isl_map_coalesce: avoid ignoring constraints redundant wrt implicit equalities

[isl.git] / isl_constraint.c

/*
 * Copyright 2008-2009 Katholieke Universiteit Leuven
 * Copyright 2010      INRIA Saclay
 *
 * Use of this software is governed by the MIT license
 *
 * Written by Sven Verdoolaege, K.U.Leuven, Departement
 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 
 */

#include <isl_map_private.h>
#include <isl_constraint_private.h>
#include <isl_space_private.h>
#include <isl_seq.h>
#include <isl_aff_private.h>
#include <isl_local_space_private.h>
#include <isl_val_private.h>
#include <isl_vec_private.h>

#include <bset_to_bmap.c>
#include <bset_from_bmap.c>

#undef EL_BASE
#define EL_BASE constraint

#include <isl_list_templ.c>

isl_ctx *isl_constraint_get_ctx(__isl_keep isl_constraint *c)
{
        return c ? isl_local_space_get_ctx(c->ls) : NULL;
}

static isl_size n(__isl_keep isl_constraint *c, enum isl_dim_type type)
{
        return isl_local_space_dim(c->ls, type);
}

static unsigned offset(__isl_keep isl_constraint *c, enum isl_dim_type type)
{
        return isl_local_space_offset(c->ls, type);
}

__isl_give isl_constraint *isl_constraint_alloc_vec(int eq,
        __isl_take isl_local_space *ls, __isl_take isl_vec *v)
{
        isl_constraint *constraint;

        if (!ls || !v)
                goto error;

        constraint = isl_alloc_type(isl_vec_get_ctx(v), isl_constraint);
        if (!constraint)
                goto error;

        constraint->ref = 1;
        constraint->eq = eq;
        constraint->ls = ls;
        constraint->v = v;

        return constraint;
error:
        isl_local_space_free(ls);
        isl_vec_free(v);
        return NULL;
}

__isl_give isl_constraint *isl_constraint_alloc(int eq,
        __isl_take isl_local_space *ls)
{
        isl_size dim;
        isl_ctx *ctx;
        isl_vec *v;

        dim = isl_local_space_dim(ls, isl_dim_all);
        if (dim < 0)
                ls = isl_local_space_free(ls);
        if (!ls)
                return NULL;

        ctx = isl_local_space_get_ctx(ls);
        v = isl_vec_alloc(ctx, 1 + dim);
        v = isl_vec_clr(v);
        return isl_constraint_alloc_vec(eq, ls, v);
}

__isl_give isl_constraint *isl_basic_map_constraint(
        __isl_take isl_basic_map *bmap, isl_int **line)
{
        int eq;
        isl_size dim;
        isl_ctx *ctx;
        isl_vec *v;
        isl_local_space *ls = NULL;
        isl_constraint *constraint;

        if (!bmap || !line)
                goto error;

        eq = line >= bmap->eq;

        ctx = isl_basic_map_get_ctx(bmap);
        ls = isl_basic_map_get_local_space(bmap);
        dim = isl_local_space_dim(ls, isl_dim_all);
        if (dim < 0)
                goto error;
        v = isl_vec_alloc(ctx, 1 + dim);
        if (!v)
                goto error;
        isl_seq_cpy(v->el, line[0], v->size);
        constraint = isl_constraint_alloc_vec(eq, ls, v);

        isl_basic_map_free(bmap);
        return constraint;
error:
        isl_local_space_free(ls);
        isl_basic_map_free(bmap);
        return NULL;
}

__isl_give isl_constraint *isl_basic_set_constraint(
        __isl_take isl_basic_set *bset, isl_int **line)
{
        return isl_basic_map_constraint(bset_to_bmap(bset), line);
}

__isl_give isl_constraint *isl_constraint_alloc_equality(
        __isl_take isl_local_space *ls)
{
        return isl_constraint_alloc(1, ls);
}

__isl_give isl_constraint *isl_constraint_alloc_inequality(
        __isl_take isl_local_space *ls)
{
        return isl_constraint_alloc(0, ls);
}

__isl_give isl_constraint *isl_constraint_dup(__isl_keep isl_constraint *c)
{
        if (!c)
                return NULL;

        return isl_constraint_alloc_vec(c->eq, isl_local_space_copy(c->ls),
                                                isl_vec_copy(c->v));
}

__isl_give isl_constraint *isl_constraint_cow(__isl_take isl_constraint *c)
{
        if (!c)
                return NULL;

        if (c->ref == 1)
                return c;
        c->ref--;
        return isl_constraint_dup(c);
}

__isl_give isl_constraint *isl_constraint_copy(
        __isl_keep isl_constraint *constraint)
{
        if (!constraint)
                return NULL;

        constraint->ref++;
        return constraint;
}

__isl_null isl_constraint *isl_constraint_free(__isl_take isl_constraint *c)
{
        if (!c)
                return NULL;

        if (--c->ref > 0)
                return NULL;

        isl_local_space_free(c->ls);
        isl_vec_free(c->v);
        free(c);

        return NULL;
}

/* Return the number of constraints in "bmap", i.e., the
 * number of times isl_basic_map_foreach_constraint will
 * call the callback.
 */
isl_size isl_basic_map_n_constraint(__isl_keep isl_basic_map *bmap)
{
        if (!bmap)
                return isl_size_error;

        return bmap->n_eq + bmap->n_ineq;
}

/* Return the number of constraints in "bset", i.e., the
 * number of times isl_basic_set_foreach_constraint will
 * call the callback.
 */
isl_size isl_basic_set_n_constraint(__isl_keep isl_basic_set *bset)
{
        return isl_basic_map_n_constraint(bset);
}

isl_stat isl_basic_map_foreach_constraint(__isl_keep isl_basic_map *bmap,
        isl_stat (*fn)(__isl_take isl_constraint *c, void *user), void *user)
{
        int i;
        struct isl_constraint *c;

        if (!bmap)
                return isl_stat_error;

        isl_assert(bmap->ctx, ISL_F_ISSET(bmap, ISL_BASIC_MAP_FINAL),
                        return isl_stat_error);

        for (i = 0; i < bmap->n_eq; ++i) {
                c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
                                                &bmap->eq[i]);
                if (!c)
                        return isl_stat_error;
                if (fn(c, user) < 0)
                        return isl_stat_error;
        }

        for (i = 0; i < bmap->n_ineq; ++i) {
                c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
                                                &bmap->ineq[i]);
                if (!c)
                        return isl_stat_error;
                if (fn(c, user) < 0)
                        return isl_stat_error;
        }

        return isl_stat_ok;
}

isl_stat isl_basic_set_foreach_constraint(__isl_keep isl_basic_set *bset,
        isl_stat (*fn)(__isl_take isl_constraint *c, void *user), void *user)
{
        return isl_basic_map_foreach_constraint(bset_to_bmap(bset), fn, user);
}

/* Add the constraint to the list that "user" points to, if it is not
 * a div constraint.
 */
static isl_stat collect_constraint(__isl_take isl_constraint *constraint,
        void *user)
{
        isl_constraint_list **list = user;
        isl_bool is_div;

        is_div = isl_constraint_is_div_constraint(constraint);
        if (is_div < 0 || is_div)
                isl_constraint_free(constraint);
        else
                *list = isl_constraint_list_add(*list, constraint);

        return is_div < 0 ? isl_stat_error : isl_stat_ok;
}

/* Return a list of constraints that, when combined, are equivalent
 * to "bmap".  The input is required to have only known divs.
 *
 * There is no need to include the div constraints as they are
 * implied by the div expressions.
 */
__isl_give isl_constraint_list *isl_basic_map_get_constraint_list(
        __isl_keep isl_basic_map *bmap)
{
        isl_size n;
        isl_bool known;
        isl_ctx *ctx;
        isl_constraint_list *list;

        known = isl_basic_map_divs_known(bmap);
        if (known < 0)
                return NULL;
        ctx = isl_basic_map_get_ctx(bmap);
        if (!known)
                isl_die(ctx, isl_error_invalid,
                        "input involves unknown divs", return NULL);

        n = isl_basic_map_n_constraint(bmap);
        if (n < 0)
                return NULL;
        list = isl_constraint_list_alloc(ctx, n);
        if (isl_basic_map_foreach_constraint(bmap,
                                            &collect_constraint, &list) < 0)
                list = isl_constraint_list_free(list);

        return list;
}

/* Return a list of constraints that, when combined, are equivalent
 * to "bset".  The input is required to have only known divs.
 */
__isl_give isl_constraint_list *isl_basic_set_get_constraint_list(
        __isl_keep isl_basic_set *bset)
{
        return isl_basic_map_get_constraint_list(bset);
}

int isl_constraint_is_equal(__isl_keep isl_constraint *constraint1,
        __isl_keep isl_constraint *constraint2)
{
        int equal;

        if (!constraint1 || !constraint2)
                return 0;
        if (constraint1->eq != constraint2->eq)
                return 0;
        equal = isl_local_space_is_equal(constraint1->ls, constraint2->ls);
        if (equal < 0 || !equal)
                return equal;
        return isl_vec_is_equal(constraint1->v, constraint2->v);
}

__isl_give isl_basic_map *isl_basic_map_add_constraint(
        __isl_take isl_basic_map *bmap, __isl_take isl_constraint *constraint)
{
        isl_ctx *ctx;
        isl_space *space;
        int equal_space;

        if (!bmap || !constraint)
                goto error;

        ctx = isl_constraint_get_ctx(constraint);
        space = isl_constraint_get_space(constraint);
        equal_space = isl_space_is_equal(bmap->dim, space);
        isl_space_free(space);
        isl_assert(ctx, equal_space, goto error);

        bmap = isl_basic_map_intersect(bmap,
                                isl_basic_map_from_constraint(constraint));
        return bmap;
error:
        isl_basic_map_free(bmap);
        isl_constraint_free(constraint);
        return NULL;
}

__isl_give isl_basic_set *isl_basic_set_add_constraint(
        __isl_take isl_basic_set *bset, __isl_take isl_constraint *constraint)
{
        return bset_from_bmap(isl_basic_map_add_constraint(bset_to_bmap(bset),
                                                            constraint));
}

__isl_give isl_map *isl_map_add_constraint(__isl_take isl_map *map,
        __isl_take isl_constraint *constraint)
{
        isl_basic_map *bmap;

        bmap = isl_basic_map_from_constraint(constraint);
        map = isl_map_intersect(map, isl_map_from_basic_map(bmap));

        return map;
}

__isl_give isl_set *isl_set_add_constraint(__isl_take isl_set *set,
        __isl_take isl_constraint *constraint)
{
        return isl_map_add_constraint(set, constraint);
}

/* Return the space of "constraint".
 */
static __isl_keep isl_space *isl_constraint_peek_space(
        __isl_keep isl_constraint *constraint)
{
        return constraint ? isl_local_space_peek_space(constraint->ls) : NULL;
}

__isl_give isl_space *isl_constraint_get_space(
        __isl_keep isl_constraint *constraint)
{
        return constraint ? isl_local_space_get_space(constraint->ls) : NULL;
}

__isl_give isl_local_space *isl_constraint_get_local_space(
        __isl_keep isl_constraint *constraint)
{
        return constraint ? isl_local_space_copy(constraint->ls) : NULL;
}

isl_size isl_constraint_dim(__isl_keep isl_constraint *constraint,
        enum isl_dim_type type)
{
        if (!constraint)
                return isl_size_error;
        return n(constraint, type);
}

#undef TYPE
#define TYPE    isl_constraint
static
#include "check_type_range_templ.c"

isl_bool isl_constraint_involves_dims(__isl_keep isl_constraint *constraint,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        int i;
        int *active = NULL;
        isl_bool involves = isl_bool_false;

        if (!constraint)
                return isl_bool_error;
        if (n == 0)
                return isl_bool_false;

        if (isl_constraint_check_range(constraint, type, first, n) < 0)
                return isl_bool_error;

        active = isl_local_space_get_active(constraint->ls,
                                            constraint->v->el + 1);
        if (!active)
                goto error;

        first += isl_local_space_offset(constraint->ls, type) - 1;
        for (i = 0; i < n; ++i)
                if (active[first + i]) {
                        involves = isl_bool_true;
                        break;
                }

        free(active);

        return involves;
error:
        free(active);
        return isl_bool_error;
}

/* Does the given constraint represent a lower bound on the given
 * dimension?
 */
isl_bool isl_constraint_is_lower_bound(__isl_keep isl_constraint *constraint,
        enum isl_dim_type type, unsigned pos)
{
        if (isl_constraint_check_range(constraint, type, pos, 1) < 0)
                return isl_bool_error;

        pos += isl_local_space_offset(constraint->ls, type);
        return isl_bool_ok(isl_int_is_pos(constraint->v->el[pos]));
}

/* Does the given constraint represent an upper bound on the given
 * dimension?
 */
isl_bool isl_constraint_is_upper_bound(__isl_keep isl_constraint *constraint,
        enum isl_dim_type type, unsigned pos)
{
        if (isl_constraint_check_range(constraint, type, pos, 1) < 0)
                return isl_bool_error;

        pos += isl_local_space_offset(constraint->ls, type);
        return isl_bool_ok(isl_int_is_neg(constraint->v->el[pos]));
}

const char *isl_constraint_get_dim_name(__isl_keep isl_constraint *constraint,
        enum isl_dim_type type, unsigned pos)
{
        return constraint ?
            isl_local_space_get_dim_name(constraint->ls, type, pos) : NULL;
}

void isl_constraint_get_constant(__isl_keep isl_constraint *constraint,
        isl_int *v)
{
        if (!constraint)
                return;
        isl_int_set(*v, constraint->v->el[0]);
}

/* Return the constant term of "constraint".
 */
__isl_give isl_val *isl_constraint_get_constant_val(
        __isl_keep isl_constraint *constraint)
{
        isl_ctx *ctx;

        if (!constraint)
                return NULL;

        ctx = isl_constraint_get_ctx(constraint);
        return isl_val_int_from_isl_int(ctx, constraint->v->el[0]);
}

void isl_constraint_get_coefficient(__isl_keep isl_constraint *constraint,
        enum isl_dim_type type, int pos, isl_int *v)
{
        if (isl_constraint_check_range(constraint, type, pos, 1) < 0)
                return;

        pos += isl_local_space_offset(constraint->ls, type);
        isl_int_set(*v, constraint->v->el[pos]);
}

/* Return the coefficient of the variable of type "type" at position "pos"
 * of "constraint".
 */
__isl_give isl_val *isl_constraint_get_coefficient_val(
        __isl_keep isl_constraint *constraint, enum isl_dim_type type, int pos)
{
        isl_ctx *ctx;

        if (isl_constraint_check_range(constraint, type, pos, 1) < 0)
                return NULL;

        ctx = isl_constraint_get_ctx(constraint);
        pos += isl_local_space_offset(constraint->ls, type);
        return isl_val_int_from_isl_int(ctx, constraint->v->el[pos]);
}

__isl_give isl_aff *isl_constraint_get_div(__isl_keep isl_constraint *constraint,
        int pos)
{
        if (!constraint)
                return NULL;

        return isl_local_space_get_div(constraint->ls, pos);
}

__isl_give isl_constraint *isl_constraint_set_constant(
        __isl_take isl_constraint *constraint, isl_int v)
{
        constraint = isl_constraint_cow(constraint);
        if (!constraint)
                return NULL;

        constraint->v = isl_vec_cow(constraint->v);
        if (!constraint->v)
                return isl_constraint_free(constraint);

        isl_int_set(constraint->v->el[0], v);
        return constraint;
}

/* Replace the constant term of "constraint" by "v".
 */
__isl_give isl_constraint *isl_constraint_set_constant_val(
        __isl_take isl_constraint *constraint, __isl_take isl_val *v)
{
        constraint = isl_constraint_cow(constraint);
        if (!constraint || !v)
                goto error;
        if (!isl_val_is_int(v))
                isl_die(isl_constraint_get_ctx(constraint), isl_error_invalid,
                        "expecting integer value", goto error);
        constraint->v = isl_vec_set_element_val(constraint->v, 0, v);
        if (!constraint->v)
                constraint = isl_constraint_free(constraint);
        return constraint;
error:
        isl_val_free(v);
        return isl_constraint_free(constraint);
}

__isl_give isl_constraint *isl_constraint_set_constant_si(
        __isl_take isl_constraint *constraint, int v)
{
        constraint = isl_constraint_cow(constraint);
        if (!constraint)
                return NULL;

        constraint->v = isl_vec_cow(constraint->v);
        if (!constraint->v)
                return isl_constraint_free(constraint);

        isl_int_set_si(constraint->v->el[0], v);
        return constraint;
}

/* Replace the coefficient of the variable of type "type" at position "pos"
 * of "constraint" by "v".
 */
__isl_give isl_constraint *isl_constraint_set_coefficient_val(
        __isl_take isl_constraint *constraint,
        enum isl_dim_type type, int pos, __isl_take isl_val *v)
{
        constraint = isl_constraint_cow(constraint);
        if (!constraint || !v)
                goto error;
        if (!isl_val_is_int(v))
                isl_die(isl_constraint_get_ctx(constraint), isl_error_invalid,
                        "expecting integer value", goto error);
        if (isl_constraint_check_range(constraint, type, pos, 1) < 0)
                goto error;

        pos += isl_local_space_offset(constraint->ls, type);
        constraint->v = isl_vec_set_element_val(constraint->v, pos, v);
        if (!constraint->v)
                constraint = isl_constraint_free(constraint);
        return constraint;
error:
        isl_val_free(v);
        return isl_constraint_free(constraint);
}

__isl_give isl_constraint *isl_constraint_set_coefficient_si(
        __isl_take isl_constraint *constraint,
        enum isl_dim_type type, int pos, int v)
{
        constraint = isl_constraint_cow(constraint);
        if (isl_constraint_check_range(constraint, type, pos, 1) < 0)
                return isl_constraint_free(constraint);

        constraint->v = isl_vec_cow(constraint->v);
        if (!constraint->v)
                return isl_constraint_free(constraint);

        pos += isl_local_space_offset(constraint->ls, type);
        isl_int_set_si(constraint->v->el[pos], v);

        return constraint;
}

__isl_give isl_constraint *isl_constraint_negate(
        __isl_take isl_constraint *constraint)
{
        isl_ctx *ctx;

        constraint = isl_constraint_cow(constraint);
        if (!constraint)
                return NULL;

        ctx = isl_constraint_get_ctx(constraint);
        if (isl_constraint_is_equality(constraint))
                isl_die(ctx, isl_error_invalid, "cannot negate equality",
                        return isl_constraint_free(constraint));
        constraint->v = isl_vec_neg(constraint->v);
        constraint->v = isl_vec_cow(constraint->v);
        if (!constraint->v)
                return isl_constraint_free(constraint);
        isl_int_sub_ui(constraint->v->el[0], constraint->v->el[0], 1);
        return constraint;
}

isl_bool isl_constraint_is_equality(struct isl_constraint *constraint)
{
        if (!constraint)
                return isl_bool_error;
        return isl_bool_ok(constraint->eq);
}

isl_bool isl_constraint_is_div_constraint(__isl_keep isl_constraint *constraint)
{
        int i;
        isl_size n_div;

        if (!constraint)
                return isl_bool_error;
        if (isl_constraint_is_equality(constraint))
                return isl_bool_false;
        n_div = isl_constraint_dim(constraint, isl_dim_div);
        if (n_div < 0)
                return isl_bool_error;
        for (i = 0; i < n_div; ++i) {
                isl_bool is_div;
                is_div = isl_local_space_is_div_constraint(constraint->ls,
                                                        constraint->v->el, i);
                if (is_div < 0 || is_div)
                        return is_div;
        }

        return isl_bool_false;
}

/* Is "constraint" an equality that corresponds to integer division "div"?
 *
 * That is, given an integer division of the form
 *
 *      a = floor((f + c)/m)
 *
 * is the equality of the form
 *
 *              -f + m d + c' = 0
 * ?
 * Note that the constant term is not checked explicitly, but given
 * that this is a valid equality constraint, the constant c' necessarily
 * has a value close to -c.
 */
isl_bool isl_constraint_is_div_equality(__isl_keep isl_constraint *constraint,
        unsigned div)
{
        isl_bool equality;

        equality = isl_constraint_is_equality(constraint);
        if (equality < 0 || !equality)
                return equality;
        return isl_local_space_is_div_equality(constraint->ls,
                                                constraint->v->el, div);
}

/* We manually set ISL_BASIC_SET_FINAL instead of calling
 * isl_basic_map_finalize because we want to keep the position
 * of the divs and we therefore do not want to throw away redundant divs.
 * This is arguably a bit fragile.
 */
__isl_give isl_basic_map *isl_basic_map_from_constraint(
        __isl_take isl_constraint *constraint)
{
        int k;
        isl_local_space *ls;
        struct isl_basic_map *bmap;
        isl_int *c;
        isl_size total;

        if (!constraint)
                return NULL;

        ls = isl_local_space_copy(constraint->ls);
        bmap = isl_basic_map_from_local_space(ls);
        bmap = isl_basic_map_extend_constraints(bmap, 1, 1);
        if (isl_constraint_is_equality(constraint)) {
                k = isl_basic_map_alloc_equality(bmap);
                if (k < 0)
                        goto error;
                c = bmap->eq[k];
        }
        else {
                k = isl_basic_map_alloc_inequality(bmap);
                if (k < 0)
                        goto error;
                c = bmap->ineq[k];
        }
        total = isl_basic_map_dim(bmap, isl_dim_all);
        if (total < 0)
                goto error;
        isl_seq_cpy(c, constraint->v->el, 1 + total);
        isl_constraint_free(constraint);
        if (bmap)
                ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
        return bmap;
error:
        isl_constraint_free(constraint);
        isl_basic_map_free(bmap);
        return NULL;
}

__isl_give isl_basic_set *isl_basic_set_from_constraint(
        __isl_take isl_constraint *constraint)
{
        isl_space *space;

        space = isl_constraint_peek_space(constraint);
        if (isl_space_check_is_set(space) < 0)
                goto error;
        return bset_from_bmap(isl_basic_map_from_constraint(constraint));
error:
        isl_constraint_free(constraint);
        return NULL;
}

/* Is the variable of "type" at position "pos" of "bmap" defined
 * in terms of earlier dimensions through an equality?
 *
 * If so, and if c is not NULL, then return a copy of this equality in *c.
 */
isl_bool isl_basic_map_has_defining_equality(
        __isl_keep isl_basic_map *bmap, enum isl_dim_type type, int pos,
        __isl_give isl_constraint **c)
{
        int i;
        unsigned offset;
        isl_size total;

        if (isl_basic_map_check_range(bmap, type, pos, 1) < 0)
                return isl_bool_error;
        offset = isl_basic_map_offset(bmap, type);
        total = isl_basic_map_dim(bmap, isl_dim_all);
        if (total < 0)
                return isl_bool_error;
        for (i = 0; i < bmap->n_eq; ++i) {
                if (isl_int_is_zero(bmap->eq[i][offset + pos]) ||
                    isl_seq_first_non_zero(bmap->eq[i]+offset+pos+1,
                                           1+total-offset-pos-1) != -1)
                        continue;
                if (c)
                        *c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
                                                                &bmap->eq[i]);
                return isl_bool_true;
        }
        return isl_bool_false;
}

/* Is the variable of "type" at position "pos" of "bset" defined
 * in terms of earlier dimensions through an equality?
 *
 * If so, and if c is not NULL, then return a copy of this equality in *c.
 */
isl_bool isl_basic_set_has_defining_equality(
        __isl_keep isl_basic_set *bset, enum isl_dim_type type, int pos,
        __isl_give isl_constraint **c)
{
        return isl_basic_map_has_defining_equality(bset_to_bmap(bset),
                                                    type, pos, c);
}

isl_bool isl_basic_set_has_defining_inequalities(
        struct isl_basic_set *bset, enum isl_dim_type type, int pos,
        struct isl_constraint **lower,
        struct isl_constraint **upper)
{
        int i, j;
        unsigned offset;
        isl_size total;
        isl_int m;
        isl_int **lower_line, **upper_line;

        if (isl_basic_set_check_range(bset, type, pos, 1) < 0)
                return isl_bool_error;
        offset = isl_basic_set_offset(bset, type);
        total = isl_basic_set_dim(bset, isl_dim_all);
        if (total < 0)
                return isl_bool_error;
        isl_int_init(m);
        for (i = 0; i < bset->n_ineq; ++i) {
                if (isl_int_is_zero(bset->ineq[i][offset + pos]))
                        continue;
                if (isl_int_is_one(bset->ineq[i][offset + pos]))
                        continue;
                if (isl_int_is_negone(bset->ineq[i][offset + pos]))
                        continue;
                if (isl_seq_first_non_zero(bset->ineq[i]+offset+pos+1,
                                                1+total-offset-pos-1) != -1)
                        continue;
                for (j = i + 1; j < bset->n_ineq; ++j) {
                        if (!isl_seq_is_neg(bset->ineq[i]+1, bset->ineq[j]+1,
                                            total))
                                continue;
                        isl_int_add(m, bset->ineq[i][0], bset->ineq[j][0]);
                        if (isl_int_abs_ge(m, bset->ineq[i][offset+pos]))
                                continue;

                        if (isl_int_is_pos(bset->ineq[i][offset+pos])) {
                                lower_line = &bset->ineq[i];
                                upper_line = &bset->ineq[j];
                        } else {
                                lower_line = &bset->ineq[j];
                                upper_line = &bset->ineq[i];
                        }
                        *lower = isl_basic_set_constraint(
                                        isl_basic_set_copy(bset), lower_line);
                        *upper = isl_basic_set_constraint(
                                        isl_basic_set_copy(bset), upper_line);
                        isl_int_clear(m);
                        return isl_bool_true;
                }
        }
        *lower = NULL;
        *upper = NULL;
        isl_int_clear(m);
        return isl_bool_false;
}

/* Given two constraints "a" and "b" on the variable at position "abs_pos"
 * (in "a" and "b"), add a constraint to "bset" that ensures that the
 * bound implied by "a" is (strictly) larger than the bound implied by "b".
 *
 * If both constraints imply lower bounds, then this means that "a" is
 * active in the result.
 * If both constraints imply upper bounds, then this means that "b" is
 * active in the result.
 */
static __isl_give isl_basic_set *add_larger_bound_constraint(
        __isl_take isl_basic_set *bset, isl_int *a, isl_int *b,
        unsigned abs_pos, int strict)
{
        int k;
        isl_int t;
        isl_size total;

        total = isl_basic_set_dim(bset, isl_dim_all);
        if (total < 0)
                return isl_basic_set_free(bset);
        k = isl_basic_set_alloc_inequality(bset);
        if (k < 0)
                goto error;

        isl_int_init(t);
        isl_int_neg(t, b[1 + abs_pos]);

        isl_seq_combine(bset->ineq[k], t, a, a[1 + abs_pos], b, 1 + abs_pos);
        isl_seq_combine(bset->ineq[k] + 1 + abs_pos,
                t, a + 1 + abs_pos + 1, a[1 + abs_pos], b + 1 + abs_pos + 1,
                total - abs_pos);

        if (strict)
                isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);

        isl_int_clear(t);

        return bset;
error:
        isl_basic_set_free(bset);
        return NULL;
}

/* Add constraints to "context" that ensure that "u" is the smallest
 * (and therefore active) upper bound on "abs_pos" in "bset" and return
 * the resulting basic set.
 */
static __isl_give isl_basic_set *set_smallest_upper_bound(
        __isl_keep isl_basic_set *context,
        __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_upper, int u)
{
        int j;

        context = isl_basic_set_copy(context);
        context = isl_basic_set_cow(context);

        context = isl_basic_set_extend_constraints(context, 0, n_upper - 1);

        for (j = 0; j < bset->n_ineq; ++j) {
                if (j == u)
                        continue;
                if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
                        continue;
                context = add_larger_bound_constraint(context,
                        bset->ineq[j], bset->ineq[u], abs_pos, j > u);
        }

        context = isl_basic_set_simplify(context);
        context = isl_basic_set_finalize(context);

        return context;
}

/* Add constraints to "context" that ensure that "u" is the largest
 * (and therefore active) upper bound on "abs_pos" in "bset" and return
 * the resulting basic set.
 */
static __isl_give isl_basic_set *set_largest_lower_bound(
        __isl_keep isl_basic_set *context,
        __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_lower, int l)
{
        int j;

        context = isl_basic_set_copy(context);
        context = isl_basic_set_cow(context);

        context = isl_basic_set_extend_constraints(context, 0, n_lower - 1);

        for (j = 0; j < bset->n_ineq; ++j) {
                if (j == l)
                        continue;
                if (!isl_int_is_pos(bset->ineq[j][1 + abs_pos]))
                        continue;
                context = add_larger_bound_constraint(context,
                        bset->ineq[l], bset->ineq[j], abs_pos, j > l);
        }

        context = isl_basic_set_simplify(context);
        context = isl_basic_set_finalize(context);

        return context;
}

static isl_stat foreach_upper_bound(__isl_keep isl_basic_set *bset,
        enum isl_dim_type type, unsigned abs_pos,
        __isl_take isl_basic_set *context, int n_upper,
        isl_stat (*fn)(__isl_take isl_constraint *lower,
                  __isl_take isl_constraint *upper,
                  __isl_take isl_basic_set *bset, void *user), void *user)
{
        isl_basic_set *context_i;
        isl_constraint *upper = NULL;
        int i;

        for (i = 0; i < bset->n_ineq; ++i) {
                if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
                        continue;

                context_i = set_smallest_upper_bound(context, bset,
                                                        abs_pos, n_upper, i);
                if (isl_basic_set_is_empty(context_i)) {
                        isl_basic_set_free(context_i);
                        continue;
                }
                upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
                                                &bset->ineq[i]);
                if (!upper || !context_i)
                        goto error;
                if (fn(NULL, upper, context_i, user) < 0)
                        break;
        }

        isl_basic_set_free(context);

        if (i < bset->n_ineq)
                return isl_stat_error;

        return isl_stat_ok;
error:
        isl_constraint_free(upper);
        isl_basic_set_free(context_i);
        isl_basic_set_free(context);
        return isl_stat_error;
}

static isl_stat foreach_lower_bound(__isl_keep isl_basic_set *bset,
        enum isl_dim_type type, unsigned abs_pos,
        __isl_take isl_basic_set *context, int n_lower,
        isl_stat (*fn)(__isl_take isl_constraint *lower,
                  __isl_take isl_constraint *upper,
                  __isl_take isl_basic_set *bset, void *user), void *user)
{
        isl_basic_set *context_i;
        isl_constraint *lower = NULL;
        int i;

        for (i = 0; i < bset->n_ineq; ++i) {
                if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
                        continue;

                context_i = set_largest_lower_bound(context, bset,
                                                        abs_pos, n_lower, i);
                if (isl_basic_set_is_empty(context_i)) {
                        isl_basic_set_free(context_i);
                        continue;
                }
                lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
                                                &bset->ineq[i]);
                if (!lower || !context_i)
                        goto error;
                if (fn(lower, NULL, context_i, user) < 0)
                        break;
        }

        isl_basic_set_free(context);

        if (i < bset->n_ineq)
                return isl_stat_error;

        return isl_stat_ok;
error:
        isl_constraint_free(lower);
        isl_basic_set_free(context_i);
        isl_basic_set_free(context);
        return isl_stat_error;
}

static isl_stat foreach_bound_pair(__isl_keep isl_basic_set *bset,
        enum isl_dim_type type, unsigned abs_pos,
        __isl_take isl_basic_set *context, int n_lower, int n_upper,
        isl_stat (*fn)(__isl_take isl_constraint *lower,
                  __isl_take isl_constraint *upper,
                  __isl_take isl_basic_set *bset, void *user), void *user)
{
        isl_basic_set *context_i, *context_j;
        isl_constraint *lower = NULL;
        isl_constraint *upper = NULL;
        int i, j;

        for (i = 0; i < bset->n_ineq; ++i) {
                if (!isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
                        continue;

                context_i = set_largest_lower_bound(context, bset,
                                                        abs_pos, n_lower, i);
                if (isl_basic_set_is_empty(context_i)) {
                        isl_basic_set_free(context_i);
                        continue;
                }

                for (j = 0; j < bset->n_ineq; ++j) {
                        if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
                                continue;

                        context_j = set_smallest_upper_bound(context_i, bset,
                                                            abs_pos, n_upper, j);
                        context_j = isl_basic_set_extend_constraints(context_j,
                                                                        0, 1);
                        context_j = add_larger_bound_constraint(context_j,
                                bset->ineq[i], bset->ineq[j], abs_pos, 0);
                        context_j = isl_basic_set_simplify(context_j);
                        context_j = isl_basic_set_finalize(context_j);
                        if (isl_basic_set_is_empty(context_j)) {
                                isl_basic_set_free(context_j);
                                continue;
                        }
                        lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
                                                        &bset->ineq[i]);
                        upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
                                                        &bset->ineq[j]);
                        if (!lower || !upper || !context_j)
                                goto error;
                        if (fn(lower, upper, context_j, user) < 0)
                                break;
                }

                isl_basic_set_free(context_i);

                if (j < bset->n_ineq)
                        break;
        }

        isl_basic_set_free(context);

        if (i < bset->n_ineq)
                return isl_stat_error;

        return isl_stat_ok;
error:
        isl_constraint_free(lower);
        isl_constraint_free(upper);
        isl_basic_set_free(context_i);
        isl_basic_set_free(context_j);
        isl_basic_set_free(context);
        return isl_stat_error;
}

/* For each pair of lower and upper bounds on the variable "pos"
 * of type "type", call "fn" with these lower and upper bounds and the
 * set of constraints on the remaining variables where these bounds
 * are active, i.e., (stricly) larger/smaller than the other lower/upper bounds.
 *
 * If the designated variable is equal to an affine combination of the
 * other variables then fn is called with both lower and upper
 * set to the corresponding equality.
 *
 * If there is no lower (or upper) bound, then NULL is passed
 * as the corresponding bound.
 *
 * We first check if the variable is involved in any equality.
 * If not, we count the number of lower and upper bounds and
 * act accordingly.
 */
isl_stat isl_basic_set_foreach_bound_pair(__isl_keep isl_basic_set *bset,
        enum isl_dim_type type, unsigned pos,
        isl_stat (*fn)(__isl_take isl_constraint *lower,
                  __isl_take isl_constraint *upper,
                  __isl_take isl_basic_set *bset, void *user), void *user)
{
        int i;
        isl_constraint *lower = NULL;
        isl_constraint *upper = NULL;
        isl_basic_set *context = NULL;
        unsigned abs_pos;
        int n_lower, n_upper;
        isl_size off;

        if (isl_basic_set_check_range(bset, type, pos, 1) < 0)
                return isl_stat_error;
        isl_assert(bset->ctx, type == isl_dim_param || type == isl_dim_set,
                return isl_stat_error);

        off = isl_basic_set_var_offset(bset, type);
        if (off < 0)
                return isl_stat_error;
        abs_pos = off + pos;

        for (i = 0; i < bset->n_eq; ++i) {
                if (isl_int_is_zero(bset->eq[i][1 + abs_pos]))
                        continue;

                lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
                                                &bset->eq[i]);
                upper = isl_constraint_copy(lower);
                context = isl_basic_set_remove_dims(isl_basic_set_copy(bset),
                                        type, pos, 1);
                if (!lower || !upper || !context)
                        goto error;
                return fn(lower, upper, context, user);
        }

        n_lower = 0;
        n_upper = 0;
        for (i = 0; i < bset->n_ineq; ++i) {
                if (isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
                        n_lower++;
                else if (isl_int_is_neg(bset->ineq[i][1 + abs_pos]))
                        n_upper++;
        }

        context = isl_basic_set_copy(bset);
        context = isl_basic_set_cow(context);
        if (!context)
                goto error;
        for (i = context->n_ineq - 1; i >= 0; --i)
                if (!isl_int_is_zero(context->ineq[i][1 + abs_pos]))
                        isl_basic_set_drop_inequality(context, i);

        context = isl_basic_set_drop(context, type, pos, 1);
        if (!n_lower && !n_upper)
                return fn(NULL, NULL, context, user);
        if (!n_lower)
                return foreach_upper_bound(bset, type, abs_pos, context, n_upper,
                                                fn, user);
        if (!n_upper)
                return foreach_lower_bound(bset, type, abs_pos, context, n_lower,
                                                fn, user);
        return foreach_bound_pair(bset, type, abs_pos, context, n_lower, n_upper,
                                        fn, user);
error:
        isl_constraint_free(lower);
        isl_constraint_free(upper);
        isl_basic_set_free(context);
        return isl_stat_error;
}

__isl_give isl_aff *isl_constraint_get_bound(
        __isl_keep isl_constraint *constraint, enum isl_dim_type type, int pos)
{
        isl_space *space;
        isl_aff *aff;
        isl_ctx *ctx;

        if (isl_constraint_check_range(constraint, type, pos, 1) < 0)
                return NULL;
        space = isl_constraint_peek_space(constraint);
        if (isl_space_check_is_set(space) < 0)
                return NULL;

        ctx = isl_constraint_get_ctx(constraint);
        pos += offset(constraint, type);
        if (isl_int_is_zero(constraint->v->el[pos]))
                isl_die(ctx, isl_error_invalid,
                        "constraint does not define a bound on given dimension",
                        return NULL);

        aff = isl_aff_alloc(isl_local_space_copy(constraint->ls));
        if (!aff)
                return NULL;

        if (isl_int_is_neg(constraint->v->el[pos]))
                isl_seq_cpy(aff->v->el + 1, constraint->v->el, aff->v->size - 1);
        else
                isl_seq_neg(aff->v->el + 1, constraint->v->el, aff->v->size - 1);
        isl_int_set_si(aff->v->el[1 + pos], 0);
        isl_int_abs(aff->v->el[0], constraint->v->el[pos]);
        aff = isl_aff_normalize(aff);

        return aff;
}

/* For an inequality constraint
 *
 *      f >= 0
 *
 * or an equality constraint
 *
 *      f = 0
 *
 * return the affine expression f.
 */
__isl_give isl_aff *isl_constraint_get_aff(
        __isl_keep isl_constraint *constraint)
{
        isl_aff *aff;

        if (!constraint)
                return NULL;

        aff = isl_aff_alloc(isl_local_space_copy(constraint->ls));
        if (!aff)
                return NULL;

        isl_seq_cpy(aff->v->el + 1, constraint->v->el, aff->v->size - 1);
        isl_int_set_si(aff->v->el[0], 1);

        return aff;
}

/* Construct an inequality (eq = 0) or equality (eq = 1) constraint from "aff".
 * In particular, construct aff >= 0 or aff = 0.
 *
 * The denominator of "aff" can be ignored.
 */
static __isl_give isl_constraint *isl_constraint_alloc_aff(int eq,
        __isl_take isl_aff *aff)
{
        isl_local_space *ls;
        isl_vec *v;

        if (!aff)
                return NULL;
        ls = isl_aff_get_domain_local_space(aff);
        v = isl_vec_drop_els(isl_vec_copy(aff->v), 0, 1);
        isl_aff_free(aff);

        return isl_constraint_alloc_vec(eq, ls, v);
}

/* Construct an equality constraint equating the given affine expression
 * to zero.
 */
__isl_give isl_constraint *isl_equality_from_aff(__isl_take isl_aff *aff)
{
        return isl_constraint_alloc_aff(1, aff);
}

/* Construct an inequality constraint enforcing the given affine expression
 * to be non-negative.
 */
__isl_give isl_constraint *isl_inequality_from_aff(__isl_take isl_aff *aff)
{
        return isl_constraint_alloc_aff(0, aff);
}

/* Compare two isl_constraints.
 *
 * Return -1 if "c1" is "smaller" than "c2", 1 if "c1" is "greater"
 * than "c2" and 0 if they are equal.
 *
 * The order is fairly arbitrary.  We do consider constraints that only involve
 * earlier dimensions as "smaller".
 */
int isl_constraint_plain_cmp(__isl_keep isl_constraint *c1,
        __isl_keep isl_constraint *c2)
{
        int cmp;
        int last1, last2;

        if (c1 == c2)
                return 0;
        if (!c1)
                return -1;
        if (!c2)
                return 1;
        cmp = isl_local_space_cmp(c1->ls, c2->ls);
        if (cmp != 0)
                return cmp;

        last1 = isl_seq_last_non_zero(c1->v->el + 1, c1->v->size - 1);
        last2 = isl_seq_last_non_zero(c2->v->el + 1, c1->v->size - 1);
        if (last1 != last2)
                return last1 - last2;

        return isl_seq_cmp(c1->v->el, c2->v->el, c1->v->size);
}

/* Compare two constraints based on their final (non-zero) coefficients.
 * In particular, the constraint that involves later variables or
 * that has a larger coefficient for a shared latest variable
 * is considered "greater" than the other constraint.
 *
 * Return -1 if "c1" is "smaller" than "c2", 1 if "c1" is "greater"
 * than "c2" and 0 if they are equal.
 *
 * If the constraints live in different local spaces, then we cannot
 * really compare the constraints so we compare the local spaces instead.
 */
int isl_constraint_cmp_last_non_zero(__isl_keep isl_constraint *c1,
        __isl_keep isl_constraint *c2)
{
        int cmp;
        int last1, last2;

        if (c1 == c2)
                return 0;
        if (!c1)
                return -1;
        if (!c2)
                return 1;
        cmp = isl_local_space_cmp(c1->ls, c2->ls);
        if (cmp != 0)
                return cmp;

        last1 = isl_seq_last_non_zero(c1->v->el + 1, c1->v->size - 1);
        last2 = isl_seq_last_non_zero(c2->v->el + 1, c1->v->size - 1);
        if (last1 != last2)
                return last1 - last2;
        if (last1 == -1)
                return 0;
        return isl_int_abs_cmp(c1->v->el[1 + last1], c2->v->el[1 + last2]);
}