl_int(qp->upoly, v);
+ if (!qp->upoly)
+ goto error;
+
+ return qp;
+error:
+ isl_qpolynomial_free(qp);
+ return NULL;
+
+}
+
__isl_give isl_qpolynomial *isl_qpolynomial_neg(__isl_take isl_qpolynomial *qp)
{
qp = isl_qpolynomial_cow(qp);
return NULL;
}
-__isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
+__isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_qpolynomial *qp,
+ unsigned power)
{
- struct isl_qpolynomial *qp;
- struct isl_upoly_cst *cst;
+ qp = isl_qpolynomial_cow(qp);
- qp = isl_qpolynomial_alloc(dim, 0);
if (!qp)
return NULL;
- qp->upoly = isl_upoly_zero(dim->ctx);
+ qp->upoly = isl_upoly_pow(qp->upoly, power);
if (!qp->upoly)
goto error;
return NULL;
}
-__isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
+__isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
{
- struct isl_qpolynomial *qp;
- struct isl_upoly_cst *cst;
+ return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
+}
- qp = isl_qpolynomial_alloc(dim, 0);
- if (!qp)
- return NULL;
+__isl_give isl_qpolynomial *isl_qpolynomial_one(__isl_take isl_dim *dim)
+{
+ return isl_qpolynomial_alloc(dim, 0, isl_upoly_one(dim->ctx));
+}
- qp->upoly = isl_upoly_infty(dim->ctx);
- if (!qp->upoly)
- goto error;
+__isl_give isl_qpolynomial *isl_qpolynomial_infty(__isl_take isl_dim *dim)
+{
+ return isl_qpolynomial_alloc(dim, 0, isl_upoly_infty(dim->ctx));
+}
- return qp;
-error:
- isl_qpolynomial_free(qp);
- return NULL;
+__isl_give isl_qpolynomial *isl_qpolynomial_neginfty(__isl_take isl_dim *dim)
+{
+ return isl_qpolynomial_alloc(dim, 0, isl_upoly_neginfty(dim->ctx));
}
__isl_give isl_qpolynomial *isl_qpolynomial_nan(__isl_take isl_dim *dim)
{
- struct isl_qpolynomial *qp;
- struct isl_upoly_cst *cst;
-
- qp = isl_qpolynomial_alloc(dim, 0);
- if (!qp)
- return NULL;
-
- qp->upoly = isl_upoly_nan(dim->ctx);
- if (!qp->upoly)
- goto error;
-
- return qp;
-error:
- isl_qpolynomial_free(qp);
- return NULL;
+ return isl_qpolynomial_alloc(dim, 0, isl_upoly_nan(dim->ctx));
}
__isl_give isl_qpolynomial *isl_qpolynomial_cst(__isl_take isl_dim *dim,
struct isl_qpolynomial *qp;
struct isl_upoly_cst *cst;
- qp = isl_qpolynomial_alloc(dim, 0);
+ qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
if (!qp)
return NULL;
- qp->upoly = isl_upoly_zero(dim->ctx);
- if (!qp->upoly)
- goto error;
cst = isl_upoly_as_cst(qp->upoly);
isl_int_set(cst->n, v);
return qp;
-error:
- isl_qpolynomial_free(qp);
- return NULL;
}
int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
return 1;
}
+int isl_upoly_is_affine(__isl_keep struct isl_upoly *up)
+{
+ int is_cst;
+ struct isl_upoly_rec *rec;
+
+ if (!up)
+ return -1;
+
+ if (up->var < 0)
+ return 1;
+
+ rec = isl_upoly_as_rec(up);
+ if (!rec)
+ return -1;
+
+ if (rec->n > 2)
+ return 0;
+
+ isl_assert(up->ctx, rec->n > 1, return -1);
+
+ is_cst = isl_upoly_is_cst(rec->p[1]);
+ if (is_cst < 0)
+ return -1;
+ if (!is_cst)
+ return 0;
+
+ return isl_upoly_is_affine(rec->p[0]);
+}
+
+int isl_qpolynomial_is_affine(__isl_keep isl_qpolynomial *qp)
+{
+ if (!qp)
+ return -1;
+
+ if (qp->div->n_row > 0)
+ return 0;
+
+ return isl_upoly_is_affine(qp->upoly);
+}
+
+static void update_coeff(__isl_keep isl_vec *aff,
+ __isl_keep struct isl_upoly_cst *cst, int pos)
+{
+ isl_int gcd;
+ isl_int f;
+
+ if (isl_int_is_zero(cst->n))
+ return;
+
+ isl_int_init(gcd);
+ isl_int_init(f);
+ isl_int_gcd(gcd, cst->d, aff->el[0]);
+ isl_int_divexact(f, cst->d, gcd);
+ isl_int_divexact(gcd, aff->el[0], gcd);
+ isl_seq_scale(aff->el, aff->el, f, aff->size);
+ isl_int_mul(aff->el[1 + pos], gcd, cst->n);
+ isl_int_clear(gcd);
+ isl_int_clear(f);
+}
+
+int isl_upoly_update_affine(__isl_keep struct isl_upoly *up,
+ __isl_keep isl_vec *aff)
+{
+ struct isl_upoly_cst *cst;
+ struct isl_upoly_rec *rec;
+
+ if (!up || !aff)
+ return -1;
+
+ if (up->var < 0) {
+ struct isl_upoly_cst *cst;
+
+ cst = isl_upoly_as_cst(up);
+ if (!cst)
+ return -1;
+ update_coeff(aff, cst, 0);
+ return 0;
+ }
+
+ rec = isl_upoly_as_rec(up);
+ if (!rec)
+ return -1;
+ isl_assert(up->ctx, rec->n == 2, return -1);
+
+ cst = isl_upoly_as_cst(rec->p[1]);
+ if (!cst)
+ return -1;
+ update_coeff(aff, cst, 1 + up->var);
+
+ return isl_upoly_update_affine(rec->p[0], aff);
+}
+
+__isl_give isl_vec *isl_qpolynomial_extract_affine(
+ __isl_keep isl_qpolynomial *qp)
+{
+ isl_vec *aff;
+ unsigned d;
+
+ if (!qp)
+ return NULL;
+
+ isl_assert(qp->div->ctx, qp->div->n_row == 0, return NULL);
+ d = isl_dim_total(qp->dim);
+ aff = isl_vec_alloc(qp->div->ctx, 2 + d);
+ if (!aff)
+ return NULL;
+
+ isl_seq_clr(aff->el + 1, 1 + d);
+ isl_int_set_si(aff->el[0], 1);
+
+ if (isl_upoly_update_affine(qp->upoly, aff) < 0)
+ goto error;
+
+ return aff;
+error:
+ isl_vec_free(aff);
+ return NULL;
+}
+
int isl_qpolynomial_is_equal(__isl_keep isl_qpolynomial *qp1,
__isl_keep isl_qpolynomial *qp2)
{
upoly_update_den(qp->upoly, d);
}
-__isl_give struct isl_upoly *isl_upoly_pow(isl_ctx *ctx, int pos, int power)
-{
- int i;
- struct isl_upoly *up;
- struct isl_upoly_rec *rec;
- struct isl_upoly_cst *cst;
-
- rec = isl_upoly_alloc_rec(ctx, pos, 1 + power);
- if (!rec)
- return NULL;
- for (i = 0; i < 1 + power; ++i) {
- rec->p[i] = isl_upoly_zero(ctx);
- if (!rec->p[i])
- goto error;
- rec->n++;
- }
- cst = isl_upoly_as_cst(rec->p[power]);
- isl_int_set_si(cst->n, 1);
-
- return &rec->up;
-error:
- isl_upoly_free(&rec->up);
- return NULL;
-}
-
-__isl_give isl_qpolynomial *isl_qpolynomial_pow(__isl_take isl_dim *dim,
+__isl_give isl_qpolynomial *isl_qpolynomial_var_pow(__isl_take isl_dim *dim,
int pos, int power)
{
- struct isl_qpolynomial *qp;
struct isl_ctx *ctx;
if (!dim)
ctx = dim->ctx;
- qp = isl_qpolynomial_alloc(dim, 0);
- if (!qp)
- return NULL;
-
- qp->upoly = isl_upoly_pow(ctx, pos, power);
- if (!qp->upoly)
- goto error;
-
- return qp;
-error:
- isl_qpolynomial_free(qp);
- return NULL;
+ return isl_qpolynomial_alloc(dim, 0, isl_upoly_var_pow(ctx, pos, power));
}
__isl_give isl_qpolynomial *isl_qpolynomial_var(__isl_take isl_dim *dim,
if (type == isl_dim_set)
pos += isl_dim_size(dim, isl_dim_param);
- return isl_qpolynomial_pow(dim, pos, 1);
+ return isl_qpolynomial_var_pow(dim, pos, 1);
error:
isl_dim_free(dim);
return NULL;
}
-__isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
- int power)
+__isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
+ unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
{
- struct isl_qpolynomial *qp = NULL;
- struct isl_upoly_rec *rec;
- struct isl_upoly_cst *cst;
int i;
- int pos;
+ struct isl_upoly_rec *rec;
+ struct isl_upoly *base, *res;
- if (!div)
+ if (!up)
return NULL;
- isl_assert(div->ctx, div->bmap->n_div == 1, goto error);
- qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap), 1);
- if (!qp)
- goto error;
+ if (isl_upoly_is_cst(up))
+ return up;
- isl_seq_cpy(qp->div->row[0], div->line[0], qp->div->n_col - 1);
- isl_int_set_si(qp->div->row[0][qp->div->n_col - 1], 0);
+ if (up->var < first)
+ return up;
- pos = isl_dim_total(qp->dim);
- qp->upoly = &isl_upoly_alloc_rec(div->ctx, pos, 1 + power)->up;
- if (!qp->upoly)
+ rec = isl_upoly_as_rec(up);
+ if (!rec)
goto error;
- rec = isl_upoly_as_rec(qp->upoly);
- for (i = 0; i < 1 + power; ++i) {
- rec->p[i] = isl_upoly_zero(div->ctx);
- if (!rec->p[i])
- goto error;
- rec->n++;
- }
- cst = isl_upoly_as_cst(rec->p[power]);
- isl_int_set_si(cst->n, 1);
- isl_div_free(div);
+ isl_assert(up->ctx, rec->n >= 1, goto error);
- return qp;
+ if (up->var >= first + n)
+ base = isl_upoly_var_pow(up->ctx, up->var, 1);
+ else
+ base = isl_upoly_copy(subs[up->var - first]);
+
+ res = isl_upoly_subs(isl_upoly_copy(rec->p[rec->n - 1]), first, n, subs);
+ for (i = rec->n - 2; i >= 0; --i) {
+ struct isl_upoly *t;
+ t = isl_upoly_subs(isl_upoly_copy(rec->p[i]), first, n, subs);
+ res = isl_upoly_mul(res, isl_upoly_copy(base));
+ res = isl_upoly_sum(res, t);
+ }
+
+ isl_upoly_free(base);
+ isl_upoly_free(up);
+
+ return res;
error:
- isl_qpolynomial_free(qp);
- isl_div_free(div);
+ isl_upoly_free(up);
return NULL;
+}
+
+__isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
+ isl_int denom, unsigned len)
+{
+ int i;
+ struct isl_upoly *up;
+
+ isl_assert(ctx, len >= 1, return NULL);
+
+ up = isl_upoly_rat_cst(ctx, f[0], denom);
+ for (i = 0; i < len - 1; ++i) {
+ struct isl_upoly *t;
+ struct isl_upoly *c;
+
+ if (isl_int_is_zero(f[1 + i]))
+ continue;
+
+ c = isl_upoly_rat_cst(ctx, f[1 + i], denom);
+ t = isl_upoly_var_pow(ctx, i, 1);
+ t = isl_upoly_mul(c, t);
+ up = isl_upoly_sum(up, t);
+ }
+
+ return up;
}
-__isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
+/* Remove common factor of non-constant terms and denominator.
+ */
+static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
{
- return isl_qpolynomial_div_pow(div, 1);
+ isl_ctx *ctx = qp->div->ctx;
+ unsigned total = qp->div->n_col - 2;
+
+ isl_seq_gcd(qp->div->row[div] + 2, total, &ctx->normalize_gcd);
+ isl_int_gcd(ctx->normalize_gcd,
+ ctx->normalize_gcd, qp->div->row[div][0]);
+ if (isl_int_is_one(ctx->normalize_gcd))
+ return;
+
+ isl_seq_scale_down(qp->div->row[div] + 2, qp->div->row[div] + 2,
+ ctx->normalize_gcd, total);
+ isl_int_divexact(qp->div->row[div][0], qp->div->row[div][0],
+ ctx->normalize_gcd);
+ isl_int_fdiv_q(qp->div->row[div][1], qp->div->row[div][1],
+ ctx->normalize_gcd);
}
-__isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
- const isl_int n, const isl_int d)
+/* Replace the integer division identified by "div" by the polynomial "s".
+ * The integer division is assumed not to appear in the definition
+ * of any other integer divisions.
+ */
+static __isl_give isl_qpolynomial *substitute_div(
+ __isl_take isl_qpolynomial *qp,
+ int div, __isl_take struct isl_upoly *s)
{
- struct isl_qpolynomial *qp;
- struct isl_upoly_cst *cst;
+ int i;
+ int total;
+ int *reordering;
+
+ if (!qp || !s)
+ goto error;
- qp = isl_qpolynomial_alloc(dim, 0);
+ qp = isl_qpolynomial_cow(qp);
if (!qp)
- return NULL;
+ goto error;
- qp->upoly = isl_upoly_zero(dim->ctx);
+ total = isl_dim_total(qp->dim);
+ qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
if (!qp->upoly)
goto error;
- cst = isl_upoly_as_cst(qp->upoly);
- isl_int_set(cst->n, n);
- isl_int_set(cst->d, d);
+ reordering = isl_alloc_array(qp->dim->ctx, int, total + qp->div->n_row);
+ if (!reordering)
+ goto error;
+ for (i = 0; i < total + div; ++i)
+ reordering[i] = i;
+ for (i = total + div + 1; i < total + qp->div->n_row; ++i)
+ reordering[i] = i - 1;
+ qp->div = isl_mat_drop_rows(qp->div, div, 1);
+ qp->div = isl_mat_drop_cols(qp->div, 2 + total + div, 1);
+ qp->upoly = reorder(qp->upoly, reordering);
+ free(reordering);
+
+ if (!qp->upoly || !qp->div)
+ goto error;
+
+ isl_upoly_free(s);
return qp;
error:
isl_qpolynomial_free(qp);
+ isl_upoly_free(s);
return NULL;
}
-static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
+/* Replace all integer divisions [e/d] that turn out to not actually be integer
+ * divisions because d is equal to 1 by their definition, i.e., e.
+ */
+static __isl_give isl_qpolynomial *substitute_non_divs(
+ __isl_take isl_qpolynomial *qp)
{
- struct isl_upoly_rec *rec;
- int i;
-
- if (!up)
- return -1;
-
- if (isl_upoly_is_cst(up))
- return 0;
+ int i, j;
+ int total;
+ struct isl_upoly *s;
- if (up->var < d)
- active[up->var] = 1;
+ if (!qp)
+ return NULL;
- rec = isl_upoly_as_rec(up);
- for (i = 0; i < rec->n; ++i)
- if (up_set_active(rec->p[i], active, d) < 0)
- return -1;
+ total = isl_dim_total(qp->dim);
+ for (i = 0; qp && i < qp->div->n_row; ++i) {
+ if (!isl_int_is_one(qp->div->row[i][0]))
+ continue;
+ for (j = i + 1; j < qp->div->n_row; ++j) {
+ if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
+ continue;
+ isl_seq_combine(qp->div->row[j] + 1,
+ qp->div->ctx->one, qp->div->row[j] + 1,
+ qp->div->row[j][2 + total + i],
+ qp->div->row[i] + 1, 1 + total + i);
+ isl_int_set_si(qp->div->row[j][2 + total + i], 0);
+ normalize_div(qp, j);
+ }
+ s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
+ qp->div->row[i][0], qp->div->n_col - 1);
+ qp = substitute_div(qp, i, s);
+ --i;
+ }
- return 0;
+ return qp;
}
-static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
+/* Reduce the coefficients of div "div" to lie in the interval [0, d-1],
+ * with d the denominator. When replacing the coefficient e of x by
+ * d * frac(e/d) = e - d * floor(e/d), we are subtracting d * floor(e/d) * x
+ * inside the division, so we need to add floor(e/d) * x outside.
+ * That is, we replace q by q' + floor(e/d) * x and we therefore need
+ * to adjust the coefficient of x in each later div that depends on the
+ * current div "div" and also in the affine expression "aff"
+ * (if it too depends on "div").
+ */
+static void reduce_div(__isl_keep isl_qpolynomial *qp, int div,
+ __isl_keep isl_vec *aff)
{
int i, j;
- int d = isl_dim_total(qp->dim);
+ isl_int v;
+ unsigned total = qp->div->n_col - qp->div->n_row - 2;
- if (!qp || !active)
- return -1;
-
- for (i = 0; i < d; ++i)
- for (j = 0; j < qp->div->n_row; ++j) {
- if (isl_int_is_zero(qp->div->row[j][2 + i]))
+ isl_int_init(v);
+ for (i = 0; i < 1 + total + div; ++i) {
+ if (isl_int_is_nonneg(qp->div->row[div][1 + i]) &&
+ isl_int_lt(qp->div->row[div][1 + i], qp->div->row[div][0]))
+ continue;
+ isl_int_fdiv_q(v, qp->div->row[div][1 + i], qp->div->row[div][0]);
+ isl_int_fdiv_r(qp->div->row[div][1 + i],
+ qp->div->row[div][1 + i], qp->div->row[div][0]);
+ if (!isl_int_is_zero(aff->el[1 + total + div]))
+ isl_int_addmul(aff->el[i], v, aff->el[1 + total + div]);
+ for (j = div + 1; j < qp->div->n_row; ++j) {
+ if (isl_int_is_zero(qp->div->row[j][2 + total + div]))
continue;
- active[i] = 1;
+ isl_int_addmul(qp->div->row[j][1 + i],
+ v, qp->div->row[j][2 + total + div]);
+ }
+ }
+ isl_int_clear(v);
+}
+
+/* Check if the last non-zero coefficient is bigger that half of the
+ * denominator. If so, we will invert the div to further reduce the number
+ * of distinct divs that may appear.
+ * If the last non-zero coefficient is exactly half the denominator,
+ * then we continue looking for earlier coefficients that are bigger
+ * than half the denominator.
+ */
+static int needs_invert(__isl_keep isl_mat *div, int row)
+{
+ int i;
+ int cmp;
+
+ for (i = div->n_col - 1; i >= 1; --i) {
+ if (isl_int_is_zero(div->row[row][i]))
+ continue;
+ isl_int_mul_ui(div->row[row][i], div->row[row][i], 2);
+ cmp = isl_int_cmp(div->row[row][i], div->row[row][0]);
+ isl_int_divexact_ui(div->row[row][i], div->row[row][i], 2);
+ if (cmp)
+ return cmp > 0;
+ if (i == 1)
+ return 1;
+ }
+
+ return 0;
+}
+
+/* Replace div "div" q = [e/d] by -[(-e+(d-1))/d].
+ * We only invert the coefficients of e (and the coefficient of q in
+ * later divs and in "aff"). After calling this function, the
+ * coefficients of e should be reduced again.
+ */
+static void invert_div(__isl_keep isl_qpolynomial *qp, int div,
+ __isl_keep isl_vec *aff)
+{
+ unsigned total = qp->div->n_col - qp->div->n_row - 2;
+
+ isl_seq_neg(qp->div->row[div] + 1,
+ qp->div->row[div] + 1, qp->div->n_col - 1);
+ isl_int_sub_ui(qp->div->row[div][1], qp->div->row[div][1], 1);
+ isl_int_add(qp->div->row[div][1],
+ qp->div->row[div][1], qp->div->row[div][0]);
+ if (!isl_int_is_zero(aff->el[1 + total + div]))
+ isl_int_neg(aff->el[1 + total + div], aff->el[1 + total + div]);
+ isl_mat_col_mul(qp->div, 2 + total + div,
+ qp->div->ctx->negone, 2 + total + div);
+}
+
+/* Assuming "qp" is a monomial, reduce all its divs to have coefficients
+ * in the interval [0, d-1], with d the denominator and such that the
+ * last non-zero coefficient that is not equal to d/2 is smaller than d/2.
+ *
+ * After the reduction, some divs may have become redundant or identical,
+ * so we call substitute_non_divs and sort_divs. If these functions
+ * eliminate divs of merge * two or more divs into one, the coefficients
+ * of the enclosing divs may have to be reduced again, so we call
+ * ourselves recursively if the number of divs decreases.
+ */
+static __isl_give isl_qpolynomial *reduce_divs(__isl_take isl_qpolynomial *qp)
+{
+ int i, j;
+ isl_vec *aff = NULL;
+ struct isl_upoly *s;
+ unsigned n_div;
+
+ if (!qp)
+ return NULL;
+
+ aff = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
+ aff = isl_vec_clr(aff);
+ if (!aff)
+ goto error;
+
+ isl_int_set_si(aff->el[1 + qp->upoly->var], 1);
+
+ for (i = 0; i < qp->div->n_row; ++i) {
+ normalize_div(qp, i);
+ reduce_div(qp, i, aff);
+ if (needs_invert(qp->div, i)) {
+ invert_div(qp, i, aff);
+ reduce_div(qp, i, aff);
+ }
+ }
+
+ s = isl_upoly_from_affine(qp->div->ctx, aff->el,
+ qp->div->ctx->one, aff->size);
+ qp->upoly = isl_upoly_subs(qp->upoly, qp->upoly->var, 1, &s);
+ isl_upoly_free(s);
+ if (!qp->upoly)
+ goto error;
+
+ isl_vec_free(aff);
+
+ n_div = qp->div->n_row;
+ qp = substitute_non_divs(qp);
+ qp = sort_divs(qp);
+ if (qp && qp->div->n_row < n_div)
+ return reduce_divs(qp);
+
+ return qp;
+error:
+ isl_qpolynomial_free(qp);
+ isl_vec_free(aff);
+ return NULL;
+}
+
+/* Assumes each div only depends on earlier divs.
+ */
+__isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
+ int power)
+{
+ struct isl_qpolynomial *qp = NULL;
+ struct isl_upoly_rec *rec;
+ struct isl_upoly_cst *cst;
+ int i, d;
+ int pos;
+
+ if (!div)
+ return NULL;
+
+ d = div->line - div->bmap->div;
+
+ pos = isl_dim_total(div->bmap->dim) + d;
+ rec = isl_upoly_alloc_rec(div->ctx, pos, 1 + power);
+ qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
+ div->bmap->n_div, &rec->up);
+ if (!qp)
+ goto error;
+
+ for (i = 0; i < div->bmap->n_div; ++i)
+ isl_seq_cpy(qp->div->row[i], div->bmap->div[i], qp->div->n_col);
+
+ for (i = 0; i < 1 + power; ++i) {
+ rec->p[i] = isl_upoly_zero(div->ctx);
+ if (!rec->p[i])
+ goto error;
+ rec->n++;
+ }
+ cst = isl_upoly_as_cst(rec->p[power]);
+ isl_int_set_si(cst->n, 1);
+
+ isl_div_free(div);
+
+ qp = reduce_divs(qp);
+
+ return qp;
+error:
+ isl_qpolynomial_free(qp);
+ isl_div_free(div);
+ return NULL;
+}
+
+__isl_give isl_qpolynomial *isl_qpolynomial_div(__isl_take isl_div *div)
+{
+ return isl_qpolynomial_div_pow(div, 1);
+}
+
+__isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(__isl_take isl_dim *dim,
+ const isl_int n, const isl_int d)
+{
+ struct isl_qpolynomial *qp;
+ struct isl_upoly_cst *cst;
+
+ qp = isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
+ if (!qp)
+ return NULL;
+
+ cst = isl_upoly_as_cst(qp->upoly);
+ isl_int_set(cst->n, n);
+ isl_int_set(cst->d, d);
+
+ return qp;
+}
+
+static int up_set_active(__isl_keep struct isl_upoly *up, int *active, int d)
+{
+ struct isl_upoly_rec *rec;
+ int i;
+
+ if (!up)
+ return -1;
+
+ if (isl_upoly_is_cst(up))
+ return 0;
+
+ if (up->var < d)
+ active[up->var] = 1;
+
+ rec = isl_upoly_as_rec(up);
+ for (i = 0; i < rec->n; ++i)
+ if (up_set_active(rec->p[i], active, d) < 0)
+ return -1;
+
+ return 0;
+}
+
+static int set_active(__isl_keep isl_qpolynomial *qp, int *active)
+{
+ int i, j;
+ int d = isl_dim_total(qp->dim);
+
+ if (!qp || !active)
+ return -1;
+
+ for (i = 0; i < d; ++i)
+ for (j = 0; j < qp->div->n_row; ++j) {
+ if (isl_int_is_zero(qp->div->row[j][2 + i]))
+ continue;
+ active[i] = 1;
break;
}
return -1;
}
-int isl_qpolynomial_fold_involves_dims(__isl_keep isl_qpolynomial_fold *fold,
- enum isl_dim_type type, unsigned first, unsigned n)
-{
- int i;
-
- if (!fold)
- return -1;
- if (fold->n == 0 || n == 0)
- return 0;
-
- for (i = 0; i < fold->n; ++i) {
- int involves = isl_qpolynomial_involves_dims(fold->qp[i],
- type, first, n);
- if (involves < 0 || involves)
- return involves;
- }
- return 0;
-}
-
__isl_give struct isl_upoly *isl_upoly_drop(__isl_take struct isl_upoly *up,
unsigned first, unsigned n)
{
return NULL;
}
+__isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
+ __isl_take isl_qpolynomial *qp,
+ enum isl_dim_type type, unsigned pos, const char *s)
+{
+ qp = isl_qpolynomial_cow(qp);
+ if (!qp)
+ return NULL;
+ qp->dim = isl_dim_set_name(qp->dim, type, pos, s);
+ if (!qp->dim)
+ goto error;
+ return qp;
+error:
+ isl_qpolynomial_free(qp);
+ return NULL;
+}
+
__isl_give isl_qpolynomial *isl_qpolynomial_drop_dims(
__isl_take isl_qpolynomial *qp,
enum isl_dim_type type, unsigned first, unsigned n)
{
if (!qp)
return NULL;
- if (n == 0)
+ if (n == 0 && !isl_dim_get_tuple_name(qp->dim, type))
return qp;
qp = isl_qpolynomial_cow(qp);
return NULL;
}
-__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_drop_dims(
- __isl_take isl_qpolynomial_fold *fold,
- enum isl_dim_type type, unsigned first, unsigned n)
+__isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
+ __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
{
- int i;
+ int i, j, k;
+ isl_int denom;
+ unsigned total;
+ unsigned n_div;
+ struct isl_upoly *up;
- if (!fold)
- return NULL;
- if (n == 0)
- return fold;
+ if (!eq)
+ goto error;
+ if (eq->n_eq == 0) {
+ isl_basic_set_free(eq);
+ return qp;
+ }
- fold = isl_qpolynomial_fold_cow(fold);
- if (!fold)
- return NULL;
- fold->dim = isl_dim_drop(fold->dim, type, first, n);
- if (!fold->dim)
+ qp = isl_qpolynomial_cow(qp);
+ if (!qp)
+ goto error;
+ qp->div = isl_mat_cow(qp->div);
+ if (!qp->div)
+ goto error;
+
+ total = 1 + isl_dim_total(eq->dim);
+ n_div = eq->n_div;
+ isl_int_init(denom);
+ for (i = 0; i < eq->n_eq; ++i) {
+ j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
+ if (j < 0 || j == 0 || j >= total)
+ continue;
+
+ for (k = 0; k < qp->div->n_row; ++k) {
+ if (isl_int_is_zero(qp->div->row[k][1 + j]))
+ continue;
+ isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
+ &qp->div->row[k][0]);
+ normalize_div(qp, k);
+ }
+
+ if (isl_int_is_pos(eq->eq[i][j]))
+ isl_seq_neg(eq->eq[i], eq->eq[i], total);
+ isl_int_abs(denom, eq->eq[i][j]);
+ isl_int_set_si(eq->eq[i][j], 0);
+
+ up = isl_upoly_from_affine(qp->dim->ctx,
+ eq->eq[i], denom, total);
+ qp->upoly = isl_upoly_subs(qp->upoly, j - 1, 1, &up);
+ isl_upoly_free(up);
+ }
+ isl_int_clear(denom);
+
+ if (!qp->upoly)
+ goto error;
+
+ isl_basic_set_free(eq);
+
+ qp = substitute_non_divs(qp);
+ qp = sort_divs(qp);
+
+ return qp;
+error:
+ isl_basic_set_free(eq);
+ isl_qpolynomial_free(qp);
+ return NULL;
+}
+
+static __isl_give isl_basic_set *add_div_constraints(
+ __isl_take isl_basic_set *bset, __isl_take isl_mat *div)
+{
+ int i;
+ unsigned total;
+
+ if (!bset || !div)
goto error;
- for (i = 0; i < fold->n; ++i) {
- fold->qp[i] = isl_qpolynomial_drop_dims(fold->qp[i],
- type, first, n);
- if (!fold->qp[i])
+ bset = isl_basic_set_extend_constraints(bset, 0, 2 * div->n_row);
+ if (!bset)
+ goto error;
+ total = isl_basic_set_total_dim(bset);
+ for (i = 0; i < div->n_row; ++i)
+ if (isl_basic_set_add_div_constraints_var(bset,
+ total - div->n_row + i, div->row[i]) < 0)
goto error;
+
+ isl_mat_free(div);
+ return bset;
+error:
+ isl_mat_free(div);
+ isl_basic_set_free(bset);
+ return NULL;
+}
+
+/* Look for equalities among the variables shared by context and qp
+ * and the integer divisions of qp, if any.
+ * The equalities are then used to eliminate variables and/or integer
+ * divisions from qp.
+ */
+__isl_give isl_qpolynomial *isl_qpolynomial_gist(
+ __isl_take isl_qpolynomial *qp, __isl_take isl_set *context)
+{
+ isl_basic_set *aff;
+
+ if (!qp)
+ goto error;
+ if (qp->div->n_row > 0) {
+ isl_basic_set *bset;
+ context = isl_set_add_dims(context, isl_dim_set,
+ qp->div->n_row);
+ bset = isl_basic_set_universe(isl_set_get_dim(context));
+ bset = add_div_constraints(bset, isl_mat_copy(qp->div));
+ context = isl_set_intersect(context,
+ isl_set_from_basic_set(bset));
}
- return fold;
+ aff = isl_set_affine_hull(context);
+ return isl_qpolynomial_substitute_equalities(qp, aff);
error:
- isl_qpolynomial_fold_free(fold);
+ isl_qpolynomial_free(qp);
+ isl_set_free(context);
return NULL;
}
#define IS_ZERO is_zero
#undef FIELD
#define FIELD qp
-#undef ADD
-#define ADD add
#include <isl_pw_templ.c>
-#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
+#undef UNION
+#define UNION isl_union_pw_qpolynomial
+#undef PART
+#define PART isl_pw_qpolynomial
+#undef PARTS
+#define PARTS pw_qpolynomial
-#include <isl_pw_templ.c>
+#include <isl_union_templ.c>
int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
{
__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
__isl_take isl_pw_qpolynomial *pwqp)
{
- int i, j, n;
- struct isl_pw_qpolynomial *res;
- isl_set *set;
+ int i;
if (!pwqp)
return NULL;
return pwqp;
pwqp = isl_pw_qpolynomial_cow(pwqp);
+ if (!pwqp)
+ return NULL;
for (i = 0; i < pwqp->n; ++i) {
pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
isl_qpolynomial_free(qp);
isl_point_free(pnt);
- qp = isl_qpolynomial_alloc(dim, 0);
- if (!qp)
- isl_upoly_free(up);
- else
- qp->upoly = up;
-
- return qp;
+ return isl_qpolynomial_alloc(dim, 0, up);
error:
isl_qpolynomial_free(qp);
isl_point_free(pnt);
return cmp;
}
-static __isl_give isl_qpolynomial *qpolynomial_min(
+int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
+ __isl_keep isl_qpolynomial *qp2)
+{
+ struct isl_upoly_cst *cst1, *cst2;
+
+ if (!qp1 || !qp2)
+ return -1;
+ isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
+ isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
+ if (isl_qpolynomial_is_nan(qp1))
+ return -1;
+ if (isl_qpolynomial_is_nan(qp2))
+ return -1;
+ cst1 = isl_upoly_as_cst(qp1->upoly);
+ cst2 = isl_upoly_as_cst(qp2->upoly);
+
+ return isl_upoly_cmp(cst1, cst2) <= 0;
+}
+
+__isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
__isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
{
struct isl_upoly_cst *cst1, *cst2;
return NULL;
}
-static __isl_give isl_qpolynomial *qpolynomial_max(
+__isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
__isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
{
struct isl_upoly_cst *cst1, *cst2;
return NULL;
}
-int isl_qpolynomial_fold_is_equal(__isl_keep isl_qpolynomial_fold *fold1,
- __isl_keep isl_qpolynomial_fold *fold2)
+__isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
+ __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
+ unsigned first, unsigned n)
{
- int i;
+ unsigned total;
+ unsigned g_pos;
+ int *exp;
- if (!fold1 || !fold2)
- return -1;
+ if (n == 0)
+ return qp;
- if (fold1->n != fold2->n)
- return 0;
+ qp = isl_qpolynomial_cow(qp);
+ if (!qp)
+ return NULL;
- /* We probably want to sort the qps first... */
- for (i = 0; i < fold1->n; ++i) {
- int eq = isl_qpolynomial_is_equal(fold1->qp[i], fold2->qp[i]);
- if (eq < 0 || !eq)
- return eq;
- }
-
- return 1;
-}
+ isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
+ goto error);
-__isl_give isl_qpolynomial *isl_qpolynomial_fold_eval(
- __isl_take isl_qpolynomial_fold *fold, __isl_take isl_point *pnt)
-{
- isl_qpolynomial *qp;
+ g_pos = pos(qp->dim, type) + first;
- if (!fold || !pnt)
+ qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
+ if (!qp->div)
goto error;
- isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, fold->dim), goto error);
- isl_assert(pnt->dim->ctx,
- fold->type == isl_fold_max || fold->type == isl_fold_min,
- goto error);
- if (fold->n == 0)
- qp = isl_qpolynomial_zero(isl_dim_copy(fold->dim));
- else {
+ total = qp->div->n_col - 2;
+ if (total > g_pos) {
int i;
- qp = isl_qpolynomial_eval(isl_qpolynomial_copy(fold->qp[0]),
- isl_point_copy(pnt));
- for (i = 1; i < fold->n; ++i) {
- isl_qpolynomial *qp_i;
- qp_i = isl_qpolynomial_eval(
- isl_qpolynomial_copy(fold->qp[i]),
- isl_point_copy(pnt));
- if (fold->type == isl_fold_max)
- qp = qpolynomial_max(qp, qp_i);
- else
- qp = qpolynomial_min(qp, qp_i);
- }
+ exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
+ if (!exp)
+ goto error;
+ for (i = 0; i < total - g_pos; ++i)
+ exp[i] = i + n;
+ qp->upoly = expand(qp->upoly, exp, g_pos);
+ free(exp);
+ if (!qp->upoly)
+ goto error;
}
- isl_qpolynomial_fold_free(fold);
- isl_point_free(pnt);
+
+ qp->dim = isl_dim_insert(qp->dim, type, first, n);
+ if (!qp->dim)
+ goto error;
return qp;
error:
- isl_qpolynomial_fold_free(fold);
- isl_point_free(pnt);
+ isl_qpolynomial_free(qp);
return NULL;
}
+__isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
+ __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
+{
+ unsigned pos;
+
+ pos = isl_qpolynomial_dim(qp, type);
+
+ return isl_qpolynomial_insert_dims(qp, type, pos, n);
+}
+
+__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
+ __isl_take isl_pw_qpolynomial *pwqp,
+ enum isl_dim_type type, unsigned n)
+{
+ unsigned pos;
+
+ pos = isl_pw_qpolynomial_dim(pwqp, type);
+
+ return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
+}
+
static int *reordering_move(isl_ctx *ctx,
unsigned len, unsigned dst, unsigned src, unsigned n)
{
return reordering;
}
-static __isl_give struct isl_upoly *reorder(__isl_take struct isl_upoly *up,
- int *r)
-{
- int i;
- struct isl_upoly_rec *rec;
- struct isl_upoly *base;
- struct isl_upoly *res;
-
- if (isl_upoly_is_cst(up))
- return up;
-
- rec = isl_upoly_as_rec(up);
- if (!rec)
- goto error;
-
- isl_assert(up->ctx, rec->n >= 1, goto error);
-
- base = isl_upoly_pow(up->ctx, r[up->var], 1);
- res = reorder(isl_upoly_copy(rec->p[rec->n - 1]), r);
-
- for (i = rec->n - 2; i >= 0; --i) {
- res = isl_upoly_mul(res, isl_upoly_copy(base));
- res = isl_upoly_sum(res, reorder(isl_upoly_copy(rec->p[i]), r));
- }
-
- isl_upoly_free(base);
- isl_upoly_free(up);
-
- return res;
-error:
- isl_upoly_free(up);
- return NULL;
-}
-
-__isl_give isl_qpolynomial *isl_qpolynomial_move(__isl_take isl_qpolynomial *qp,
+__isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
+ __isl_take isl_qpolynomial *qp,
enum isl_dim_type dst_type, unsigned dst_pos,
enum isl_dim_type src_type, unsigned src_pos, unsigned n)
{
g_dst_pos -= n;
qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
- qp->div = sort_divs(qp->div);
if (!qp->div)
goto error;
+ qp = sort_divs(qp);
+ if (!qp)
+ goto error;
reordering = reordering_move(qp->dim->ctx,
qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
return NULL;
}
-__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_move(
- __isl_take isl_pw_qpolynomial *pwqp,
- enum isl_dim_type dst_type, unsigned dst_pos,
- enum isl_dim_type src_type, unsigned src_pos, unsigned n)
+__isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
+ isl_int *f, isl_int denom)
+{
+ struct isl_upoly *up;
+
+ if (!dim)
+ return NULL;
+
+ up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
+
+ return isl_qpolynomial_alloc(dim, 0, up);
+}
+
+__isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
+ __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
+{
+ isl_int denom;
+ isl_dim *dim;
+ struct isl_upoly *up;
+ isl_qpolynomial *qp;
+ int sgn;
+
+ if (!c)
+ return NULL;
+
+ isl_int_init(denom);
+
+ isl_constraint_get_coefficient(c, type, pos, &denom);
+ isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
+ sgn = isl_int_sgn(denom);
+ isl_int_abs(denom, denom);
+ up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
+ 1 + isl_constraint_dim(c, isl_dim_all));
+ if (sgn < 0)
+ isl_int_neg(denom, denom);
+ isl_constraint_set_coefficient(c, type, pos, denom);
+
+ dim = isl_dim_copy(c->bmap->dim);
+
+ isl_int_clear(denom);
+ isl_constraint_free(c);
+
+ qp = isl_qpolynomial_alloc(dim, 0, up);
+ if (sgn > 0)
+ qp = isl_qpolynomial_neg(qp);
+ return qp;
+}
+
+/* For each 0 <= i < "n", replace variable "first" + i of type "type"
+ * in "qp" by subs[i].
+ */
+__isl_give isl_qpolynomial *isl_qpolynomial_substitute(
+ __isl_take isl_qpolynomial *qp,
+ enum isl_dim_type type, unsigned first, unsigned n,
+ __isl_keep isl_qpolynomial **subs)
{
int i;
+ struct isl_upoly **ups;
- pwqp = isl_pw_qpolynomial_cow(pwqp);
- if (!pwqp)
+ if (n == 0)
+ return qp;
+
+ qp = isl_qpolynomial_cow(qp);
+ if (!qp)
return NULL;
+ for (i = 0; i < n; ++i)
+ if (!subs[i])
+ goto error;
+
+ isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
+ goto error);
+
+ for (i = 0; i < n; ++i)
+ isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
+ goto error);
- pwqp->dim = isl_dim_move(pwqp->dim,
- dst_type, dst_pos, src_type, src_pos, n);
- if (!pwqp->dim)
+ isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
+ for (i = 0; i < n; ++i)
+ isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
+
+ first += pos(qp->dim, type);
+
+ ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
+ if (!ups)
goto error;
+ for (i = 0; i < n; ++i)
+ ups[i] = subs[i]->upoly;
- for (i = 0; i < pwqp->n; ++i) {
- pwqp->p[i].set = isl_set_move(pwqp->p[i].set, dst_type, dst_pos,
- src_type, src_pos, n);
- if (!pwqp->p[i].set)
- goto error;
- pwqp->p[i].qp = isl_qpolynomial_move(pwqp->p[i].qp,
- dst_type, dst_pos, src_type, src_pos, n);
- if (!pwqp->p[i].qp)
+ qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
+
+ free(ups);
+
+ if (!qp->upoly)
+ goto error;
+
+ return qp;
+error:
+ isl_qpolynomial_free(qp);
+ return NULL;
+}
+
+/* Extend "bset" with extra set dimensions for each integer division
+ * in "qp" and then call "fn" with the extended bset and the polynomial
+ * that results from replacing each of the integer divisions by the
+ * corresponding extra set dimension.
+ */
+int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
+ __isl_keep isl_basic_set *bset,
+ int (*fn)(__isl_take isl_basic_set *bset,
+ __isl_take isl_qpolynomial *poly, void *user), void *user)
+{
+ isl_dim *dim;
+ isl_mat *div;
+ isl_qpolynomial *poly;
+
+ if (!qp || !bset)
+ goto error;
+ if (qp->div->n_row == 0)
+ return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
+ user);
+
+ div = isl_mat_copy(qp->div);
+ dim = isl_dim_copy(qp->dim);
+ dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
+ poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
+ bset = isl_basic_set_copy(bset);
+ bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
+ bset = add_div_constraints(bset, div);
+
+ return fn(bset, poly, user);
+error:
+ return -1;
+}
+
+/* Return total degree in variables first (inclusive) up to last (exclusive).
+ */
+int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
+{
+ int deg = -1;
+ int i;
+ struct isl_upoly_rec *rec;
+
+ if (!up)
+ return -2;
+ if (isl_upoly_is_zero(up))
+ return -1;
+ if (isl_upoly_is_cst(up) || up->var < first)
+ return 0;
+
+ rec = isl_upoly_as_rec(up);
+ if (!rec)
+ return -2;
+
+ for (i = 0; i < rec->n; ++i) {
+ int d;
+
+ if (isl_upoly_is_zero(rec->p[i]))
+ continue;
+ d = isl_upoly_degree(rec->p[i], first, last);
+ if (up->var < last)
+ d += i;
+ if (d > deg)
+ deg = d;
+ }
+
+ return deg;
+}
+
+/* Return total degree in set variables.
+ */
+int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
+{
+ unsigned ovar;
+ unsigned nvar;
+
+ if (!poly)
+ return -2;
+
+ ovar = isl_dim_offset(poly->dim, isl_dim_set);
+ nvar = isl_dim_size(poly->dim, isl_dim_set);
+ return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
+}
+
+__isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
+ unsigned pos, int deg)
+{
+ int i;
+ struct isl_upoly_rec *rec;
+
+ if (!up)
+ return NULL;
+
+ if (isl_upoly_is_cst(up) || up->var < pos) {
+ if (deg == 0)
+ return isl_upoly_copy(up);
+ else
+ return isl_upoly_zero(up->ctx);
+ }
+
+ rec = isl_upoly_as_rec(up);
+ if (!rec)
+ return NULL;
+
+ if (up->var == pos) {
+ if (deg < rec->n)
+ return isl_upoly_copy(rec->p[deg]);
+ else
+ return isl_upoly_zero(up->ctx);
+ }
+
+ up = isl_upoly_copy(up);
+ up = isl_upoly_cow(up);
+ rec = isl_upoly_as_rec(up);
+ if (!rec)
+ goto error;
+
+ for (i = 0; i < rec->n; ++i) {
+ struct isl_upoly *t;
+ t = isl_upoly_coeff(rec->p[i], pos, deg);
+ if (!t)
goto error;
+ isl_upoly_free(rec->p[i]);
+ rec->p[i] = t;
}
- return pwqp;
+ return up;
error:
- isl_pw_qpolynomial_free(pwqp);
+ isl_upoly_free(up);
return NULL;
}
-__isl_give isl_dim *isl_pw_qpolynomial_get_dim(
- __isl_keep isl_pw_qpolynomial *pwqp)
+/* Return coefficient of power "deg" of variable "t_pos" of type "type".
+ */
+__isl_give isl_qpolynomial *isl_qpolynomial_coeff(
+ __isl_keep isl_qpolynomial *qp,
+ enum isl_dim_type type, unsigned t_pos, int deg)
{
- if (!pwqp)
+ unsigned g_pos;
+ struct isl_upoly *up;
+ isl_qpolynomial *c;
+
+ if (!qp)
return NULL;
- return isl_dim_copy(pwqp->dim);
+ isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
+ return NULL);
+
+ g_pos = pos(qp->dim, type) + t_pos;
+ up = isl_upoly_coeff(qp->upoly, g_pos, deg);
+
+ c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
+ if (!c)
+ return NULL;
+ isl_mat_free(c->div);
+ c->div = isl_mat_copy(qp->div);
+ if (!c->div)
+ goto error;
+ return c;
+error:
+ isl_qpolynomial_free(c);
+ return NULL;
}
-unsigned isl_pw_qpolynomial_dim(__isl_keep isl_pw_qpolynomial *pwqp,
- enum isl_dim_type type)
+/* Homogenize the polynomial in the variables first (inclusive) up to
+ * last (exclusive) by inserting powers of variable first.
+ * Variable first is assumed not to appear in the input.
+ */
+__isl_give struct isl_upoly *isl_upoly_homogenize(
+ __isl_take struct isl_upoly *up, int deg, int target,
+ int first, int last)
+{
+ int i;
+ struct isl_upoly_rec *rec;
+
+ if (!up)
+ return NULL;
+ if (isl_upoly_is_zero(up))
+ return up;
+ if (deg == target)
+ return up;
+ if (isl_upoly_is_cst(up) || up->var < first) {
+ struct isl_upoly *hom;
+
+ hom = isl_upoly_var_pow(up->ctx, first, target - deg);
+ if (!hom)
+ goto error;
+ rec = isl_upoly_as_rec(hom);
+ rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
+
+ return hom;
+ }
+
+ up = isl_upoly_cow(up);
+ rec = isl_upoly_as_rec(up);
+ if (!rec)
+ goto error;
+
+ for (i = 0; i < rec->n; ++i) {
+ if (isl_upoly_is_zero(rec->p[i]))
+ continue;
+ rec->p[i] = isl_upoly_homogenize(rec->p[i],
+ up->var < last ? deg + i : i, target,
+ first, last);
+ if (!rec->p[i])
+ goto error;
+ }
+
+ return up;
+error:
+ isl_upoly_free(up);
+ return NULL;
+}
+
+/* Homogenize the polynomial in the set variables by introducing
+ * powers of an extra set variable at position 0.
+ */
+__isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
+ __isl_take isl_qpolynomial *poly)
{
- return pwqp ? isl_dim_size(pwqp->dim, type) : 0;
+ unsigned ovar;
+ unsigned nvar;
+ int deg = isl_qpolynomial_degree(poly);
+
+ if (deg < -1)
+ goto error;
+
+ poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
+ poly = isl_qpolynomial_cow(poly);
+ if (!poly)
+ goto error;
+
+ ovar = isl_dim_offset(poly->dim, isl_dim_set);
+ nvar = isl_dim_size(poly->dim, isl_dim_set);
+ poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
+ ovar, ovar + nvar);
+ if (!poly->upoly)
+ goto error;
+
+ return poly;
+error:
+ isl_qpolynomial_free(poly);
+ return NULL;
}
__isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
case isl_dim_out: return isl_dim_size(term->dim, type);
case isl_dim_div: return term->div->n_row;
case isl_dim_all: return isl_dim_total(term->dim) + term->div->n_row;
+ default: return 0;
}
}
return term ? 0 : -1;
}
-int isl_pw_qpolynomial_foreach_piece(__isl_keep isl_pw_qpolynomial *pwqp,
- int (*fn)(__isl_take isl_set *set, __isl_take isl_qpolynomial *qp,
- void *user), void *user)
+__isl_give isl_qpolynomial *isl_qpolynomial_from_term(__isl_take isl_term *term)
{
- int i;
+ struct isl_upoly *up;
+ isl_qpolynomial *qp;
+ int i, n;
- if (!pwqp)
- return -1;
-
- for (i = 0; i < pwqp->n; ++i)
- if (fn(isl_set_copy(pwqp->p[i].set),
- isl_qpolynomial_copy(pwqp->p[i].qp), user) < 0)
- return -1;
+ if (!term)
+ return NULL;
- return 0;
-}
+ n = isl_dim_total(term->dim) + term->div->n_row;
-static int any_divs(__isl_keep isl_set *set)
-{
- int i;
-
- if (!set)
- return -1;
+ up = isl_upoly_rat_cst(term->dim->ctx, term->n, term->d);
+ for (i = 0; i < n; ++i) {
+ if (!term->pow[i])
+ continue;
+ up = isl_upoly_mul(up,
+ isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
+ }
- for (i = 0; i < set->n; ++i)
- if (set->p[i]->n_div > 0)
- return 1;
+ qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
+ if (!qp)
+ goto error;
+ isl_mat_free(qp->div);
+ qp->div = isl_mat_copy(term->div);
+ if (!qp->div)
+ goto error;
- return 0;
+ isl_term_free(term);
+ return qp;
+error:
+ isl_qpolynomial_free(qp);
+ isl_term_free(term);
+ return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_lift(__isl_take isl_qpolynomial *qp,
__isl_take isl_dim *dim)
{
+ int i;
+ int extra;
+ unsigned total;
+
if (!qp || !dim)
goto error;
if (!qp)
goto error;
+ extra = isl_dim_size(dim, isl_dim_set) -
+ isl_dim_size(qp->dim, isl_dim_set);
+ total = isl_dim_total(qp->dim);
if (qp->div->n_row) {
- int i;
- int extra;
- unsigned total;
int *exp;
- extra = isl_dim_size(dim, isl_dim_set) -
- isl_dim_size(qp->dim, isl_dim_set);
- total = isl_dim_total(qp->dim);
exp = isl_alloc_array(qp->div->ctx, int, qp->div->n_row);
if (!exp)
goto error;
free(exp);
if (!qp->upoly)
goto error;
- qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
- if (!qp->div)
- goto error;
- for (i = 0; i < qp->div->n_row; ++i)
- isl_seq_clr(qp->div->row[i] + 2 + total, extra);
}
+ qp->div = isl_mat_insert_cols(qp->div, 2 + total, extra);
+ if (!qp->div)
+ goto error;
+ for (i = 0; i < qp->div->n_row; ++i)
+ isl_seq_clr(qp->div->row[i] + 2 + total, extra);
isl_dim_free(qp->dim);
qp->dim = dim;
return NULL;
}
-static int foreach_lifted_subset(__isl_take isl_set *set,
- __isl_take isl_qpolynomial *qp,
- int (*fn)(__isl_take isl_set *set, __isl_take isl_qpolynomial *qp,
- void *user), void *user)
+/* For each parameter or variable that does not appear in qp,
+ * first eliminate the variable from all constraints and then set it to zero.
+ */
+static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
+ __isl_keep isl_qpolynomial *qp)
{
+ int *active = NULL;
int i;
+ int d;
+ unsigned nparam;
+ unsigned nvar;
if (!set || !qp)
goto error;
- for (i = 0; i < set->n; ++i) {
- isl_set *lift;
- isl_qpolynomial *copy;
+ d = isl_dim_total(set->dim);
+ active = isl_calloc_array(set->ctx, int, d);
+ if (set_active(qp, active) < 0)
+ goto error;
- lift = isl_set_from_basic_set(isl_basic_set_copy(set->p[i]));
- lift = isl_set_lift(lift);
+ for (i = 0; i < d; ++i)
+ if (!active[i])
+ break;
- copy = isl_qpolynomial_copy(qp);
- copy = isl_qpolynomial_lift(copy, isl_set_get_dim(lift));
+ if (i == d) {
+ free(active);
+ return set;
+ }
- if (fn(lift, copy, user) < 0)
- goto error;
+ nparam = isl_dim_size(set->dim, isl_dim_param);
+ nvar = isl_dim_size(set->dim, isl_dim_set);
+ for (i = 0; i < nparam; ++i) {
+ if (active[i])
+ continue;
+ set = isl_set_eliminate(set, isl_dim_param, i, 1);
+ set = isl_set_fix_si(set, isl_dim_param, i, 0);
+ }
+ for (i = 0; i < nvar; ++i) {
+ if (active[nparam + i])
+ continue;
+ set = isl_set_eliminate(set, isl_dim_set, i, 1);
+ set = isl_set_fix_si(set, isl_dim_set, i, 0);
}
- isl_set_free(set);
- isl_qpolynomial_free(qp);
+ free(active);
- return 0;
+ return set;
error:
+ free(active);
isl_set_free(set);
- isl_qpolynomial_free(qp);
- return -1;
+ return NULL;
}
-int isl_pw_qpolynomial_foreach_lifted_piece(__isl_keep isl_pw_qpolynomial *pwqp,
- int (*fn)(__isl_take isl_set *set, __isl_take isl_qpolynomial *qp,
- void *user), void *user)
-{
- int i;
+struct isl_opt_data {
+ isl_qpolynomial *qp;
+ int first;
+ isl_qpolynomial *opt;
+ int max;
+};
- if (!pwqp)
- return -1;
+static int opt_fn(__isl_take isl_point *pnt, void *user)
+{
+ struct isl_opt_data *data = (struct isl_opt_data *)user;
+ isl_qpolynomial *val;
- for (i = 0; i < pwqp->n; ++i) {
- isl_set *set;
- isl_qpolynomial *qp;
-
- set = isl_set_copy(pwqp->p[i].set);
- qp = isl_qpolynomial_copy(pwqp->p[i].qp);
- if (!any_divs(set)) {
- if (fn(set, qp, user) < 0)
- return -1;
- continue;
- }
- if (foreach_lifted_subset(set, qp, fn, user) < 0)
- return -1;
+ val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
+ if (data->first) {
+ data->first = 0;
+ data->opt = val;
+ } else if (data->max) {
+ data->opt = isl_qpolynomial_max_cst(data->opt, val);
+ } else {
+ data->opt = isl_qpolynomial_min_cst(data->opt, val);
}
return 0;
}
-static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
- enum isl_fold type, __isl_take isl_dim *dim, int n)
+__isl_give isl_qpolynomial *isl_qpolynomial_opt_on_domain(
+ __isl_take isl_qpolynomial *qp, __isl_take isl_set *set, int max)
{
- isl_qpolynomial_fold *fold;
+ struct isl_opt_data data = { NULL, 1, NULL, max };
- if (!dim)
+ if (!set || !qp)
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)
+ if (isl_upoly_is_cst(qp->upoly)) {
+ isl_set_free(set);
+ return qp;
+ }
+
+ set = fix_inactive(set, qp);
+
+ data.qp = qp;
+ if (isl_set_foreach_point(set, opt_fn, &data) < 0)
goto error;
- fold->ref = 1;
- fold->size = n;
- fold->n = 0;
- fold->type = type;
- fold->dim = dim;
+ if (data.first)
+ data.opt = isl_qpolynomial_zero(isl_qpolynomial_get_dim(qp));
- return fold;
+ isl_set_free(set);
+ isl_qpolynomial_free(qp);
+ return data.opt;
error:
- isl_dim_free(dim);
+ isl_set_free(set);
+ isl_qpolynomial_free(qp);
+ isl_qpolynomial_free(data.opt);
return NULL;
}
-__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_empty(enum isl_fold type,
- __isl_take isl_dim *dim)
+__isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp,
+ __isl_take isl_morph *morph)
{
- return qpolynomial_fold_alloc(type, dim, 0);
-}
+ int i;
+ int n_sub;
+ isl_ctx *ctx;
+ struct isl_upoly *up;
+ unsigned n_div;
+ struct isl_upoly **subs;
+ isl_mat *mat;
-__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_alloc(
- enum isl_fold type, __isl_take isl_qpolynomial *qp)
-{
- isl_qpolynomial_fold *fold;
+ qp = isl_qpolynomial_cow(qp);
+ if (!qp || !morph)
+ goto error;
- if (!qp)
- return NULL;
+ ctx = qp->dim->ctx;
+ isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
- fold = qpolynomial_fold_alloc(type, isl_dim_copy(qp->dim), 1);
- if (!fold)
+ n_sub = morph->inv->n_row - 1;
+ if (morph->inv->n_row != morph->inv->n_col)
+ n_sub += qp->div->n_row;
+ subs = isl_calloc_array(ctx, struct isl_upoly *, n_sub);
+ if (!subs)
goto error;
- fold->qp[0] = qp;
- fold->n++;
+ for (i = 0; 1 + i < morph->inv->n_row; ++i)
+ subs[i] = isl_upoly_from_affine(ctx, morph->inv->row[1 + i],
+ morph->inv->row[0][0], morph->inv->n_col);
+ if (morph->inv->n_row != morph->inv->n_col)
+ for (i = 0; i < qp->div->n_row; ++i)
+ subs[morph->inv->n_row - 1 + i] =
+ isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
+
+ qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
+
+ for (i = 0; i < n_sub; ++i)
+ isl_upoly_free(subs[i]);
+ free(subs);
+
+ mat = isl_mat_diagonal(isl_mat_identity(ctx, 1), isl_mat_copy(morph->inv));
+ mat = isl_mat_diagonal(mat, isl_mat_identity(ctx, qp->div->n_row));
+ qp->div = isl_mat_product(qp->div, mat);
+ isl_dim_free(qp->dim);
+ qp->dim = isl_dim_copy(morph->ran->dim);
- return fold;
+ if (!qp->upoly || !qp->div || !qp->dim)
+ goto error;
+
+ isl_morph_free(morph);
+
+ return qp;
error:
- isl_qpolynomial_fold_free(fold);
isl_qpolynomial_free(qp);
+ isl_morph_free(morph);
return NULL;
}
-__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
- __isl_keep isl_qpolynomial_fold *fold)
+static int neg_entry(void **entry, void *user)
{
- if (!fold)
- return NULL;
+ isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
+
+ *pwqp = isl_pw_qpolynomial_neg(*pwqp);
- fold->ref++;
- return fold;
+ return *pwqp ? 0 : -1;
}
-__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_dup(
- __isl_keep isl_qpolynomial_fold *fold)
+__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_neg(
+ __isl_take isl_union_pw_qpolynomial *upwqp)
{
- int i;
- isl_qpolynomial_fold *dup;
-
- if (!fold)
- return NULL;
- dup = qpolynomial_fold_alloc(fold->type,
- isl_dim_copy(fold->dim), fold->n);
- if (!dup)
+ upwqp = isl_union_pw_qpolynomial_cow(upwqp);
+ if (!upwqp)
return NULL;
-
- for (i = 0; i < fold->n; ++i) {
- dup->qp[i] = isl_qpolynomial_copy(fold->qp[i]);
- if (!dup->qp[i])
- goto error;
- }
- return dup;
+ if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
+ &neg_entry, NULL) < 0)
+ goto error;
+
+ return upwqp;
error:
- isl_qpolynomial_fold_free(dup);
+ isl_union_pw_qpolynomial_free(upwqp);
return NULL;
}
-__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_cow(
- __isl_take isl_qpolynomial_fold *fold)
+__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
+ __isl_take isl_union_pw_qpolynomial *upwqp1,
+ __isl_take isl_union_pw_qpolynomial *upwqp2)
{
- if (!fold)
- return NULL;
-
- if (fold->ref == 1)
- return fold;
- fold->ref--;
- return isl_qpolynomial_fold_dup(fold);
+ return isl_union_pw_qpolynomial_add(upwqp1,
+ isl_union_pw_qpolynomial_neg(upwqp2));
}
-void isl_qpolynomial_fold_free(__isl_take isl_qpolynomial_fold *fold)
+static int mul_entry(void **entry, void *user)
{
- int i;
+ struct isl_union_pw_qpolynomial_match_bin_data *data = user;
+ uint32_t hash;
+ struct isl_hash_table_entry *entry2;
+ isl_pw_qpolynomial *pwpq = *entry;
+ int empty;
+
+ hash = isl_dim_get_hash(pwpq->dim);
+ entry2 = isl_hash_table_find(data->u2->dim->ctx, &data->u2->table,
+ hash, &has_dim, pwpq->dim, 0);
+ if (!entry2)
+ return 0;
- if (!fold)
- return;
- if (--fold->ref > 0)
- return;
+ pwpq = isl_pw_qpolynomial_copy(pwpq);
+ pwpq = isl_pw_qpolynomial_mul(pwpq,
+ isl_pw_qpolynomial_copy(entry2->data));
+
+ empty = isl_pw_qpolynomial_is_zero(pwpq);
+ if (empty < 0) {
+ isl_pw_qpolynomial_free(pwpq);
+ return -1;
+ }
+ if (empty) {
+ isl_pw_qpolynomial_free(pwpq);
+ return 0;
+ }
+
+ data->res = isl_union_pw_qpolynomial_add_pw_qpolynomial(data->res, pwpq);
- for (i = 0; i < fold->n; ++i)
- isl_qpolynomial_free(fold->qp[i]);
- isl_dim_free(fold->dim);
- free(fold);
+ return 0;
}
-int isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold *fold)
+__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
+ __isl_take isl_union_pw_qpolynomial *upwqp1,
+ __isl_take isl_union_pw_qpolynomial *upwqp2)
{
- if (!fold)
- return -1;
-
- return fold->n == 0;
+ return match_bin_op(upwqp1, upwqp2, &mul_entry);
}
-__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold(
- __isl_take isl_qpolynomial_fold *fold1,
- __isl_take isl_qpolynomial_fold *fold2)
+/* Reorder the columns of the given div definitions according to the
+ * given reordering.
+ */
+static __isl_give isl_mat *reorder_divs(__isl_take isl_mat *div,
+ __isl_take isl_reordering *r)
{
- int i;
- struct isl_qpolynomial_fold *res = NULL;
+ int i, j;
+ isl_mat *mat;
+ int extra;
- if (!fold1 || !fold2)
+ if (!div || !r)
goto error;
- 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);
+ extra = isl_dim_total(r->dim) + div->n_row - r->len;
+ mat = isl_mat_alloc(div->ctx, div->n_row, div->n_col + extra);
+ if (!mat)
+ goto error;
- if (isl_qpolynomial_fold_is_empty(fold1)) {
- isl_qpolynomial_fold_free(fold1);
- return fold2;
+ for (i = 0; i < div->n_row; ++i) {
+ isl_seq_cpy(mat->row[i], div->row[i], 2);
+ isl_seq_clr(mat->row[i] + 2, mat->n_col - 2);
+ for (j = 0; j < r->len; ++j)
+ isl_int_set(mat->row[i][2 + r->pos[j]],
+ div->row[i][2 + j]);
}
- if (isl_qpolynomial_fold_is_empty(fold2)) {
- isl_qpolynomial_fold_free(fold2);
- return fold1;
- }
+ isl_reordering_free(r);
+ isl_mat_free(div);
+ return mat;
+error:
+ isl_reordering_free(r);
+ isl_mat_free(div);
+ return NULL;
+}
- res = qpolynomial_fold_alloc(fold1->type, isl_dim_copy(fold1->dim),
- fold1->n + fold2->n);
- if (!res)
+/* Reorder the dimension of "qp" according to the given reordering.
+ */
+__isl_give isl_qpolynomial *isl_qpolynomial_realign(
+ __isl_take isl_qpolynomial *qp, __isl_take isl_reordering *r)
+{
+ qp = isl_qpolynomial_cow(qp);
+ if (!qp)
goto error;
- 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++;
- }
+ r = isl_reordering_extend(r, qp->div->n_row);
+ if (!r)
+ goto error;
- for (i = 0; i < fold2->n; ++i) {
- res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
- if (!res->qp[res->n])
- goto error;
- res->n++;
- }
+ qp->div = reorder_divs(qp->div, isl_reordering_copy(r));
+ if (!qp->div)
+ goto error;
- isl_qpolynomial_fold_free(fold1);
- isl_qpolynomial_fold_free(fold2);
+ qp->upoly = reorder(qp->upoly, r->pos);
+ if (!qp->upoly)
+ goto error;
- return res;
+ qp = isl_qpolynomial_reset_dim(qp, isl_dim_copy(r->dim));
+
+ isl_reordering_free(r);
+ return qp;
error:
- isl_qpolynomial_fold_free(res);
- isl_qpolynomial_fold_free(fold1);
- isl_qpolynomial_fold_free(fold2);
+ isl_qpolynomial_free(qp);
+ isl_reordering_free(r);
return NULL;
}
-__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_from_pw_qpolynomial(
- enum isl_fold type, __isl_take isl_pw_qpolynomial *pwqp)
+struct isl_split_periods_data {
+ int max_periods;
+ isl_pw_qpolynomial *res;
+};
+
+/* Create a slice where the integer division "div" has the fixed value "v".
+ * In particular, if "div" refers to floor(f/m), then create a slice
+ *
+ * m v <= f <= m v + (m - 1)
+ *
+ * or
+ *
+ * f - m v >= 0
+ * -f + m v + (m - 1) >= 0
+ */
+static __isl_give isl_set *set_div_slice(__isl_take isl_dim *dim,
+ __isl_keep isl_qpolynomial *qp, int div, isl_int v)
+{
+ int total;
+ isl_basic_set *bset = NULL;
+ int k;
+
+ if (!dim || !qp)
+ goto error;
+
+ total = isl_dim_total(dim);
+ bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0, 0, 2);
+
+ k = isl_basic_set_alloc_inequality(bset);
+ if (k < 0)
+ goto error;
+ isl_seq_cpy(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
+ isl_int_submul(bset->ineq[k][0], v, qp->div->row[div][0]);
+
+ k = isl_basic_set_alloc_inequality(bset);
+ if (k < 0)
+ goto error;
+ isl_seq_neg(bset->ineq[k], qp->div->row[div] + 1, 1 + total);
+ isl_int_addmul(bset->ineq[k][0], v, qp->div->row[div][0]);
+ isl_int_add(bset->ineq[k][0], bset->ineq[k][0], qp->div->row[div][0]);
+ isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
+
+ isl_dim_free(dim);
+ return isl_set_from_basic_set(bset);
+error:
+ isl_basic_set_free(bset);
+ isl_dim_free(dim);
+ return NULL;
+}
+
+static int split_periods(__isl_take isl_set *set,
+ __isl_take isl_qpolynomial *qp, void *user);
+
+/* Create a slice of the domain "set" such that integer division "div"
+ * has the fixed value "v" and add the results to data->res,
+ * replacing the integer division by "v" in "qp".
+ */
+static int set_div(__isl_take isl_set *set,
+ __isl_take isl_qpolynomial *qp, int div, isl_int v,
+ struct isl_split_periods_data *data)
{
int i;
- isl_pw_qpolynomial_fold *pwf;
+ int total;
+ isl_set *slice;
+ struct isl_upoly *cst;
- if (!pwqp)
- return NULL;
-
- pwf = isl_pw_qpolynomial_fold_alloc_(isl_dim_copy(pwqp->dim), pwqp->n);
+ slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
+ set = isl_set_intersect(set, slice);
- for (i = 0; i < pwqp->n; ++i)
- pwf = isl_pw_qpolynomial_fold_add_piece(pwf,
- isl_set_copy(pwqp->p[i].set),
- isl_qpolynomial_fold_alloc(type,
- isl_qpolynomial_copy(pwqp->p[i].qp)));
+ if (!qp)
+ goto error;
- isl_pw_qpolynomial_free(pwqp);
+ total = isl_dim_total(qp->dim);
- return pwf;
+ for (i = div + 1; i < qp->div->n_row; ++i) {
+ if (isl_int_is_zero(qp->div->row[i][2 + total + div]))
+ continue;
+ isl_int_addmul(qp->div->row[i][1],
+ qp->div->row[i][2 + total + div], v);
+ isl_int_set_si(qp->div->row[i][2 + total + div], 0);
+ }
+
+ cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
+ qp = substitute_div(qp, div, cst);
+
+ return split_periods(set, qp, data);
+error:
+ isl_set_free(set);
+ isl_qpolynomial_free(qp);
+ return -1;
}
-/* For each parameter or variable that does not appear in qp,
- * first eliminate the variable from all constraints and then set it to zero.
+/* Split the domain "set" such that integer division "div"
+ * has a fixed value (ranging from "min" to "max") on each slice
+ * and add the results to data->res.
*/
-static __isl_give isl_set *fix_inactive(__isl_take isl_set *set,
- __isl_keep isl_qpolynomial *qp)
+static int split_div(__isl_take isl_set *set,
+ __isl_take isl_qpolynomial *qp, int div, isl_int min, isl_int max,
+ struct isl_split_periods_data *data)
+{
+ for (; isl_int_le(min, max); isl_int_add_ui(min, min, 1)) {
+ isl_set *set_i = isl_set_copy(set);
+ isl_qpolynomial *qp_i = isl_qpolynomial_copy(qp);
+
+ if (set_div(set_i, qp_i, div, min, data) < 0)
+ goto error;
+ }
+ isl_set_free(set);
+ isl_qpolynomial_free(qp);
+ return 0;
+error:
+ isl_set_free(set);
+ isl_qpolynomial_free(qp);
+ return -1;
+}
+
+/* If "qp" refers to any integer division
+ * that can only attain "max_periods" distinct values on "set"
+ * then split the domain along those distinct values.
+ * Add the results (or the original if no splitting occurs)
+ * to data->res.
+ */
+static int split_periods(__isl_take isl_set *set,
+ __isl_take isl_qpolynomial *qp, void *user)
{
- int *active = NULL;
int i;
- int d;
- unsigned nparam;
- unsigned nvar;
+ isl_pw_qpolynomial *pwqp;
+ struct isl_split_periods_data *data;
+ isl_int min, max;
+ int total;
+ int r = 0;
+
+ data = (struct isl_split_periods_data *)user;
if (!set || !qp)
goto error;
- d = isl_dim_total(set->dim);
- active = isl_calloc_array(set->ctx, int, d);
- if (set_active(qp, active) < 0)
- goto error;
+ if (qp->div->n_row == 0) {
+ pwqp = isl_pw_qpolynomial_alloc(set, qp);
+ data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
+ return 0;
+ }
- for (i = 0; i < d; ++i)
- if (!active[i])
- break;
+ isl_int_init(min);
+ isl_int_init(max);
+ total = isl_dim_total(qp->dim);
+ for (i = 0; i < qp->div->n_row; ++i) {
+ enum isl_lp_result lp_res;
- if (i == d) {
- free(active);
- return set;
- }
+ if (isl_seq_first_non_zero(qp->div->row[i] + 2 + total,
+ qp->div->n_row) != -1)
+ continue;
- nparam = isl_dim_size(set->dim, isl_dim_param);
- nvar = isl_dim_size(set->dim, isl_dim_set);
- for (i = 0; i < nparam; ++i) {
- if (active[i])
+ lp_res = isl_set_solve_lp(set, 0, qp->div->row[i] + 1,
+ set->ctx->one, &min, NULL, NULL);
+ if (lp_res == isl_lp_error)
+ goto error2;
+ if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
continue;
- set = isl_set_eliminate(set, isl_dim_param, i, 1);
- set = isl_set_fix_si(set, isl_dim_param, i, 0);
- }
- for (i = 0; i < nvar; ++i) {
- if (active[i])
+ isl_int_fdiv_q(min, min, qp->div->row[i][0]);
+
+ lp_res = isl_set_solve_lp(set, 1, qp->div->row[i] + 1,
+ set->ctx->one, &max, NULL, NULL);
+ if (lp_res == isl_lp_error)
+ goto error2;
+ if (lp_res == isl_lp_unbounded || lp_res == isl_lp_empty)
continue;
- set = isl_set_eliminate(set, isl_dim_set, i, 1);
- set = isl_set_fix_si(set, isl_dim_set, i, 0);
+ isl_int_fdiv_q(max, max, qp->div->row[i][0]);
+
+ isl_int_sub(max, max, min);
+ if (isl_int_cmp_si(max, data->max_periods) < 0) {
+ isl_int_add(max, max, min);
+ break;
+ }
}
- free(active);
+ if (i < qp->div->n_row) {
+ r = split_div(set, qp, i, min, max, data);
+ } else {
+ pwqp = isl_pw_qpolynomial_alloc(set, qp);
+ data->res = isl_pw_qpolynomial_add_disjoint(data->res, pwqp);
+ }
- return set;
+ isl_int_clear(max);
+ isl_int_clear(min);
+
+ return r;
+error2:
+ isl_int_clear(max);
+ isl_int_clear(min);
error:
- free(active);
isl_set_free(set);
+ isl_qpolynomial_free(qp);
+ return -1;
+}
+
+/* If any quasi-polynomial in pwqp refers to any integer division
+ * that can only attain "max_periods" distinct values on its domain
+ * then split the domain along those distinct values.
+ */
+__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_split_periods(
+ __isl_take isl_pw_qpolynomial *pwqp, int max_periods)
+{
+ struct isl_split_periods_data data;
+
+ data.max_periods = max_periods;
+ data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
+
+ if (isl_pw_qpolynomial_foreach_piece(pwqp, &split_periods, &data) < 0)
+ goto error;
+
+ isl_pw_qpolynomial_free(pwqp);
+
+ return data.res;
+error:
+ isl_pw_qpolynomial_free(data.res);
+ isl_pw_qpolynomial_free(pwqp);
return NULL;
}
-struct isl_max_data {
+/* Construct a piecewise quasipolynomial that is constant on the given
+ * domain. In particular, it is
+ * 0 if cst == 0
+ * 1 if cst == 1
+ * infinity if cst == -1
+ */
+static __isl_give isl_pw_qpolynomial *constant_on_domain(
+ __isl_take isl_basic_set *bset, int cst)
+{
+ isl_dim *dim;
isl_qpolynomial *qp;
- int first;
- isl_qpolynomial *max;
-};
-static int max_fn(__isl_take isl_point *pnt, void *user)
+ if (!bset)
+ return NULL;
+
+ bset = isl_basic_map_domain(isl_basic_map_from_range(bset));
+ dim = isl_basic_set_get_dim(bset);
+ if (cst < 0)
+ qp = isl_qpolynomial_infty(dim);
+ else if (cst == 0)
+ qp = isl_qpolynomial_zero(dim);
+ else
+ qp = isl_qpolynomial_one(dim);
+ return isl_pw_qpolynomial_alloc(isl_set_from_basic_set(bset), qp);
+}
+
+/* Factor bset, call fn on each of the factors and return the product.
+ *
+ * If no factors can be found, simply call fn on the input.
+ * Otherwise, construct the factors based on the factorizer,
+ * call fn on each factor and compute the product.
+ */
+static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
+ __isl_take isl_basic_set *bset,
+ __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
{
- struct isl_max_data *data = (struct isl_max_data *)user;
- isl_qpolynomial *val;
+ int i, n;
+ isl_dim *dim;
+ isl_set *set;
+ isl_factorizer *f;
+ isl_qpolynomial *qp;
+ isl_pw_qpolynomial *pwqp;
+ unsigned nparam;
+ unsigned nvar;
- val = isl_qpolynomial_eval(isl_qpolynomial_copy(data->qp), pnt);
- if (data->first) {
- data->first = 0;
- data->max = val;
- } else {
- data->max = qpolynomial_max(data->max, val);
+ f = isl_basic_set_factorizer(bset);
+ if (!f)
+ goto error;
+ if (f->n_group == 0) {
+ isl_factorizer_free(f);
+ return fn(bset);
}
- return 0;
+ nparam = isl_basic_set_dim(bset, isl_dim_param);
+ nvar = isl_basic_set_dim(bset, isl_dim_set);
+
+ dim = isl_basic_set_get_dim(bset);
+ dim = isl_dim_domain(dim);
+ set = isl_set_universe(isl_dim_copy(dim));
+ qp = isl_qpolynomial_one(dim);
+ pwqp = isl_pw_qpolynomial_alloc(set, qp);
+
+ bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
+
+ for (i = 0, n = 0; i < f->n_group; ++i) {
+ isl_basic_set *bset_i;
+ isl_pw_qpolynomial *pwqp_i;
+
+ bset_i = isl_basic_set_copy(bset);
+ bset_i = isl_basic_set_drop_constraints_involving(bset_i,
+ nparam + n + f->len[i], nvar - n - f->len[i]);
+ bset_i = isl_basic_set_drop_constraints_involving(bset_i,
+ nparam, n);
+ bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
+ n + f->len[i], nvar - n - f->len[i]);
+ bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
+
+ pwqp_i = fn(bset_i);
+ pwqp = isl_pw_qpolynomial_mul(pwqp, pwqp_i);
+
+ n += f->len[i];
+ }
+
+ isl_basic_set_free(bset);
+ isl_factorizer_free(f);
+
+ return pwqp;
+error:
+ isl_basic_set_free(bset);
+ return NULL;
}
-static __isl_give isl_qpolynomial *guarded_qpolynomial_max(
- __isl_take isl_set *set, __isl_take isl_qpolynomial *qp)
+/* Factor bset, call fn on each of the factors and return the product.
+ * The function is assumed to evaluate to zero on empty domains,
+ * to one on zero-dimensional domains and to infinity on unbounded domains
+ * and will not be called explicitly on zero-dimensional or unbounded domains.
+ *
+ * We first check for some special cases and remove all equalities.
+ * Then we hand over control to compressed_multiplicative_call.
+ */
+__isl_give isl_pw_qpolynomial *isl_basic_set_multiplicative_call(
+ __isl_take isl_basic_set *bset,
+ __isl_give isl_pw_qpolynomial *(*fn)(__isl_take isl_basic_set *bset))
{
- struct isl_max_data data = { NULL, 1, NULL };
+ int bounded;
+ isl_morph *morph;
+ isl_pw_qpolynomial *pwqp;
+ unsigned orig_nvar, final_nvar;
- if (!set || !qp)
+ if (!bset)
+ return NULL;
+
+ if (isl_basic_set_fast_is_empty(bset))
+ return constant_on_domain(bset, 0);
+
+ orig_nvar = isl_basic_set_dim(bset, isl_dim_set);
+
+ if (orig_nvar == 0)
+ return constant_on_domain(bset, 1);
+
+ bounded = isl_basic_set_is_bounded(bset);
+ if (bounded < 0)
goto error;
+ if (!bounded)
+ return constant_on_domain(bset, -1);
- if (isl_upoly_is_cst(qp->upoly)) {
- isl_set_free(set);
+ if (bset->n_eq == 0)
+ return compressed_multiplicative_call(bset, fn);
+
+ morph = isl_basic_set_full_compression(bset);
+ bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
+
+ final_nvar = isl_basic_set_dim(bset, isl_dim_set);
+
+ pwqp = compressed_multiplicative_call(bset, fn);
+
+ morph = isl_morph_remove_dom_dims(morph, isl_dim_set, 0, orig_nvar);
+ morph = isl_morph_remove_ran_dims(morph, isl_dim_set, 0, final_nvar);
+ morph = isl_morph_inverse(morph);
+
+ pwqp = isl_pw_qpolynomial_morph(pwqp, morph);
+
+ return pwqp;
+error:
+ isl_basic_set_free(bset);
+ return NULL;
+}
+
+/* Drop all floors in "qp", turning each integer division [a/m] into
+ * a rational division a/m. If "down" is set, then the integer division
+ * is replaces by (a-(m-1))/m instead.
+ */
+static __isl_give isl_qpolynomial *qp_drop_floors(
+ __isl_take isl_qpolynomial *qp, int down)
+{
+ int i;
+ struct isl_upoly *s;
+
+ if (!qp)
+ return NULL;
+ if (qp->div->n_row == 0)
return qp;
+
+ qp = isl_qpolynomial_cow(qp);
+ if (!qp)
+ return NULL;
+
+ for (i = qp->div->n_row - 1; i >= 0; --i) {
+ if (down) {
+ isl_int_sub(qp->div->row[i][1],
+ qp->div->row[i][1], qp->div->row[i][0]);
+ isl_int_add_ui(qp->div->row[i][1],
+ qp->div->row[i][1], 1);
+ }
+ s = isl_upoly_from_affine(qp->dim->ctx, qp->div->row[i] + 1,
+ qp->div->row[i][0], qp->div->n_col - 1);
+ qp = substitute_div(qp, i, s);
+ if (!qp)
+ return NULL;
}
- set = fix_inactive(set, qp);
+ return qp;
+}
- data.qp = qp;
- if (isl_set_foreach_point(set, max_fn, &data) < 0)
+/* Drop all floors in "pwqp", turning each integer division [a/m] into
+ * a rational division a/m.
+ */
+static __isl_give isl_pw_qpolynomial *pwqp_drop_floors(
+ __isl_take isl_pw_qpolynomial *pwqp)
+{
+ int i;
+
+ if (!pwqp)
+ return NULL;
+
+ if (isl_pw_qpolynomial_is_zero(pwqp))
+ return pwqp;
+
+ pwqp = isl_pw_qpolynomial_cow(pwqp);
+ if (!pwqp)
+ return NULL;
+
+ for (i = 0; i < pwqp->n; ++i) {
+ pwqp->p[i].qp = qp_drop_floors(pwqp->p[i].qp, 0);
+ if (!pwqp->p[i].qp)
+ goto error;
+ }
+
+ return pwqp;
+error:
+ isl_pw_qpolynomial_free(pwqp);
+ return NULL;
+}
+
+/* Adjust all the integer divisions in "qp" such that they are at least
+ * one over the given orthant (identified by "signs"). This ensures
+ * that they will still be non-negative even after subtracting (m-1)/m.
+ *
+ * In particular, f is replaced by f' + v, changing f = [a/m]
+ * to f' = [(a - m v)/m].
+ * If the constant term k in a is smaller than m,
+ * the constant term of v is set to floor(k/m) - 1.
+ * For any other term, if the coefficient c and the variable x have
+ * the same sign, then no changes are needed.
+ * Otherwise, if the variable is positive (and c is negative),
+ * then the coefficient of x in v is set to floor(c/m).
+ * If the variable is negative (and c is positive),
+ * then the coefficient of x in v is set to ceil(c/m).
+ */
+static __isl_give isl_qpolynomial *make_divs_pos(__isl_take isl_qpolynomial *qp,
+ int *signs)
+{
+ int i, j;
+ int total;
+ isl_vec *v = NULL;
+ struct isl_upoly *s;
+
+ qp = isl_qpolynomial_cow(qp);
+ if (!qp)
+ return NULL;
+ qp->div = isl_mat_cow(qp->div);
+ if (!qp->div)
goto error;
- isl_set_free(set);
- isl_qpolynomial_free(qp);
- return data.max;
+ total = isl_dim_total(qp->dim);
+ v = isl_vec_alloc(qp->div->ctx, qp->div->n_col - 1);
+
+ for (i = 0; i < qp->div->n_row; ++i) {
+ isl_int *row = qp->div->row[i];
+ v = isl_vec_clr(v);
+ if (!v)
+ goto error;
+ if (isl_int_lt(row[1], row[0])) {
+ isl_int_fdiv_q(v->el[0], row[1], row[0]);
+ isl_int_sub_ui(v->el[0], v->el[0], 1);
+ isl_int_submul(row[1], row[0], v->el[0]);
+ }
+ for (j = 0; j < total; ++j) {
+ if (isl_int_sgn(row[2 + j]) * signs[j] >= 0)
+ continue;
+ if (signs[j] < 0)
+ isl_int_cdiv_q(v->el[1 + j], row[2 + j], row[0]);
+ else
+ isl_int_fdiv_q(v->el[1 + j], row[2 + j], row[0]);
+ isl_int_submul(row[2 + j], row[0], v->el[1 + j]);
+ }
+ for (j = 0; j < i; ++j) {
+ if (isl_int_sgn(row[2 + total + j]) >= 0)
+ continue;
+ isl_int_fdiv_q(v->el[1 + total + j],
+ row[2 + total + j], row[0]);
+ isl_int_submul(row[2 + total + j],
+ row[0], v->el[1 + total + j]);
+ }
+ for (j = i + 1; j < qp->div->n_row; ++j) {
+ if (isl_int_is_zero(qp->div->row[j][2 + total + i]))
+ continue;
+ isl_seq_combine(qp->div->row[j] + 1,
+ qp->div->ctx->one, qp->div->row[j] + 1,
+ qp->div->row[j][2 + total + i], v->el, v->size);
+ }
+ isl_int_set_si(v->el[1 + total + i], 1);
+ s = isl_upoly_from_affine(qp->dim->ctx, v->el,
+ qp->div->ctx->one, v->size);
+ qp->upoly = isl_upoly_subs(qp->upoly, total + i, 1, &s);
+ isl_upoly_free(s);
+ if (!qp->upoly)
+ goto error;
+ }
+
+ isl_vec_free(v);
+ return qp;
error:
- isl_set_free(set);
+ isl_vec_free(v);
isl_qpolynomial_free(qp);
- isl_qpolynomial_free(data.max);
return NULL;
}
-/* Compute the maximal value attained by the piecewise quasipolynomial
- * on its domain or zero if the domain is empty.
- * In the worst case, the domain is scanned completely,
- * so the domain is assumed to be bounded.
+struct isl_to_poly_data {
+ int sign;
+ isl_pw_qpolynomial *res;
+ isl_qpolynomial *qp;
+};
+
+/* Appoximate data->qp by a polynomial on the orthant identified by "signs".
+ * We first make all integer divisions positive and then split the
+ * quasipolynomials into terms with sign data->sign (the direction
+ * of the requested approximation) and terms with the opposite sign.
+ * In the first set of terms, each integer division [a/m] is
+ * overapproximated by a/m, while in the second it is underapproximated
+ * by (a-(m-1))/m.
*/
-__isl_give isl_qpolynomial *isl_pw_qpolynomial_max(
- __isl_take isl_pw_qpolynomial *pwqp)
+static int to_polynomial_on_orthant(__isl_take isl_set *orthant, int *signs,
+ void *user)
+{
+ struct isl_to_poly_data *data = user;
+ isl_pw_qpolynomial *t;
+ isl_qpolynomial *qp, *up, *down;
+
+ qp = isl_qpolynomial_copy(data->qp);
+ qp = make_divs_pos(qp, signs);
+
+ up = isl_qpolynomial_terms_of_sign(qp, signs, data->sign);
+ up = qp_drop_floors(up, 0);
+ down = isl_qpolynomial_terms_of_sign(qp, signs, -data->sign);
+ down = qp_drop_floors(down, 1);
+
+ isl_qpolynomial_free(qp);
+ qp = isl_qpolynomial_add(up, down);
+
+ t = isl_pw_qpolynomial_alloc(orthant, qp);
+ data->res = isl_pw_qpolynomial_add_disjoint(data->res, t);
+
+ return 0;
+}
+
+/* Approximate each quasipolynomial by a polynomial. If "sign" is positive,
+ * the polynomial will be an overapproximation. If "sign" is negative,
+ * it will be an underapproximation. If "sign" is zero, the approximation
+ * will lie somewhere in between.
+ *
+ * In particular, is sign == 0, we simply drop the floors, turning
+ * the integer divisions into rational divisions.
+ * Otherwise, we split the domains into orthants, make all integer divisions
+ * positive and then approximate each [a/m] by either a/m or (a-(m-1))/m,
+ * depending on the requested sign and the sign of the term in which
+ * the integer division appears.
+ */
+__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
+ __isl_take isl_pw_qpolynomial *pwqp, int sign)
{
int i;
- isl_qpolynomial *max;
+ struct isl_to_poly_data data;
+
+ if (sign == 0)
+ return pwqp_drop_floors(pwqp);
if (!pwqp)
return NULL;
- if (pwqp->n == 0) {
- isl_dim *dim = isl_dim_copy(pwqp->dim);
- isl_pw_qpolynomial_free(pwqp);
- return isl_qpolynomial_zero(dim);
- }
+ data.sign = sign;
+ data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
- max = guarded_qpolynomial_max(isl_set_copy(pwqp->p[0].set),
- isl_qpolynomial_copy(pwqp->p[0].qp));
- for (i = 1; i < pwqp->n; ++i) {
- isl_qpolynomial *max_i;
- max_i = guarded_qpolynomial_max(isl_set_copy(pwqp->p[i].set),
- isl_qpolynomial_copy(pwqp->p[i].qp));
- max = qpolynomial_max(max, max_i);
+ for (i = 0; i < pwqp->n; ++i) {
+ if (pwqp->p[i].qp->div->n_row == 0) {
+ isl_pw_qpolynomial *t;
+ t = isl_pw_qpolynomial_alloc(
+ isl_set_copy(pwqp->p[i].set),
+ isl_qpolynomial_copy(pwqp->p[i].qp));
+ data.res = isl_pw_qpolynomial_add_disjoint(data.res, t);
+ continue;
+ }
+ data.qp = pwqp->p[i].qp;
+ if (isl_set_foreach_orthant(pwqp->p[i].set,
+ &to_polynomial_on_orthant, &data) < 0)
+ goto error;
}
isl_pw_qpolynomial_free(pwqp);
- return max;
+
+ return data.res;
+error:
+ isl_pw_qpolynomial_free(pwqp);
+ isl_pw_qpolynomial_free(data.res);
+ return NULL;
+}
+
+static int poly_entry(void **entry, void *user)
+{
+ int *sign = user;
+ isl_pw_qpolynomial **pwqp = (isl_pw_qpolynomial **)entry;
+
+ *pwqp = isl_pw_qpolynomial_to_polynomial(*pwqp, *sign);
+
+ return *pwqp ? 0 : -1;
+}
+
+__isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_to_polynomial(
+ __isl_take isl_union_pw_qpolynomial *upwqp, int sign)
+{
+ upwqp = isl_union_pw_qpolynomial_cow(upwqp);
+ if (!upwqp)
+ return NULL;
+
+ if (isl_hash_table_foreach(upwqp->dim->ctx, &upwqp->table,
+ &poly_entry, &sign) < 0)
+ goto error;
+
+ return upwqp;
+error:
+ isl_union_pw_qpolynomial_free(upwqp);
+ return NULL;
}
projects / platform / upstream / isl.git / blobdiff