#include <stdlib.h>
#include <isl_factorization.h>
-#include <isl_lp.h>
-#include <isl_seq.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_mat_private.h>
+#include <isl_range.h>
static unsigned pos(__isl_keep isl_dim *dim, enum isl_dim_type type)
{
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, __isl_take struct isl_upoly *up)
{
free(qp);
}
-__isl_give struct isl_upoly *isl_upoly_pow(isl_ctx *ctx, int pos, int power)
+__isl_give struct isl_upoly *isl_upoly_var_pow(isl_ctx *ctx, int pos, int power)
{
int i;
struct isl_upoly *up;
isl_assert(up->ctx, rec->n >= 1, goto error);
- base = isl_upoly_pow(up->ctx, r[up->var], 1);
+ 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) {
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++;
__isl_take isl_qpolynomial *qp1,
__isl_take isl_qpolynomial *qp2)
{
- return isl_qpolynomial_add(qp1, 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,
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_pow(__isl_take isl_qpolynomial *qp,
+ unsigned power)
+{
+ qp = isl_qpolynomial_cow(qp);
+
+ if (!qp)
+ return NULL;
+
+ qp->upoly = isl_upoly_pow(qp->upoly, power);
+ if (!qp->upoly)
+ goto error;
+
+ return qp;
+error:
+ isl_qpolynomial_free(qp);
+ return NULL;
+}
+
__isl_give isl_qpolynomial *isl_qpolynomial_zero(__isl_take isl_dim *dim)
{
return isl_qpolynomial_alloc(dim, 0, isl_upoly_zero(dim->ctx));
upoly_update_den(qp->upoly, d);
}
-__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_ctx *ctx;
ctx = dim->ctx;
- return isl_qpolynomial_alloc(dim, 0, isl_upoly_pow(ctx, pos, power));
+ 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 struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
+ unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
+{
+ int i;
+ struct isl_upoly_rec *rec;
+ struct isl_upoly *base, *res;
+
+ if (!up)
+ return NULL;
+
+ if (isl_upoly_is_cst(up))
+ return up;
+
+ if (up->var < first)
+ return up;
+
+ rec = isl_upoly_as_rec(up);
+ if (!rec)
+ goto error;
+
+ isl_assert(up->ctx, rec->n >= 1, goto error);
+
+ 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_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;
+}
+
+/* Remove common factor of non-constant terms and denominator.
+ */
+static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
+{
+ 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);
+}
+
+/* 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)
+{
+ int i;
+ int total;
+ int *reordering;
+
+ if (!qp || !s)
+ goto error;
+
+ qp = isl_qpolynomial_cow(qp);
+ if (!qp)
+ goto error;
+
+ total = isl_dim_total(qp->dim);
+ qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &s);
+ if (!qp->upoly)
+ goto error;
+
+ 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;
+}
+
+/* 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)
+{
+ int i, j;
+ int total;
+ struct isl_upoly *s;
+
+ if (!qp)
+ return NULL;
+
+ 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 qp;
+}
+
+/* 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;
+ isl_int v;
+ unsigned total = qp->div->n_col - qp->div->n_row - 2;
+
+ 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;
+ 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;
+ int i, d;
int pos;
if (!div)
return NULL;
- isl_assert(div->ctx, div->bmap->n_div == 1, goto error);
- pos = isl_dim_total(div->bmap->dim);
+ 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), 1,
- &rec->up);
+ qp = isl_qpolynomial_alloc(isl_basic_map_get_dim(div->bmap),
+ div->bmap->n_div, &rec->up);
if (!qp)
goto error;
- 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);
+ 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);
isl_div_free(div);
+ qp = reduce_divs(qp);
+
return qp;
error:
isl_qpolynomial_free(qp);
if (!qp->dim)
goto error;
- if (type == isl_dim_set)
- first += isl_dim_size(qp->dim, isl_dim_param);
-
- qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
- if (!qp->div)
- goto error;
-
- qp->upoly = isl_upoly_drop(qp->upoly, first, n);
- if (!qp->upoly)
- goto error;
-
- return qp;
-error:
- isl_qpolynomial_free(qp);
- return NULL;
-}
-
-__isl_give struct isl_upoly *isl_upoly_subs(__isl_take struct isl_upoly *up,
- unsigned first, unsigned n, __isl_keep struct isl_upoly **subs)
-{
- int i;
- struct isl_upoly_rec *rec;
- struct isl_upoly *base, *res;
-
- if (!up)
- return NULL;
-
- if (isl_upoly_is_cst(up))
- return up;
-
- if (up->var < first)
- return up;
-
- rec = isl_upoly_as_rec(up);
- if (!rec)
- goto error;
-
- isl_assert(up->ctx, rec->n >= 1, goto error);
-
- if (up->var >= first + n)
- base = isl_upoly_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_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_pow(ctx, i, 1);
- t = isl_upoly_mul(c, t);
- up = isl_upoly_sum(up, t);
- }
-
- return up;
-}
+ if (type == isl_dim_set)
+ first += isl_dim_size(qp->dim, isl_dim_param);
-/* Remove common factor of non-constant terms and denominator.
- */
-static void normalize_div(__isl_keep isl_qpolynomial *qp, int div)
-{
- isl_ctx *ctx = qp->div->ctx;
- unsigned total = qp->div->n_col - 2;
+ qp->div = isl_mat_drop_cols(qp->div, 2 + first, n);
+ if (!qp->div)
+ goto error;
- 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;
+ qp->upoly = isl_upoly_drop(qp->upoly, first, n);
+ if (!qp->upoly)
+ goto error;
- 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);
+ return qp;
+error:
+ isl_qpolynomial_free(qp);
+ return NULL;
}
__isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
isl_basic_set_free(eq);
+ qp = substitute_non_divs(qp);
qp = sort_divs(qp);
return 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;
+
+ 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));
+ }
+
+ aff = isl_set_affine_hull(context);
+ return isl_qpolynomial_substitute_equalities(qp, aff);
+error:
+ isl_qpolynomial_free(qp);
+ isl_set_free(context);
+ return NULL;
+}
+
#undef PW
#define PW isl_pw_qpolynomial
#undef EL
return NULL;
}
-__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;
-
- 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;
-}
-
/* 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
if (isl_upoly_is_cst(up) || up->var < first) {
struct isl_upoly *hom;
- hom = isl_upoly_pow(up->ctx, first, target - deg);
+ hom = isl_upoly_var_pow(up->ctx, first, target - deg);
if (!hom)
goto error;
rec = isl_upoly_as_rec(hom);
if (!term->pow[i])
continue;
up = isl_upoly_mul(up,
- isl_upoly_pow(term->dim->ctx, i, term->pow[i]));
+ isl_upoly_var_pow(term->dim->ctx, i, term->pow[i]));
}
qp = isl_qpolynomial_alloc(isl_dim_copy(term->dim), term->div->n_row, up);
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_pow(ctx, morph->inv->n_col - 1 + i, 1);
+ isl_upoly_var_pow(ctx, morph->inv->n_col - 1 + i, 1);
qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
struct isl_split_periods_data *data)
{
int i;
- int *reordering;
+ int total;
isl_set *slice;
struct isl_upoly *cst;
- int total;
slice = set_div_slice(isl_set_get_dim(set), qp, div, v);
set = isl_set_intersect(set, slice);
- qp = isl_qpolynomial_cow(qp);
if (!qp)
goto error;
- cst = isl_upoly_rat_cst(qp->dim->ctx, v, qp->dim->ctx->one);
- if (!cst)
- goto error;
total = isl_dim_total(qp->dim);
- qp->upoly = isl_upoly_subs(qp->upoly, total + div, 1, &cst);
- isl_upoly_free(cst);
- if (!qp->upoly)
- goto error;
- 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);
+ 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);
+ }
- if (!qp->upoly || !qp->div)
- goto error;
+ 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_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;
+ }
+
+ return qp;
+}
+
+/* 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;
+
+ 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_vec_free(v);
+ isl_qpolynomial_free(qp);
+ return NULL;
+}
+
+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.
+ */
+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;
+ struct isl_to_poly_data data;
+
+ if (sign == 0)
+ return pwqp_drop_floors(pwqp);
+
+ if (!pwqp)
+ return NULL;
+
+ data.sign = sign;
+ data.res = isl_pw_qpolynomial_zero(isl_pw_qpolynomial_get_dim(pwqp));
+
+ 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 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