isl backend: scattering relation now maps domain dimensions to time dimensions

[cloog/uuh.git] / source / isl / domain.c

#include <assert.h>
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#include <cloog/isl/cloog.h>
#include <isl_list.h>

CloogDomain *cloog_domain_from_isl_set(struct isl_set *set)
{
        set = isl_set_detect_equalities(set);
        return (CloogDomain *)set;
}

CloogScattering *cloog_scattering_from_isl_map(struct isl_map *map)
{
        return (CloogScattering *)map;
}


/**
 * Returns true if each scattering dimension is defined in terms
 * of the original iterators.
 */
int cloog_scattering_fully_specified(CloogScattering *scattering,
                                      CloogDomain *domain)
{
        int i;
        int scattering_dim = cloog_scattering_dimension(scattering, domain);
        for (i = 0; i < scattering->map.n; ++i)
                if (scattering->map.p[i]->n_eq < scattering_dim)
                        return 0;
        return 1;
}


CloogConstraintSet *cloog_domain_constraints(CloogDomain *domain)
{
        assert(domain->set.n == 1);
        return cloog_constraint_set_from_isl_basic_set(
                                        isl_basic_set_copy(domain->set.p[0]));
}


void cloog_domain_print_constraints(FILE *foo, CloogDomain *domain,
                                        int print_number)
{
        if (print_number)
                isl_set_print(&domain->set, foo, 0, ISL_FORMAT_POLYLIB);
        else {
                assert(domain->set.n == 1);
                isl_basic_set_print(domain->set.p[0], foo,
                                        0, NULL, NULL, ISL_FORMAT_POLYLIB);
        }
}


void cloog_domain_free(CloogDomain * domain)
{
        isl_set_free(&domain->set);
}


void cloog_scattering_free(CloogScattering *scatt)
{
        isl_map_free(&scatt->map);
}


CloogDomain * cloog_domain_copy(CloogDomain * domain)
{
        return cloog_domain_from_isl_set(isl_set_copy(&domain->set));
}


/**
 * cloog_domain_convex function:
 * Computes the convex hull of domain.
 */ 
CloogDomain *cloog_domain_convex(CloogDomain *domain)
{
        struct isl_set *set = &domain->set;
        set = isl_set_from_basic_set(isl_set_convex_hull(isl_set_copy(set)));
        return cloog_domain_from_isl_set(set);
}


/**
 * cloog_domain_simple_convex:
 * Given a list (union) of polyhedra, this function returns a "simple"
 * convex hull of this union.  In particular, the constraints of the
 * the returned polyhedron consist of (parametric) lower and upper
 * bounds on individual variables and constraints that appear in the
 * original polyhedra.
 */
CloogDomain *cloog_domain_simple_convex(CloogDomain *domain)
{
        struct isl_basic_set *hull;
        unsigned dim = isl_set_n_dim(&domain->set);

        if (cloog_domain_isconvex(domain))
                return cloog_domain_copy(domain);

        if (dim == 0)
                return cloog_domain_convex(domain);

        hull = isl_set_bounded_simple_hull(isl_set_copy(&domain->set));
        return cloog_domain_from_isl_set(isl_set_from_basic_set(hull));
}


/**
 * cloog_domain_simplify function:
 * Given two polyhedral domains (dom1) and (dom2),
 * this function finds the largest domain set (or the smallest list
 * of non-redundant constraints), that when intersected with polyhedral
 * domain (dom2) equals (dom1)intersect(dom2). The output is a new CloogDomain
 * structure with a polyhedral domain with the "redundant" constraints removed.
 * NB: the second domain is required not to be a union.
 */ 
CloogDomain *cloog_domain_simplify(CloogDomain *dom1, CloogDomain *dom2)
{
        struct isl_set *set;
        assert(dom2->set.n == 1);
        set = isl_set_gist(isl_set_copy(&dom1->set),
                                isl_basic_set_copy(dom2->set.p[0]));
        return cloog_domain_from_isl_set(set);
}


/**
 * cloog_domain_union function:
 * This function returns a new polyhedral domain which is the union of
 * two polyhedral domains (dom1) U (dom2).
 */
CloogDomain *cloog_domain_union(CloogDomain *dom1, CloogDomain *dom2)
{
        struct isl_set *set;
        set = isl_set_union(isl_set_copy(&dom1->set), isl_set_copy(&dom2->set));
        return cloog_domain_from_isl_set(set);
}



/**
 * cloog_domain_intersection function:
 * This function returns a new polyhedral domain which is the intersection of
 * two polyhedral domains (dom1) \cap (dom2).
 */ 
CloogDomain *cloog_domain_intersection(CloogDomain *dom1, CloogDomain *dom2)
{
        struct isl_set *set;
        set = isl_set_intersect(isl_set_copy(&dom1->set),
                                isl_set_copy(&dom2->set));
        return cloog_domain_from_isl_set(set);
}


/**
 * cloog_domain_difference function:
 * Returns the set difference domain \ minus.
 */ 
CloogDomain *cloog_domain_difference(CloogDomain *domain, CloogDomain *minus)
{
        struct isl_set *set;
        set = isl_set_subtract(isl_set_copy(&domain->set),
                               isl_set_copy(&minus->set));
        return cloog_domain_from_isl_set(set);
}


/**
 * cloog_domain_sort function:
 * This function topologically sorts (nb_doms) domains. Here (doms) is an
 * array of pointers to CloogDomains, (nb_doms) is the number of domains,
 * (level) is the level to consider for partial ordering (nb_par) is the
 * parameter space dimension, (permut) if not NULL, is an array of (nb_doms)
 * integers that contains a permutation specification after call in order to
 * apply the topological sorting. 
 */
void cloog_domain_sort(CloogDomain **doms, unsigned nb_doms, unsigned level,
                        int *permut)
{
        int i, j, k, cmp;
        struct isl_ctx *ctx;
        unsigned char **follows;

        if (!nb_doms)
                return;
        ctx = doms[0]->set.ctx;
        for (i = 0; i < nb_doms; i++)
                assert(doms[i]->set.n == 1);

        follows = isl_alloc_array(ctx, unsigned char *, nb_doms);
        assert(follows);
        for (i = 0; i < nb_doms; ++i) {
                follows[i] = isl_alloc_array(ctx, unsigned char, nb_doms);
                assert(follows[i]);
                for (j = 0; j < nb_doms; ++j)
                        follows[i][j] = 0;
        }

        for (i = 1; i < nb_doms; ++i) {
                for (j = 0; j < i; ++j) {
                        if (follows[i][j] || follows[j][i])
                                continue;
                        cmp = isl_basic_set_compare_at(doms[i]->set.p[0],
                                        doms[j]->set.p[0], level-1);
                        if (!cmp)
                                continue;
                        if (cmp > 0) {
                                follows[i][j] = 1;
                                for (k = 0; k < i; ++k)
                                        follows[i][k] |= follows[j][k];
                        } else {
                                follows[j][i] = 1;
                                for (k = 0; k < i; ++k)
                                        follows[k][i] |= follows[k][j];
                        }
                }
        }

        for (i = 0, j = 0; i < nb_doms; j = (j + 1) % nb_doms) {
                for (k = 0; k < nb_doms; ++k)
                        if (follows[j][k])
                                break;
                if (k < nb_doms)
                        continue;
                for (k = 0; k < nb_doms; ++k)
                        follows[k][j] = 0;
                follows[j][j] = 1;
                permut[i] = 1 + j;
                ++i;
        }

        for (i = 0; i < nb_doms; ++i)
                free(follows[i]);
        free(follows);
}


/**
 * Check whether there is or may be any value of dom1 at the given level
 * that is greater than or equal to a value of dom2 at the same level.
 *
 * Return
 *       1 is there is or may be a greater-than pair.
 *       0 if there is no greater-than pair, but there may be an equal-to pair
 *      -1 if there is definitely no such pair
 */
int cloog_domain_follows(CloogDomain *dom1, CloogDomain *dom2, unsigned level)
{
        int follows;

        follows = isl_set_follows_at(&dom1->set, &dom2->set, level - 1);
        assert(follows >= -1);

        return follows;
}


/**
 * cloog_domain_empty function:
 * Returns an empty domain of the same dimensions as template.
 */
CloogDomain *cloog_domain_empty(CloogDomain *template)
{
        return cloog_domain_from_isl_set(isl_set_empty_like(&template->set));
}


/******************************************************************************
 *                          Structure display function                        *
 ******************************************************************************/


/**
 * cloog_domain_print_structure :
 * this function is a more human-friendly way to display the CloogDomain data
 * structure, it only shows the constraint system and includes an indentation
 * level (level) in order to work with others print_structure functions.
 */
void cloog_domain_print_structure(FILE *file, CloogDomain *domain, int level,
                                  const char *name)
{
        int i ;
        char *suffix = " ]";
        char *prefix;
        struct isl_set *set = &domain->set;

        /* Go to the right level. */
        for (i = 0; i < level; i++)
                fprintf(file, "|\t");
  
        if (!set) {
                fprintf(file, "+-- Null CloogDomain\n");
                return;
        }
        fprintf(file, "+-- %s\n", name);
        prefix = isl_alloc_array(set->ctx, char, 2*(level+1)+3);
        assert(prefix);
        for (i = 0; i < level+1; ++i)
                memcpy(prefix+2*i, "|\t", 2);
        strcpy(prefix+2*(level+1), "[ ");

        for (i = 0; i < set->n; ++i) {
                isl_basic_set_print(set->p[i], file, 0, prefix, suffix,
                                        ISL_FORMAT_POLYLIB_CONSTRAINTS);
                prefix[2*(level+1)] = '\0';
                fprintf(file, "%s\n", prefix);
                prefix[2*(level+1)] = '[';
        }
        free(prefix);
}


/******************************************************************************
 *                         Memory deallocation function                       *
 ******************************************************************************/


/**
 * cloog_scattering_list_free function:
 * This function frees the allocated memory for a CloogScatteringList structure.
 */
void cloog_scattering_list_free(CloogScatteringList *list)
{
        while (list != NULL) {
                CloogScatteringList *temp = list->next;
                isl_map_free(&list->scatt->map);
                free(list);
                list = temp;
        }
}


/******************************************************************************
 *                               Reading function                             *
 ******************************************************************************/


/**
 * cloog_domain_read_context function:
 * Read parameter domain.
 */
CloogDomain *cloog_domain_read_context(CloogState *state, FILE *input)
{
        struct isl_ctx *ctx = state->backend->ctx;
        struct isl_dim *param_dim;
        struct isl_basic_set *bset;
        struct isl_basic_set *model;

        bset = isl_basic_set_read_from_file(ctx, input, 0);
        assert(bset);
        param_dim = isl_dim_set_alloc(ctx, isl_basic_set_n_dim(bset), 0);
        model = isl_basic_set_empty(param_dim);
        bset = isl_basic_set_from_underlying_set(bset, model);

        return cloog_domain_from_isl_set(isl_set_from_basic_set(bset));
}


/**
 * cloog_domain_from_context
 * Reinterpret context by turning parameters into variables.
 */
CloogDomain *cloog_domain_from_context(CloogDomain *context)
{
        struct isl_dim *dim;
        struct isl_basic_set *model;
        struct isl_set *ctx_set = &context->set;
        struct isl_set *set;

        dim = isl_dim_set_alloc(ctx_set->ctx, 0, isl_set_n_param(ctx_set));
        model = isl_basic_set_empty(dim);
        ctx_set = isl_set_to_underlying_set(ctx_set);
        set = isl_set_from_underlying_set(ctx_set, model);
        return cloog_domain_from_isl_set(set);
}


/**
 * cloog_domain_union_read function:
 * This function reads a union of polyhedra into a file (input) and
 * returns a pointer to a CloogDomain containing the read information. 
 */
CloogDomain *cloog_domain_union_read(CloogState *state,
                                        FILE *input, int nb_parameters)
{
        struct isl_ctx *ctx = state->backend->ctx;
        struct isl_set *set;

        set = isl_set_read_from_file(ctx, input, nb_parameters);
        return cloog_domain_from_isl_set(set);
}


/**
 * cloog_domain_read_scattering function:
 * This function reads in a scattering function from the file input.
 */
CloogScattering *cloog_domain_read_scattering(CloogDomain *domain, FILE *input)
{
        struct isl_ctx *ctx = domain->set.ctx;
        struct isl_set *set;
        struct isl_map *scat;
        struct isl_dim *dims;
        unsigned nparam;
        unsigned dim;
        unsigned n_scat;

        nparam = isl_set_n_param(&domain->set);
        set = isl_set_read_from_file(ctx, input, nparam);
        dim = isl_set_n_dim(&domain->set);
        n_scat = isl_set_n_dim(set) - dim;
        dims = isl_dim_alloc(ctx, nparam, n_scat, dim);
        scat = isl_map_from_set(set, dims);
        scat = isl_map_reverse(scat);
        return cloog_scattering_from_isl_map(scat);
}

/******************************************************************************
 *                      CloogMatrix Reading function                          *
 ******************************************************************************/

/**
 * isl_constraint_read_from_matrix:
 * Convert a single line of a matrix to a isl_constraint.
 * Returns a pointer to the constraint if successful; NULL otherwise.
 */
static struct isl_constraint *isl_constraint_read_from_matrix(
        struct isl_dim *dim, cloog_int_t *row)
{
        struct isl_constraint *constraint;
        int j;
        int nvariables = isl_dim_size(dim, isl_dim_set);
        int nparam = isl_dim_size(dim, isl_dim_param);

        if (cloog_int_is_zero(row[0]))
                constraint = isl_equality_alloc(dim);
        else
                constraint = isl_inequality_alloc(dim);

        for (j = 0; j < nvariables; ++j)
                isl_constraint_set_coefficient(constraint, isl_dim_out, j,
                                               row[1 + j]);

        for (j = 0; j < nparam; ++j)
                isl_constraint_set_coefficient(constraint, isl_dim_param, j,
                                               row[1 + nvariables + j]);

        isl_constraint_set_constant(constraint, row[1 + nvariables + nparam]);

        return constraint;
}

/**
 * isl_basic_set_read_from_matrix:
 * Convert matrix to basic_set. The matrix contains nparam parameter columns.
 * Returns a pointer to the basic_set if successful; NULL otherwise.
 */
static struct isl_basic_set *isl_basic_set_read_from_matrix(struct isl_ctx *ctx,
        CloogMatrix* matrix, int nparam)
{
        struct isl_dim *dim;
        struct isl_basic_set *bset;
        int i;
        unsigned nrows, ncolumns;

        nrows = matrix->NbRows;
        ncolumns = matrix->NbColumns;
        int nvariables = ncolumns - 2 - nparam;

        dim = isl_dim_set_alloc(ctx, nparam, nvariables);

        bset = isl_basic_set_universe(isl_dim_copy(dim));

        for (i = 0; i < nrows; ++i) {
                cloog_int_t *row = matrix->p[i];
                struct isl_constraint *constraint =
                        isl_constraint_read_from_matrix(isl_dim_copy(dim), row);
                bset = isl_basic_set_add_constraint(bset, constraint);
        }

        isl_dim_free(dim);

        return bset;
}

/**
 * cloog_domain_from_cloog_matrix:
 * Create a CloogDomain containing the constraints described in matrix.
 * nparam is the number of parameters contained in the domain.
 * Returns a pointer to the CloogDomain if successful; NULL otherwise.
 */
CloogDomain *cloog_domain_from_cloog_matrix(CloogState *state,
        CloogMatrix *matrix, int nparam)
{
        struct isl_ctx *ctx = state->backend->ctx;
        struct isl_basic_set *bset;

        bset = isl_basic_set_read_from_matrix(ctx, matrix, nparam);

        return cloog_domain_from_isl_set(isl_set_from_basic_set(bset));
}

/**
 * cloog_scattering_from_cloog_matrix:
 * Create a CloogScattering containing the constraints described in matrix.
 * nparam is the number of parameters contained in the domain.
 * Returns a pointer to the CloogScattering if successful; NULL otherwise.
 */
CloogScattering *cloog_scattering_from_cloog_matrix(CloogState *state,
        CloogMatrix *matrix, int nb_scat, int nb_par)
{
        struct isl_ctx *ctx = state->backend->ctx;
        struct isl_basic_set *bset;
        struct isl_basic_map *scat;
        struct isl_dim *dims;
        unsigned dim;

        bset = isl_basic_set_read_from_matrix(ctx, matrix, nb_par);
        dim = isl_basic_set_n_dim(bset) - nb_scat;
        dims = isl_dim_alloc(ctx, nb_par, nb_scat, dim);

        scat = isl_basic_map_from_basic_set(bset, dims);
        scat = isl_basic_map_reverse(scat);
        return cloog_scattering_from_isl_map(isl_map_from_basic_map(scat));
}


/******************************************************************************
 *                            Processing functions                            *
 ******************************************************************************/



/**
 * cloog_domain_isempty function:
 */ 
int cloog_domain_isempty(CloogDomain *domain)
{
        return isl_set_is_empty(&domain->set);
}


/**
 * cloog_domain_universe function:
 * This function returns the complete dim-dimensional space.
 */
CloogDomain *cloog_domain_universe(CloogState *state, unsigned dim)
{
        struct isl_dim *dims;
        struct isl_basic_set *bset;

        dims = isl_dim_set_alloc(state->backend->ctx, 0, dim);
        bset = isl_basic_set_universe(dims);
        return cloog_domain_from_isl_set(isl_set_from_basic_set(bset));
}


/**
 * cloog_domain_project function:
 * This function returns the projection of
 * (domain) on the (level) first dimensions (i.e. outer loops).
 */ 
CloogDomain *cloog_domain_project(CloogDomain *domain, int level)
{
        struct isl_set *set = &domain->set;
        set = isl_set_remove_dims(isl_set_copy(set),
                                        level, isl_set_n_dim(set) - level);
        return cloog_domain_from_isl_set(set);
}


/**
 * cloog_domain_extend function:
 * This function returns the (domain) given as input with (dim)
 * dimensions and (nb_par) parameters.
 * This function does not free (domain), and returns a new CloogDomain.
 */ 
CloogDomain *cloog_domain_extend(CloogDomain *domain, int dim)
{
        struct isl_set *set = &domain->set;
        set = isl_set_extend(isl_set_copy(set), isl_set_n_param(set), dim);
        return cloog_domain_from_isl_set(set);
}


/**
 * cloog_domain_never_integral function:
 * For us, an equality like 3*i -4 = 0 is always false since 4%3 != 0.
 * There is no need to check for such constraints explicitly for the isl
 * backend.
 */
int cloog_domain_never_integral(CloogDomain * domain)
{
        return isl_set_is_empty(&domain->set);
}


/**
 * cloog_domain_stride function:
 * This function finds the stride imposed to unknown with the column number
 * 'strided_level' in order to be integral. For instance, if we have a
 * constraint like -i - 2j + 2k = 0, and we consider k, then k can be integral
 * only if (i + 2j)%2 = 0. Then only if i%2 = 0. Then k imposes a stride 2 to
 * the unknown i. The function returns the imposed stride in a parameter field.
 * - domain is the set of constraint we have to consider,
 * - strided_level is the column number of the unknown for which a stride have
 *   to be found,
 * - looking_level is the column number of the unknown that impose a stride to
 *   the first unknown.
 * - stride is the stride that is returned back as a function parameter. 
 * - offset is the value of the constant c if the condition is of the shape
 *   (i + c)%s = 0, s being the stride.
 */
void cloog_domain_stride(CloogDomain *domain, int strided_level,
        cloog_int_t *stride, cloog_int_t *offset)
{
        struct isl_set *set = &domain->set;
        isl_set_dim_residue_class(set, strided_level - 1, stride, offset);
        if (!isl_int_is_zero(*offset))
                isl_int_sub(*offset, *stride, *offset);
        return;
}


/**
 * cloog_domain_integral_lowerbound function:
 * This function returns 1 if the lower bound of an iterator (such as its
 * column rank in the constraint set 'domain' is 'level') is integral,
 * 0 otherwise. If the lower bound is actually integral, the function fills
 * the 'lower' field with the lower bound value.
 */
int cloog_domain_integral_lowerbound(CloogDomain *domain, int level,
                                        cloog_int_t *lower)
{
        return isl_set_fast_dim_has_fixed_lower_bound(&domain->set, level-1, lower);
}


/**
 * cloog_domain_lazy_equal function:
 * This function returns 1 if the domains given as input are the same, 0 if it
 * is unable to decide.
 */
int cloog_domain_lazy_equal(CloogDomain *d1, CloogDomain *d2)
{
        return isl_set_fast_is_equal(&d1->set, &d2->set);
}


/**
 * cloog_scattering_lazy_block function:
 * This function returns 1 if the two scattering functions s1 and s2 given
 * as input are the same (except possibly for the final dimension, where we
 * allow a difference of 1), assuming that the domains on which this
 * scatterings are applied are the same.
 * In fact this function answers the question "can I
 * safely consider the two domains as only one with two statements (a block) ?".
 * - s1 and s2 are the two domains to check for blocking,
 * - scattering is the linked list of all domains,
 * - scattdims is the total number of scattering dimentions.
 */
int cloog_scattering_lazy_block(CloogScattering *s1, CloogScattering *s2,
                            CloogScatteringList *scattering, int scattdims)
{
        int i;
        struct isl_dim *dim;
        struct isl_map *rel;
        struct isl_set *delta;
        int fixed, block;
        isl_int cst;
        unsigned n_scat;

        n_scat = isl_map_dim(&s1->map, isl_dim_out);
        if (n_scat != isl_map_dim(&s2->map, isl_dim_out))
                return 0;

        dim = isl_dim_copy(s1->map.dim);
        dim = isl_dim_domain(dim);
        rel = isl_map_identity(dim);
        rel = isl_map_apply_domain(rel, isl_map_copy(&s1->map));
        rel = isl_map_apply_range(rel, isl_map_copy(&s2->map));
        delta = isl_map_deltas(rel);
        isl_int_init(cst);
        for (i = 0; i < n_scat; ++i) {
                fixed = isl_set_fast_dim_is_fixed(delta, i, &cst);
                if (fixed != 1)
                        break;
                if (i+1 < n_scat && !isl_int_is_zero(cst))
                        break;
                if (!isl_int_is_zero(cst) && !isl_int_is_one(cst))
                        break;
        }
        block = i >= n_scat;
        isl_int_clear(cst);
        isl_set_free(delta);
        return block;
}


/**
 * cloog_domain_lazy_disjoint function:
 * This function returns 1 if the domains given as input are disjoint, 0 if it
 * is unable to decide.
 */
int cloog_domain_lazy_disjoint(CloogDomain *d1, CloogDomain *d2)
{
        return isl_set_fast_is_disjoint(&d1->set, &d2->set);
} 
 
 
/**
 * cloog_scattering_list_lazy_same function:
 * This function returns 1 if two domains in the list are the same, 0 if it
 * is unable to decide.
 */
int cloog_scattering_list_lazy_same(CloogScatteringList *list)
{
        CloogScatteringList *one, *other;

        for (one = list; one; one = one->next)
                for (other = one->next; other; other = other->next)
                        if (isl_map_fast_is_equal(&one->scatt->map,
                                                  &other->scatt->map))
                                return 1;
        return 0;
}

int cloog_domain_dimension(CloogDomain * domain)
{
        return isl_set_n_dim(&domain->set);
}

int cloog_domain_parameter_dimension(CloogDomain *domain)
{
        return isl_set_n_param(&domain->set);
}

int cloog_scattering_dimension(CloogScattering *scatt, CloogDomain *domain)
{
        return isl_map_dim(&scatt->map, isl_dim_out);
}

int cloog_domain_isconvex(CloogDomain * domain)
{
        return domain->set.n <= 1;
}


/**
 * cloog_domain_cut_first function:
 * This function splits off and returns the first convex set in the
 * union "domain".  The remainder of the union is returned in rest.
 * The original "domain" itself is destroyed and may not be used
 * after a call to this function.
 */
CloogDomain *cloog_domain_cut_first(CloogDomain *domain, CloogDomain **rest)
{
        struct isl_set *set;
        struct isl_basic_set *first;

        set = &domain->set;
        first = isl_set_copy_basic_set(set);
        set = isl_set_drop_basic_set(set, first);
        *rest = cloog_domain_from_isl_set(set);

        return cloog_domain_from_isl_set(isl_set_from_basic_set(first));
}


/**
 * Given a union domain, try to find a simpler representation
 * using fewer sets in the union.
 * The original "domain" itself is destroyed and may not be used
 * after a call to this function.
 */
CloogDomain *cloog_domain_simplify_union(CloogDomain *domain)
{
      return cloog_domain_from_isl_set(isl_set_coalesce(&domain->set));
}


/**
 * cloog_scattering_lazy_isscalar function:
 * this function returns 1 if the scattering dimension 'dimension' in the
 * scattering 'scatt' is constant.
 * If value is not NULL, then it is set to the constant value of dimension.
 */
int cloog_scattering_lazy_isscalar(CloogScattering *scatt, int dimension,
                                        cloog_int_t *value)
{
        return isl_map_fast_is_fixed(&scatt->map, isl_dim_out, dimension, value);
}


/**
 * cloog_domain_lazy_isconstant function:
 * this function returns 1 if the dimension 'dimension' in the
 * domain 'domain' is constant.
 * If value is not NULL, then it is set to the constant value of dimension.
 */
int cloog_domain_lazy_isconstant(CloogDomain *domain, int dimension)
{
        return isl_set_fast_dim_is_fixed(&domain->set, dimension, NULL);
}


/**
 * cloog_scattering_erase_dimension function:
 * this function returns a CloogDomain structure builds from 'domain' where
 * we removed the dimension 'dimension' and every constraint involving this
 * dimension.
 */
CloogScattering *cloog_scattering_erase_dimension(CloogScattering *domain,
                                                int dimension)
{
        struct isl_map *map;
        map = isl_map_remove(isl_map_copy(&domain->map), isl_dim_out, dimension, 1);
        return cloog_scattering_from_isl_map(map);
}

/**
 * cloog_domain_cube:
 * Construct and return a dim-dimensional cube, with values ranging
 * between min and max in each dimension.
 */
CloogDomain *cloog_domain_cube(CloogState *state,
                                int dim, cloog_int_t min, cloog_int_t max)
{
        int i;
        struct isl_basic_set *cube;
        struct isl_basic_set *interval;
        struct isl_basic_set_list *list;

        if (dim == 0)
                return cloog_domain_universe(state, dim);

        interval = isl_basic_set_interval(state->backend->ctx, min, max);
        list = isl_basic_set_list_alloc(state->backend->ctx, dim);
        for (i = 0; i < dim; ++i)
                list = isl_basic_set_list_add(list, isl_basic_set_copy(interval));
        isl_basic_set_free(interval);
        cube = isl_basic_set_product(list);
        return cloog_domain_from_isl_set(isl_set_from_basic_set(cube));
}


/**
 * cloog_domain_scatter function:
 * This function add the scattering (scheduling) informations to a domain.
 */
CloogDomain *cloog_domain_scatter(CloogDomain *domain, CloogScattering *scatt)
{
        struct isl_map *map;

        map = isl_map_reverse(isl_map_copy(&scatt->map));
        map = isl_map_intersect_range(map, &domain->set);
        return cloog_domain_from_isl_set(isl_set_from_map(map));
}