isl_qpolynomial: properly merge identical nested divs
[platform/upstream/isl.git] / isl_polynomial.c
index 444d8eb..92e8b2f 100644 (file)
 
 #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)
 {
@@ -1141,6 +1142,8 @@ static __isl_give isl_qpolynomial *sort_divs(__isl_take isl_qpolynomial *qp)
                    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++;
@@ -1641,28 +1644,52 @@ error:
        return NULL;
 }
 
+/* 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);
+}
+
 __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);
+               normalize_div(qp, i);
+       }
 
        for (i = 0; i < 1 + power; ++i) {
                rec->p[i] = isl_upoly_zero(div->ctx);
@@ -1675,6 +1702,8 @@ __isl_give isl_qpolynomial *isl_qpolynomial_div_pow(__isl_take isl_div *div,
 
        isl_div_free(div);
 
+       qp = sort_divs(qp);
+
        return qp;
 error:
        isl_qpolynomial_free(qp);
@@ -1816,6 +1845,22 @@ error:
        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)
@@ -1924,12 +1969,96 @@ __isl_give struct isl_upoly *isl_upoly_from_affine(isl_ctx *ctx, isl_int *f,
        return up;
 }
 
+/* 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;
+}
+
 __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
        __isl_take isl_qpolynomial *qp, __isl_take isl_basic_set *eq)
 {
        int i, j, k;
        isl_int denom;
        unsigned total;
+       unsigned n_div;
        struct isl_upoly *up;
 
        if (!eq)
@@ -1947,10 +2076,11 @@ __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
                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);
-               if (j < 0 || j == 0)
+               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) {
@@ -1958,8 +2088,7 @@ __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
                                continue;
                        isl_seq_elim(qp->div->row[k] + 1, eq->eq[i], j, total,
                                        &qp->div->row[k][0]);
-                       isl_seq_normalize(qp->div->ctx,
-                                         qp->div->row[k], 1 + total);
+                       normalize_div(qp, k);
                }
 
                if (isl_int_is_pos(eq->eq[i][j]))
@@ -1979,6 +2108,7 @@ __isl_give isl_qpolynomial *isl_qpolynomial_substitute_equalities(
 
        isl_basic_set_free(eq);
 
+       qp = substitute_non_divs(qp);
        qp = sort_divs(qp);
 
        return qp;
@@ -1988,6 +2118,62 @@ error:
        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
@@ -2544,32 +2730,6 @@ error:
        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
@@ -3254,6 +3414,7 @@ __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp
        __isl_take isl_morph *morph)
 {
        int i;
+       int n_sub;
        isl_ctx *ctx;
        struct isl_upoly *up;
        unsigned n_div;
@@ -3267,17 +3428,24 @@ __isl_give isl_qpolynomial *isl_qpolynomial_morph(__isl_take isl_qpolynomial *qp
        ctx = qp->dim->ctx;
        isl_assert(ctx, isl_dim_equal(qp->dim, morph->dom->dim), goto error);
 
-       subs = isl_calloc_array(ctx, struct isl_upoly *, morph->inv->n_row - 1);
+       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;
 
        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_pow(ctx, morph->inv->n_col - 1 + i, 1);
 
-       qp->upoly = isl_upoly_subs(qp->upoly, 0, morph->inv->n_row - 1, subs);
+       qp->upoly = isl_upoly_subs(qp->upoly, 0, n_sub, subs);
 
-       for (i = 0; 1 + i < morph->inv->n_row; ++i)
+       for (i = 0; i < n_sub; ++i)
                isl_upoly_free(subs[i]);
        free(subs);
 
@@ -3501,41 +3669,28 @@ static int set_div(__isl_take isl_set *set,
        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:
@@ -3745,9 +3900,9 @@ static __isl_give isl_pw_qpolynomial *compressed_multiplicative_call(
                            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_dims(bset_i,
-                           nparam + n + f->len[i], nvar - n - f->len[i]);
-               bset_i = isl_basic_set_drop_dims(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);
@@ -3819,3 +3974,269 @@ 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;
+}