generalize isl_multi_aff_sub

[isl.git] / isl_ast_build.c

/*
 * Copyright 2012      Ecole Normale Superieure
 * Copyright 2014      INRIA Rocquencourt
 *
 * Use of this software is governed by the MIT license
 *
 * Written by Sven Verdoolaege,
 * Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
 * B.P. 105 - 78153 Le Chesnay, France
 */

#include <isl/map.h>
#include <isl/aff.h>
#include <isl/map.h>
#include <isl_ast_build_private.h>
#include <isl_ast_private.h>

/* Construct a map that isolates the current dimension.
 *
 * Essentially, the current dimension of "set" is moved to the single output
 * dimension in the result, with the current dimension in the domain replaced
 * by an unconstrained variable.
 */
__isl_give isl_map *isl_ast_build_map_to_iterator(
        __isl_keep isl_ast_build *build, __isl_take isl_set *set)
{
        isl_map *map;

        map = isl_map_from_domain(set);
        map = isl_map_add_dims(map, isl_dim_out, 1);

        if (!build)
                return isl_map_free(map);

        map = isl_map_equate(map, isl_dim_in, build->depth, isl_dim_out, 0);
        map = isl_map_eliminate(map, isl_dim_in, build->depth, 1);

        return map;
}

/* Initialize the information derived during the AST generation to default
 * values for a schedule domain in "space".
 *
 * We also check that the remaining fields are not NULL so that
 * the calling functions don't have to perform this test.
 */
static __isl_give isl_ast_build *isl_ast_build_init_derived(
        __isl_take isl_ast_build *build, __isl_take isl_space *space)
{
        isl_ctx *ctx;
        isl_vec *strides;

        build = isl_ast_build_cow(build);
        if (!build || !build->domain)
                goto error;

        ctx = isl_ast_build_get_ctx(build);
        strides = isl_vec_alloc(ctx, isl_space_dim(space, isl_dim_set));
        strides = isl_vec_set_si(strides, 1);

        isl_vec_free(build->strides);
        build->strides = strides;

        space = isl_space_map_from_set(space);
        isl_multi_aff_free(build->offsets);
        build->offsets = isl_multi_aff_zero(isl_space_copy(space));
        isl_multi_aff_free(build->values);
        build->values = isl_multi_aff_identity(space);

        if (!build->iterators || !build->domain || !build->generated ||
            !build->pending || !build->values ||
            !build->strides || !build->offsets || !build->options)
                return isl_ast_build_free(build);

        return build;
error:
        isl_space_free(space);
        return isl_ast_build_free(build);
}

/* Return an isl_id called "c%d", with "%d" set to "i".
 * If an isl_id with such a name already appears among the parameters
 * in build->domain, then adjust the name to "c%d_%d".
 */
static __isl_give isl_id *generate_name(isl_ctx *ctx, int i,
        __isl_keep isl_ast_build *build)
{
        int j;
        char name[16];
        isl_set *dom = build->domain;

        snprintf(name, sizeof(name), "c%d", i);
        j = 0;
        while (isl_set_find_dim_by_name(dom, isl_dim_param, name) >= 0)
                snprintf(name, sizeof(name), "c%d_%d", i, j++);
        return isl_id_alloc(ctx, name, NULL);
}

/* Create an isl_ast_build with "set" as domain.
 *
 * The input set is usually a parameter domain, but we currently allow it to
 * be any kind of set.  We set the domain of the returned isl_ast_build
 * to "set" and initialize all the other fields to default values.
 */
__isl_give isl_ast_build *isl_ast_build_from_context(__isl_take isl_set *set)
{
        int i, n;
        isl_ctx *ctx;
        isl_space *space;
        isl_ast_build *build;

        set = isl_set_compute_divs(set);
        if (!set)
                return NULL;

        ctx = isl_set_get_ctx(set);

        build = isl_calloc_type(ctx, isl_ast_build);
        if (!build)
                goto error;

        build->ref = 1;
        build->domain = set;
        build->generated = isl_set_copy(build->domain);
        build->pending = isl_set_universe(isl_set_get_space(build->domain));
        build->options = isl_union_map_empty(isl_space_params_alloc(ctx, 0));
        n = isl_set_dim(set, isl_dim_set);
        build->depth = n;
        build->iterators = isl_id_list_alloc(ctx, n);
        for (i = 0; i < n; ++i) {
                isl_id *id;
                if (isl_set_has_dim_id(set, isl_dim_set, i))
                        id = isl_set_get_dim_id(set, isl_dim_set, i);
                else
                        id = generate_name(ctx, i, build);
                build->iterators = isl_id_list_add(build->iterators, id);
        }
        space = isl_set_get_space(set);
        if (isl_space_is_params(space))
                space = isl_space_set_from_params(space);

        return isl_ast_build_init_derived(build, space);
error:
        isl_set_free(set);
        return NULL;
}

__isl_give isl_ast_build *isl_ast_build_copy(__isl_keep isl_ast_build *build)
{
        if (!build)
                return NULL;

        build->ref++;
        return build;
}

__isl_give isl_ast_build *isl_ast_build_dup(__isl_keep isl_ast_build *build)
{
        isl_ctx *ctx;
        isl_ast_build *dup;

        if (!build)
                return NULL;

        ctx = isl_ast_build_get_ctx(build);
        dup = isl_calloc_type(ctx, isl_ast_build);
        if (!dup)
                return NULL;

        dup->ref = 1;
        dup->outer_pos = build->outer_pos;
        dup->depth = build->depth;
        dup->iterators = isl_id_list_copy(build->iterators);
        dup->domain = isl_set_copy(build->domain);
        dup->generated = isl_set_copy(build->generated);
        dup->pending = isl_set_copy(build->pending);
        dup->values = isl_multi_aff_copy(build->values);
        dup->value = isl_pw_aff_copy(build->value);
        dup->strides = isl_vec_copy(build->strides);
        dup->offsets = isl_multi_aff_copy(build->offsets);
        dup->executed = isl_union_map_copy(build->executed);
        dup->single_valued = build->single_valued;
        dup->options = isl_union_map_copy(build->options);
        dup->at_each_domain = build->at_each_domain;
        dup->at_each_domain_user = build->at_each_domain_user;
        dup->before_each_for = build->before_each_for;
        dup->before_each_for_user = build->before_each_for_user;
        dup->after_each_for = build->after_each_for;
        dup->after_each_for_user = build->after_each_for_user;
        dup->create_leaf = build->create_leaf;
        dup->create_leaf_user = build->create_leaf_user;

        if (!dup->iterators || !dup->domain || !dup->generated ||
            !dup->pending || !dup->values ||
            !dup->strides || !dup->offsets || !dup->options ||
            (build->executed && !dup->executed) ||
            (build->value && !dup->value))
                return isl_ast_build_free(dup);

        return dup;
}

/* Align the parameters of "build" to those of "model", introducing
 * additional parameters if needed.
 */
__isl_give isl_ast_build *isl_ast_build_align_params(
        __isl_take isl_ast_build *build, __isl_take isl_space *model)
{
        build = isl_ast_build_cow(build);
        if (!build)
                goto error;

        build->domain = isl_set_align_params(build->domain,
                                                isl_space_copy(model));
        build->generated = isl_set_align_params(build->generated,
                                                isl_space_copy(model));
        build->pending = isl_set_align_params(build->pending,
                                                isl_space_copy(model));
        build->values = isl_multi_aff_align_params(build->values,
                                                isl_space_copy(model));
        build->offsets = isl_multi_aff_align_params(build->offsets,
                                                isl_space_copy(model));
        build->options = isl_union_map_align_params(build->options,
                                                isl_space_copy(model));
        isl_space_free(model);

        if (!build->domain || !build->values || !build->offsets ||
            !build->options)
                return isl_ast_build_free(build);

        return build;
error:
        isl_space_free(model);
        return NULL;
}

__isl_give isl_ast_build *isl_ast_build_cow(__isl_take isl_ast_build *build)
{
        if (!build)
                return NULL;

        if (build->ref == 1)
                return build;
        build->ref--;
        return isl_ast_build_dup(build);
}

__isl_null isl_ast_build *isl_ast_build_free(
        __isl_take isl_ast_build *build)
{
        if (!build)
                return NULL;

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

        isl_id_list_free(build->iterators);
        isl_set_free(build->domain);
        isl_set_free(build->generated);
        isl_set_free(build->pending);
        isl_multi_aff_free(build->values);
        isl_pw_aff_free(build->value);
        isl_vec_free(build->strides);
        isl_multi_aff_free(build->offsets);
        isl_multi_aff_free(build->schedule_map);
        isl_union_map_free(build->executed);
        isl_union_map_free(build->options);

        free(build);

        return NULL;
}

isl_ctx *isl_ast_build_get_ctx(__isl_keep isl_ast_build *build)
{
        return build ? isl_set_get_ctx(build->domain) : NULL;
}

/* Replace build->options by "options".
 */
__isl_give isl_ast_build *isl_ast_build_set_options(
        __isl_take isl_ast_build *build, __isl_take isl_union_map *options)
{
        build = isl_ast_build_cow(build);

        if (!build || !options)
                goto error;

        isl_union_map_free(build->options);
        build->options = options;

        return build;
error:
        isl_union_map_free(options);
        return isl_ast_build_free(build);
}

/* Set the iterators for the next code generation.
 *
 * If we still have some iterators left from the previous code generation
 * (if any) or if iterators have already been set by a previous
 * call to this function, then we remove them first.
 */
__isl_give isl_ast_build *isl_ast_build_set_iterators(
        __isl_take isl_ast_build *build, __isl_take isl_id_list *iterators)
{
        int dim, n_it;

        build = isl_ast_build_cow(build);
        if (!build)
                goto error;

        dim = isl_set_dim(build->domain, isl_dim_set);
        n_it = isl_id_list_n_id(build->iterators);
        if (n_it < dim)
                isl_die(isl_ast_build_get_ctx(build), isl_error_internal,
                        "isl_ast_build in inconsistent state", goto error);
        if (n_it > dim)
                build->iterators = isl_id_list_drop(build->iterators,
                                                        dim, n_it - dim);
        build->iterators = isl_id_list_concat(build->iterators, iterators);
        if (!build->iterators)
                return isl_ast_build_free(build);

        return build;
error:
        isl_id_list_free(iterators);
        return isl_ast_build_free(build);
}

/* Set the "at_each_domain" callback of "build" to "fn".
 */
__isl_give isl_ast_build *isl_ast_build_set_at_each_domain(
        __isl_take isl_ast_build *build,
        __isl_give isl_ast_node *(*fn)(__isl_take isl_ast_node *node,
                __isl_keep isl_ast_build *build, void *user), void *user)
{
        build = isl_ast_build_cow(build);

        if (!build)
                return NULL;

        build->at_each_domain = fn;
        build->at_each_domain_user = user;

        return build;
}

/* Set the "before_each_for" callback of "build" to "fn".
 */
__isl_give isl_ast_build *isl_ast_build_set_before_each_for(
        __isl_take isl_ast_build *build,
        __isl_give isl_id *(*fn)(__isl_keep isl_ast_build *build,
                void *user), void *user)
{
        build = isl_ast_build_cow(build);

        if (!build)
                return NULL;

        build->before_each_for = fn;
        build->before_each_for_user = user;

        return build;
}

/* Set the "after_each_for" callback of "build" to "fn".
 */
__isl_give isl_ast_build *isl_ast_build_set_after_each_for(
        __isl_take isl_ast_build *build,
        __isl_give isl_ast_node *(*fn)(__isl_take isl_ast_node *node,
                __isl_keep isl_ast_build *build, void *user), void *user)
{
        build = isl_ast_build_cow(build);

        if (!build)
                return NULL;

        build->after_each_for = fn;
        build->after_each_for_user = user;

        return build;
}

/* Set the "create_leaf" callback of "build" to "fn".
 */
__isl_give isl_ast_build *isl_ast_build_set_create_leaf(
        __isl_take isl_ast_build *build,
        __isl_give isl_ast_node *(*fn)(__isl_take isl_ast_build *build,
                void *user), void *user)
{
        build = isl_ast_build_cow(build);

        if (!build)
                return NULL;

        build->create_leaf = fn;
        build->create_leaf_user = user;

        return build;
}

/* Clear all information that is specific to this code generation
 * and that is (probably) not meaningful to any nested code generation.
 */
__isl_give isl_ast_build *isl_ast_build_clear_local_info(
        __isl_take isl_ast_build *build)
{
        isl_space *space;

        build = isl_ast_build_cow(build);
        if (!build)
                return NULL;

        space = isl_union_map_get_space(build->options);
        isl_union_map_free(build->options);
        build->options = isl_union_map_empty(space);

        build->at_each_domain = NULL;
        build->at_each_domain_user = NULL;
        build->before_each_for = NULL;
        build->before_each_for_user = NULL;
        build->after_each_for = NULL;
        build->after_each_for_user = NULL;
        build->create_leaf = NULL;
        build->create_leaf_user = NULL;

        if (!build->options)
                return isl_ast_build_free(build);

        return build;
}

/* Have any loops been eliminated?
 * That is, do any of the original schedule dimensions have a fixed
 * value that has been substituted?
 */
static int any_eliminated(isl_ast_build *build)
{
        int i;

        for (i = 0; i < build->depth; ++i)
                if (isl_ast_build_has_affine_value(build, i))
                        return 1;

        return 0;
}

/* Clear build->schedule_map.
 * This function should be called whenever anything that might affect
 * the result of isl_ast_build_get_schedule_map_multi_aff changes.
 * In particular, it should be called when the depth is changed or
 * when an iterator is determined to have a fixed value.
 */
static void isl_ast_build_reset_schedule_map(__isl_keep isl_ast_build *build)
{
        if (!build)
                return;
        isl_multi_aff_free(build->schedule_map);
        build->schedule_map = NULL;
}

/* Do we need a (non-trivial) schedule map?
 * That is, is the internal schedule space different from
 * the external schedule space?
 *
 * The internal and external schedule spaces are only the same
 * if code has been generated for the entire schedule and if none
 * of the loops have been eliminated.
 */
__isl_give int isl_ast_build_need_schedule_map(__isl_keep isl_ast_build *build)
{
        int dim;

        if (!build)
                return -1;

        dim = isl_set_dim(build->domain, isl_dim_set);
        return build->depth != dim || any_eliminated(build);
}

/* Return a mapping from the internal schedule space to the external
 * schedule space in the form of an isl_multi_aff.
 * The internal schedule space originally corresponds to that of the
 * input schedule.  This may change during the code generation if
 * if isl_ast_build_insert_dim is ever called.
 * The external schedule space corresponds to the
 * loops that have been generated.
 *
 * Currently, the only difference between the internal schedule domain
 * and the external schedule domain is that some dimensions are projected
 * out in the external schedule domain.  In particular, the dimensions
 * for which no code has been generated yet and the dimensions that correspond
 * to eliminated loops.
 *
 * We cache a copy of the schedule_map in build->schedule_map.
 * The cache is cleared through isl_ast_build_reset_schedule_map
 * whenever anything changes that might affect the result of this function.
 */
__isl_give isl_multi_aff *isl_ast_build_get_schedule_map_multi_aff(
        __isl_keep isl_ast_build *build)
{
        isl_space *space;
        isl_multi_aff *ma;

        if (!build)
                return NULL;
        if (build->schedule_map)
                return isl_multi_aff_copy(build->schedule_map);

        space = isl_ast_build_get_space(build, 1);
        space = isl_space_map_from_set(space);
        ma = isl_multi_aff_identity(space);
        if (isl_ast_build_need_schedule_map(build)) {
                int i;
                int dim = isl_set_dim(build->domain, isl_dim_set);
                ma = isl_multi_aff_drop_dims(ma, isl_dim_out,
                                        build->depth, dim - build->depth);
                for (i = build->depth - 1; i >= 0; --i)
                        if (isl_ast_build_has_affine_value(build, i))
                                ma = isl_multi_aff_drop_dims(ma,
                                                        isl_dim_out, i, 1);
        }

        build->schedule_map = ma;
        return isl_multi_aff_copy(build->schedule_map);
}

/* Return a mapping from the internal schedule space to the external
 * schedule space in the form of an isl_map.
 */
__isl_give isl_map *isl_ast_build_get_schedule_map(
        __isl_keep isl_ast_build *build)
{
        isl_multi_aff *ma;

        ma = isl_ast_build_get_schedule_map_multi_aff(build);
        return isl_map_from_multi_aff(ma);
}

/* Return the position of the dimension in build->domain for which
 * an AST node is currently being generated.
 */
int isl_ast_build_get_depth(__isl_keep isl_ast_build *build)
{
        return build ? build->depth : -1;
}

/* Prepare for generating code for the next level.
 * In particular, increase the depth and reset any information
 * that is local to the current depth.
 */
__isl_give isl_ast_build *isl_ast_build_increase_depth(
        __isl_take isl_ast_build *build)
{
        build = isl_ast_build_cow(build);
        if (!build)
                return NULL;
        build->depth++;
        isl_ast_build_reset_schedule_map(build);
        build->value = isl_pw_aff_free(build->value);
        return build;
}

void isl_ast_build_dump(__isl_keep isl_ast_build *build)
{
        if (!build)
                return;

        fprintf(stderr, "domain: ");
        isl_set_dump(build->domain);
        fprintf(stderr, "generated: ");
        isl_set_dump(build->generated);
        fprintf(stderr, "pending: ");
        isl_set_dump(build->pending);
        fprintf(stderr, "iterators: ");
        isl_id_list_dump(build->iterators);
        fprintf(stderr, "values: ");
        isl_multi_aff_dump(build->values);
        if (build->value) {
                fprintf(stderr, "value: ");
                isl_pw_aff_dump(build->value);
        }
        fprintf(stderr, "strides: ");
        isl_vec_dump(build->strides);
        fprintf(stderr, "offsets: ");
        isl_multi_aff_dump(build->offsets);
}

/* Initialize "build" for AST construction in schedule space "space"
 * in the case that build->domain is a parameter set.
 *
 * build->iterators is assumed to have been updated already.
 */
static __isl_give isl_ast_build *isl_ast_build_init(
        __isl_take isl_ast_build *build, __isl_take isl_space *space)
{
        isl_set *set;

        build = isl_ast_build_cow(build);
        if (!build)
                goto error;

        set = isl_set_universe(isl_space_copy(space));
        build->domain = isl_set_intersect_params(isl_set_copy(set),
                                                    build->domain);
        build->pending = isl_set_intersect_params(isl_set_copy(set),
                                                    build->pending);
        build->generated = isl_set_intersect_params(set, build->generated);

        return isl_ast_build_init_derived(build, space);
error:
        isl_ast_build_free(build);
        isl_space_free(space);
        return NULL;
}

/* Assign "aff" to *user and return -1, effectively extracting
 * the first (and presumably only) affine expression in the isl_pw_aff
 * on which this function is used.
 */
static int extract_single_piece(__isl_take isl_set *set,
        __isl_take isl_aff *aff, void *user)
{
        isl_aff **p = user;

        *p = aff;
        isl_set_free(set);

        return -1;
}

/* Intersect "set" with the stride constraint of "build", if any.
 */
static __isl_give isl_set *intersect_stride_constraint(__isl_take isl_set *set,
        __isl_keep isl_ast_build *build)
{
        isl_set *stride;

        if (!build)
                return isl_set_free(set);
        if (!isl_ast_build_has_stride(build, build->depth))
                return set;

        stride = isl_ast_build_get_stride_constraint(build);
        return isl_set_intersect(set, stride);
}

/* Check if the given bounds on the current dimension (together with
 * the stride constraint, if any) imply that
 * this current dimension attains only a single value (in terms of
 * parameters and outer dimensions).
 * If so, we record it in build->value.
 * If, moreover, this value can be represented as a single affine expression,
 * then we also update build->values, effectively marking the current
 * dimension as "eliminated".
 *
 * When computing the gist of the fixed value that can be represented
 * as a single affine expression, it is important to only take into
 * account the domain constraints in the original AST build and
 * not the domain of the affine expression itself.
 * Otherwise, a [i/3] is changed into a i/3 because we know that i
 * is a multiple of 3, but then we end up not expressing anywhere
 * in the context that i is a multiple of 3.
 */
static __isl_give isl_ast_build *update_values(
        __isl_take isl_ast_build *build, __isl_take isl_basic_set *bounds)
{
        int sv;
        isl_pw_multi_aff *pma;
        isl_aff *aff = NULL;
        isl_map *it_map;
        isl_set *set;

        set = isl_set_from_basic_set(bounds);
        set = isl_set_intersect(set, isl_set_copy(build->domain));
        set = intersect_stride_constraint(set, build);
        it_map = isl_ast_build_map_to_iterator(build, set);

        sv = isl_map_is_single_valued(it_map);
        if (sv < 0)
                build = isl_ast_build_free(build);
        if (!build || !sv) {
                isl_map_free(it_map);
                return build;
        }

        pma = isl_pw_multi_aff_from_map(it_map);
        build->value = isl_pw_multi_aff_get_pw_aff(pma, 0);
        build->value = isl_ast_build_compute_gist_pw_aff(build, build->value);
        build->value = isl_pw_aff_coalesce(build->value);
        isl_pw_multi_aff_free(pma);

        if (!build->value)
                return isl_ast_build_free(build);

        if (isl_pw_aff_n_piece(build->value) != 1)
                return build;

        isl_pw_aff_foreach_piece(build->value, &extract_single_piece, &aff);

        build->values = isl_multi_aff_set_aff(build->values, build->depth, aff);
        if (!build->values)
                return isl_ast_build_free(build);
        isl_ast_build_reset_schedule_map(build);
        return build;
}

/* Update the AST build based on the given loop bounds for
 * the current dimension and the stride information available in the build.
 *
 * We first make sure that the bounds do not refer to any iterators
 * that have already been eliminated.
 * Then, we check if the bounds imply that the current iterator
 * has a fixed value.
 * If they do and if this fixed value can be expressed as a single
 * affine expression, we eliminate the iterators from the bounds.
 * Note that we cannot simply plug in this single value using
 * isl_basic_set_preimage_multi_aff as the single value may only
 * be defined on a subset of the domain.  Plugging in the value
 * would restrict the build domain to this subset, while this
 * restriction may not be reflected in the generated code.
 * Finally, we intersect build->domain with the updated bounds.
 * We also add the stride constraint unless we have been able
 * to find a fixed value expressed as a single affine expression.
 *
 * Note that the check for a fixed value in update_values requires
 * us to intersect the bounds with the current build domain.
 * When we intersect build->domain with the updated bounds in
 * the final step, we make sure that these updated bounds have
 * not been intersected with the old build->domain.
 * Otherwise, we would indirectly intersect the build domain with itself,
 * which can lead to inefficiencies, in particular if the build domain
 * contains any unknown divs.
 */
__isl_give isl_ast_build *isl_ast_build_set_loop_bounds(
        __isl_take isl_ast_build *build, __isl_take isl_basic_set *bounds)
{
        isl_set *set;

        build = isl_ast_build_cow(build);
        if (!build)
                goto error;

        bounds = isl_basic_set_preimage_multi_aff(bounds,
                                        isl_multi_aff_copy(build->values));
        build = update_values(build, isl_basic_set_copy(bounds));
        if (!build)
                goto error;
        set = isl_set_from_basic_set(isl_basic_set_copy(bounds));
        if (isl_ast_build_has_affine_value(build, build->depth)) {
                set = isl_set_eliminate(set, isl_dim_set, build->depth, 1);
                set = isl_set_compute_divs(set);
                build->pending = isl_set_intersect(build->pending,
                                                        isl_set_copy(set));
                build->domain = isl_set_intersect(build->domain, set);
        } else {
                isl_basic_set *generated, *pending;

                pending = isl_basic_set_copy(bounds);
                pending = isl_basic_set_drop_constraints_involving_dims(pending,
                                        isl_dim_set, build->depth, 1);
                build->pending = isl_set_intersect(build->pending,
                                        isl_set_from_basic_set(pending));
                generated = isl_basic_set_copy(bounds);
                generated = isl_basic_set_drop_constraints_not_involving_dims(
                                    generated, isl_dim_set, build->depth, 1);
                build->generated = isl_set_intersect(build->generated,
                                        isl_set_from_basic_set(generated));
                build->domain = isl_set_intersect(build->domain, set);
                build = isl_ast_build_include_stride(build);
                if (!build)
                        goto error;
        }
        isl_basic_set_free(bounds);

        if (!build->domain || !build->pending || !build->generated)
                return isl_ast_build_free(build);

        return build;
error:
        isl_ast_build_free(build);
        isl_basic_set_free(bounds);
        return NULL;
}

/* Intersect build->domain with "set", where "set" is specified
 * in terms of the internal schedule domain.
 */
static __isl_give isl_ast_build *isl_ast_build_restrict_internal(
        __isl_take isl_ast_build *build, __isl_take isl_set *set)
{
        build = isl_ast_build_cow(build);
        if (!build)
                goto error;

        set = isl_set_compute_divs(set);
        build->domain = isl_set_intersect(build->domain, set);
        build->domain = isl_set_coalesce(build->domain);

        if (!build->domain)
                return isl_ast_build_free(build);

        return build;
error:
        isl_ast_build_free(build);
        isl_set_free(set);
        return NULL;
}

/* Intersect build->generated and build->domain with "set",
 * where "set" is specified in terms of the internal schedule domain.
 */
__isl_give isl_ast_build *isl_ast_build_restrict_generated(
        __isl_take isl_ast_build *build, __isl_take isl_set *set)
{
        set = isl_set_compute_divs(set);
        build = isl_ast_build_restrict_internal(build, isl_set_copy(set));
        build = isl_ast_build_cow(build);
        if (!build)
                goto error;

        build->generated = isl_set_intersect(build->generated, set);
        build->generated = isl_set_coalesce(build->generated);

        if (!build->generated)
                return isl_ast_build_free(build);

        return build;
error:
        isl_ast_build_free(build);
        isl_set_free(set);
        return NULL;
}

/* Replace the set of pending constraints by "guard", which is then
 * no longer considered as pending.
 * That is, add "guard" to the generated constraints and clear all pending
 * constraints, making the domain equal to the generated constraints.
 */
__isl_give isl_ast_build *isl_ast_build_replace_pending_by_guard(
        __isl_take isl_ast_build *build, __isl_take isl_set *guard)
{
        build = isl_ast_build_restrict_generated(build, guard);
        build = isl_ast_build_cow(build);
        if (!build)
                return NULL;

        isl_set_free(build->domain);
        build->domain = isl_set_copy(build->generated);
        isl_set_free(build->pending);
        build->pending = isl_set_universe(isl_set_get_space(build->domain));

        if (!build->pending)
                return isl_ast_build_free(build);

        return build;
}

/* Intersect build->pending and build->domain with "set",
 * where "set" is specified in terms of the internal schedule domain.
 */
__isl_give isl_ast_build *isl_ast_build_restrict_pending(
        __isl_take isl_ast_build *build, __isl_take isl_set *set)
{
        set = isl_set_compute_divs(set);
        build = isl_ast_build_restrict_internal(build, isl_set_copy(set));
        build = isl_ast_build_cow(build);
        if (!build)
                goto error;

        build->pending = isl_set_intersect(build->pending, set);
        build->pending = isl_set_coalesce(build->pending);

        if (!build->pending)
                return isl_ast_build_free(build);

        return build;
error:
        isl_ast_build_free(build);
        isl_set_free(set);
        return NULL;
}

/* Intersect build->domain with "set", where "set" is specified
 * in terms of the external schedule domain.
 */
__isl_give isl_ast_build *isl_ast_build_restrict(
        __isl_take isl_ast_build *build, __isl_take isl_set *set)
{
        if (isl_set_is_params(set))
                return isl_ast_build_restrict_generated(build, set);

        if (isl_ast_build_need_schedule_map(build)) {
                isl_multi_aff *ma;
                ma = isl_ast_build_get_schedule_map_multi_aff(build);
                set = isl_set_preimage_multi_aff(set, ma);
        }
        return isl_ast_build_restrict_generated(build, set);
}

/* Replace build->executed by "executed".
 */
__isl_give isl_ast_build *isl_ast_build_set_executed(
        __isl_take isl_ast_build *build, __isl_take isl_union_map *executed)
{
        build = isl_ast_build_cow(build);
        if (!build)
                goto error;

        isl_union_map_free(build->executed);
        build->executed = executed;

        return build;
error:
        isl_ast_build_free(build);
        isl_union_map_free(executed);
        return NULL;
}

/* Return a copy of the current schedule domain.
 */
__isl_give isl_set *isl_ast_build_get_domain(__isl_keep isl_ast_build *build)
{
        return build ? isl_set_copy(build->domain) : NULL;
}

/* Return a copy of the set of pending constraints.
 */
__isl_give isl_set *isl_ast_build_get_pending(
        __isl_keep isl_ast_build *build)
{
        return build ? isl_set_copy(build->pending) : NULL;
}

/* Return a copy of the set of generated constraints.
 */
__isl_give isl_set *isl_ast_build_get_generated(
        __isl_keep isl_ast_build *build)
{
        return build ? isl_set_copy(build->generated) : NULL;
}

/* Return the number of variables of the given type
 * in the (internal) schedule space.
 */
unsigned isl_ast_build_dim(__isl_keep isl_ast_build *build,
        enum isl_dim_type type)
{
        if (!build)
                return 0;
        return isl_set_dim(build->domain, type);
}

/* Return the (schedule) space of "build".
 *
 * If "internal" is set, then this space is the space of the internal
 * representation of the entire schedule, including those parts for
 * which no code has been generated yet.
 *
 * If "internal" is not set, then this space is the external representation
 * of the loops generated so far.
 */
__isl_give isl_space *isl_ast_build_get_space(__isl_keep isl_ast_build *build,
        int internal)
{
        int i;
        int dim;
        isl_space *space;

        if (!build)
                return NULL;

        space = isl_set_get_space(build->domain);
        if (internal)
                return space;

        if (!isl_ast_build_need_schedule_map(build))
                return space;

        dim = isl_set_dim(build->domain, isl_dim_set);
        space = isl_space_drop_dims(space, isl_dim_set,
                                    build->depth, dim - build->depth);
        for (i = build->depth - 1; i >= 0; --i)
                if (isl_ast_build_has_affine_value(build, i))
                        space = isl_space_drop_dims(space, isl_dim_set, i, 1);

        return space;
}

/* Return the external representation of the schedule space of "build",
 * i.e., a space with a dimension for each loop generated so far,
 * with the names of the dimensions set to the loop iterators.
 */
__isl_give isl_space *isl_ast_build_get_schedule_space(
        __isl_keep isl_ast_build *build)
{
        isl_space *space;
        int i, skip;

        if (!build)
                return NULL;

        space = isl_ast_build_get_space(build, 0);

        skip = 0;
        for (i = 0; i < build->depth; ++i) {
                isl_id *id;

                if (isl_ast_build_has_affine_value(build, i)) {
                        skip++;
                        continue;
                }

                id = isl_ast_build_get_iterator_id(build, i);
                space = isl_space_set_dim_id(space, isl_dim_set, i - skip, id);
        }

        return space;
}

/* Return the current schedule, as stored in build->executed, in terms
 * of the external schedule domain.
 */
__isl_give isl_union_map *isl_ast_build_get_schedule(
        __isl_keep isl_ast_build *build)
{
        isl_union_map *executed;
        isl_union_map *schedule;

        if (!build)
                return NULL;

        executed = isl_union_map_copy(build->executed);
        if (isl_ast_build_need_schedule_map(build)) {
                isl_map *proj = isl_ast_build_get_schedule_map(build);
                executed = isl_union_map_apply_domain(executed,
                                        isl_union_map_from_map(proj));
        }
        schedule = isl_union_map_reverse(executed);

        return schedule;
}

/* Return the iterator attached to the internal schedule dimension "pos".
 */
__isl_give isl_id *isl_ast_build_get_iterator_id(
        __isl_keep isl_ast_build *build, int pos)
{
        if (!build)
                return NULL;

        return isl_id_list_get_id(build->iterators, pos);
}

/* Set the stride and offset of the current dimension to the given
 * value and expression.
 *
 * If we had already found a stride before, then the two strides
 * are combined into a single stride.
 *
 * In particular, if the new stride information is of the form
 *
 *      i = f + s (...)
 *
 * and the old stride information is of the form
 *
 *      i = f2 + s2 (...)
 *
 * then we compute the extended gcd of s and s2
 *
 *      a s + b s2 = g,
 *
 * with g = gcd(s,s2), multiply the first equation with t1 = b s2/g
 * and the second with t2 = a s1/g.
 * This results in
 *
 *      i = (b s2 + a s1)/g i = t1 f + t2 f2 + (s s2)/g (...)
 *
 * so that t1 f + t2 f2 is the combined offset and (s s2)/g = lcm(s,s2)
 * is the combined stride.
 */
static __isl_give isl_ast_build *set_stride(__isl_take isl_ast_build *build,
        __isl_take isl_val *stride, __isl_take isl_aff *offset)
{
        int pos;

        build = isl_ast_build_cow(build);
        if (!build || !stride || !offset)
                goto error;

        pos = build->depth;

        if (isl_ast_build_has_stride(build, pos)) {
                isl_val *stride2, *a, *b, *g;
                isl_aff *offset2;

                stride2 = isl_vec_get_element_val(build->strides, pos);
                g = isl_val_gcdext(isl_val_copy(stride), isl_val_copy(stride2),
                                        &a, &b);
                a = isl_val_mul(a, isl_val_copy(stride));
                a = isl_val_div(a, isl_val_copy(g));
                stride2 = isl_val_div(stride2, g);
                b = isl_val_mul(b, isl_val_copy(stride2));
                stride = isl_val_mul(stride, stride2);

                offset2 = isl_multi_aff_get_aff(build->offsets, pos);
                offset2 = isl_aff_scale_val(offset2, a);
                offset = isl_aff_scale_val(offset, b);
                offset = isl_aff_add(offset, offset2);
        }

        build->strides = isl_vec_set_element_val(build->strides, pos, stride);
        build->offsets = isl_multi_aff_set_aff(build->offsets, pos, offset);
        if (!build->strides || !build->offsets)
                return isl_ast_build_free(build);

        return build;
error:
        isl_val_free(stride);
        isl_aff_free(offset);
        return isl_ast_build_free(build);
}

/* Return a set expressing the stride constraint at the current depth.
 *
 * In particular, if the current iterator (i) is known to attain values
 *
 *      f + s a
 *
 * where f is the offset and s is the stride, then the returned set
 * expresses the constraint
 *
 *      (f - i) mod s = 0
 */
__isl_give isl_set *isl_ast_build_get_stride_constraint(
        __isl_keep isl_ast_build *build)
{
        isl_aff *aff;
        isl_set *set;
        isl_val *stride;
        int pos;

        if (!build)
                return NULL;

        pos = build->depth;

        if (!isl_ast_build_has_stride(build, pos))
                return isl_set_universe(isl_ast_build_get_space(build, 1));

        stride = isl_ast_build_get_stride(build, pos);
        aff = isl_ast_build_get_offset(build, pos);
        aff = isl_aff_add_coefficient_si(aff, isl_dim_in, pos, -1);
        aff = isl_aff_mod_val(aff, stride);
        set = isl_set_from_basic_set(isl_aff_zero_basic_set(aff));

        return set;
}

/* Return the expansion implied by the stride and offset at the current
 * depth.
 *
 * That is, return the mapping
 *
 *      [i_0, ..., i_{d-1}, i_d, i_{d+1}, ...]
 *              -> [i_0, ..., i_{d-1}, s * i_d + offset(i),  i_{d+1}, ...]
 *
 * where s is the stride at the current depth d and offset(i) is
 * the corresponding offset.
 */
__isl_give isl_multi_aff *isl_ast_build_get_stride_expansion(
        __isl_keep isl_ast_build *build)
{
        isl_space *space;
        isl_multi_aff *ma;
        int pos;
        isl_aff *aff, *offset;
        isl_val *stride;

        if (!build)
                return NULL;

        pos = isl_ast_build_get_depth(build);
        space = isl_ast_build_get_space(build, 1);
        space = isl_space_map_from_set(space);
        ma = isl_multi_aff_identity(space);

        if (!isl_ast_build_has_stride(build, pos))
                return ma;

        offset = isl_ast_build_get_offset(build, pos);
        stride = isl_ast_build_get_stride(build, pos);
        aff = isl_multi_aff_get_aff(ma, pos);
        aff = isl_aff_scale_val(aff, stride);
        aff = isl_aff_add(aff, offset);
        ma = isl_multi_aff_set_aff(ma, pos, aff);

        return ma;
}

/* Add constraints corresponding to any previously detected
 * stride on the current dimension to build->domain.
 */
__isl_give isl_ast_build *isl_ast_build_include_stride(
        __isl_take isl_ast_build *build)
{
        isl_set *set;

        if (!build)
                return NULL;
        if (!isl_ast_build_has_stride(build, build->depth))
                return build;
        build = isl_ast_build_cow(build);
        if (!build)
                return NULL;

        set = isl_ast_build_get_stride_constraint(build);

        build->domain = isl_set_intersect(build->domain, isl_set_copy(set));
        build->generated = isl_set_intersect(build->generated, set);
        if (!build->domain || !build->generated)
                return isl_ast_build_free(build);

        return build;
}

/* Information used inside detect_stride.
 *
 * "build" may be updated by detect_stride to include stride information.
 * "pos" is equal to build->depth.
 */
struct isl_detect_stride_data {
        isl_ast_build *build;
        int pos;
};

/* Check if constraint "c" imposes any stride on dimension data->pos
 * and, if so, update the stride information in data->build.
 *
 * In order to impose a stride on the dimension, "c" needs to be an equality
 * and it needs to involve the dimension.  Note that "c" may also be
 * a div constraint and thus an inequality that we cannot use.
 *
 * Let c be of the form
 *
 *      h(p) + g * v * i + g * stride * f(alpha) = 0
 *
 * with h(p) an expression in terms of the parameters and outer dimensions
 * and f(alpha) an expression in terms of the existentially quantified
 * variables.  Note that the inner dimensions have been eliminated so
 * they do not appear in "c".
 *
 * If "stride" is not zero and not one, then it represents a non-trivial stride
 * on "i".  We compute a and b such that
 *
 *      a v + b stride = 1
 *
 * We have
 *
 *      g v i = -h(p) + g stride f(alpha)
 *
 *      a g v i = -a h(p) + g stride f(alpha)
 *
 *      a g v i + b g stride i = -a h(p) + g stride * (...)
 *
 *      g i = -a h(p) + g stride * (...)
 *
 *      i = -a h(p)/g + stride * (...)
 *
 * The expression "-a h(p)/g" can therefore be used as offset.
 */
static int detect_stride(__isl_take isl_constraint *c, void *user)
{
        struct isl_detect_stride_data *data = user;
        int i, n_div;
        isl_ctx *ctx;
        isl_val *v, *stride, *m;

        if (!isl_constraint_is_equality(c) ||
            !isl_constraint_involves_dims(c, isl_dim_set, data->pos, 1)) {
                isl_constraint_free(c);
                return 0;
        }

        ctx = isl_constraint_get_ctx(c);
        stride = isl_val_zero(ctx);
        n_div = isl_constraint_dim(c, isl_dim_div);
        for (i = 0; i < n_div; ++i) {
                v = isl_constraint_get_coefficient_val(c, isl_dim_div, i);
                stride = isl_val_gcd(stride, v);
        }

        v = isl_constraint_get_coefficient_val(c, isl_dim_set, data->pos);
        m = isl_val_gcd(isl_val_copy(stride), isl_val_copy(v));
        stride = isl_val_div(stride, isl_val_copy(m));
        v = isl_val_div(v, isl_val_copy(m));

        if (!isl_val_is_zero(stride) && !isl_val_is_one(stride)) {
                isl_aff *aff;
                isl_val *gcd, *a, *b;

                gcd = isl_val_gcdext(v, isl_val_copy(stride), &a, &b);
                isl_val_free(gcd);
                isl_val_free(b);

                aff = isl_constraint_get_aff(c);
                for (i = 0; i < n_div; ++i)
                        aff = isl_aff_set_coefficient_si(aff,
                                                         isl_dim_div, i, 0);
                aff = isl_aff_set_coefficient_si(aff, isl_dim_in, data->pos, 0);
                a = isl_val_neg(a);
                aff = isl_aff_scale_val(aff, a);
                aff = isl_aff_scale_down_val(aff, m);
                data->build = set_stride(data->build, stride, aff);
        } else {
                isl_val_free(stride);
                isl_val_free(m);
                isl_val_free(v);
        }

        isl_constraint_free(c);
        return 0;
}

/* Check if the constraints in "set" imply any stride on the current
 * dimension and, if so, record the stride information in "build"
 * and return the updated "build".
 *
 * We compute the affine hull and then check if any of the constraints
 * in the hull imposes any stride on the current dimension.
 *
 * We assume that inner dimensions have been eliminated from "set"
 * by the caller.  This is needed because the common stride
 * may be imposed by different inner dimensions on different parts of
 * the domain.
 */
__isl_give isl_ast_build *isl_ast_build_detect_strides(
        __isl_take isl_ast_build *build, __isl_take isl_set *set)
{
        isl_basic_set *hull;
        struct isl_detect_stride_data data;

        if (!build)
                goto error;

        data.build = build;
        data.pos = isl_ast_build_get_depth(build);
        hull = isl_set_affine_hull(set);

        if (isl_basic_set_foreach_constraint(hull, &detect_stride, &data) < 0)
                data.build = isl_ast_build_free(data.build);

        isl_basic_set_free(hull);
        return data.build;
error:
        isl_set_free(set);
        return NULL;
}

struct isl_ast_build_involves_data {
        int depth;
        int involves;
};

/* Check if "map" involves the input dimension data->depth.
 */
static int involves_depth(__isl_take isl_map *map, void *user)
{
        struct isl_ast_build_involves_data *data = user;

        data->involves = isl_map_involves_dims(map, isl_dim_in, data->depth, 1);
        isl_map_free(map);

        if (data->involves < 0 || data->involves)
                return -1;
        return 0;
}

/* Do any options depend on the value of the dimension at the current depth?
 */
int isl_ast_build_options_involve_depth(__isl_keep isl_ast_build *build)
{
        struct isl_ast_build_involves_data data;

        if (!build)
                return -1;

        data.depth = build->depth;
        data.involves = 0;

        if (isl_union_map_foreach_map(build->options,
                                        &involves_depth, &data) < 0) {
                if (data.involves < 0 || !data.involves)
                        return -1;
        }

        return data.involves;
}

/* Construct the map
 *
 *      { [i] -> [i] : i < pos; [i] -> [i + 1] : i >= pos }
 *
 * with "space" the parameter space of the constructed map.
 */
static __isl_give isl_map *construct_insertion_map(__isl_take isl_space *space,
        int pos)
{
        isl_constraint *c;
        isl_basic_map *bmap1, *bmap2;

        space = isl_space_set_from_params(space);
        space = isl_space_add_dims(space, isl_dim_set, 1);
        space = isl_space_map_from_set(space);
        c = isl_equality_alloc(isl_local_space_from_space(space));
        c = isl_constraint_set_coefficient_si(c, isl_dim_in, 0, 1);
        c = isl_constraint_set_coefficient_si(c, isl_dim_out, 0, -1);
        bmap1 = isl_basic_map_from_constraint(isl_constraint_copy(c));
        c = isl_constraint_set_constant_si(c, 1);
        bmap2 = isl_basic_map_from_constraint(c);

        bmap1 = isl_basic_map_upper_bound_si(bmap1, isl_dim_in, 0, pos - 1);
        bmap2 = isl_basic_map_lower_bound_si(bmap2, isl_dim_in, 0, pos);

        return isl_basic_map_union(bmap1, bmap2);
}

static const char *option_str[] = {
        [atomic] = "atomic",
        [unroll] = "unroll",
        [separate] = "separate"
};

/* Update the "options" to reflect the insertion of a dimension
 * at position "pos" in the schedule domain space.
 * "space" is the original domain space before the insertion and
 * may be named and/or structured.
 *
 * The (relevant) input options all have "space" as domain, which
 * has to be mapped to the extended space.
 * The values of the ranges also refer to the schedule domain positions
 * and they therefore also need to be adjusted.  In particular, values
 * smaller than pos do not need to change, while values greater than or
 * equal to pos need to be incremented.
 * That is, we need to apply the following map.
 *
 *      { atomic[i] -> atomic[i] : i < pos; [i] -> [i + 1] : i >= pos;
 *        unroll[i] -> unroll[i] : i < pos; [i] -> [i + 1] : i >= pos;
 *        separate[i] -> separate[i] : i < pos; [i] -> [i + 1] : i >= pos;
 *        separation_class[[i] -> [c]]
 *              -> separation_class[[i] -> [c]] : i < pos;
 *        separation_class[[i] -> [c]]
 *              -> separation_class[[i + 1] -> [c]] : i >= pos }
 */
static __isl_give isl_union_map *options_insert_dim(
        __isl_take isl_union_map *options, __isl_take isl_space *space, int pos)
{
        isl_map *map;
        isl_union_map *insertion;
        enum isl_ast_build_domain_type type;
        const char *name = "separation_class";

        space = isl_space_map_from_set(space);
        map = isl_map_identity(space);
        map = isl_map_insert_dims(map, isl_dim_out, pos, 1);
        options = isl_union_map_apply_domain(options,
                                                isl_union_map_from_map(map));

        if (!options)
                return NULL;

        map = construct_insertion_map(isl_union_map_get_space(options), pos);

        insertion = isl_union_map_empty(isl_union_map_get_space(options));

        for (type = atomic; type <= separate; ++type) {
                isl_map *map_type = isl_map_copy(map);
                const char *name = option_str[type];
                map_type = isl_map_set_tuple_name(map_type, isl_dim_in, name);
                map_type = isl_map_set_tuple_name(map_type, isl_dim_out, name);
                insertion = isl_union_map_add_map(insertion, map_type);
        }

        map = isl_map_product(map, isl_map_identity(isl_map_get_space(map)));
        map = isl_map_set_tuple_name(map, isl_dim_in, name);
        map = isl_map_set_tuple_name(map, isl_dim_out, name);
        insertion = isl_union_map_add_map(insertion, map);

        options = isl_union_map_apply_range(options, insertion);

        return options;
}

/* Insert a single dimension in the schedule domain at position "pos".
 * The new dimension is given an isl_id with the empty string as name.
 *
 * The main difficulty is updating build->options to reflect the
 * extra dimension.  This is handled in options_insert_dim.
 *
 * Note that because of the dimension manipulations, the resulting
 * schedule domain space will always be unnamed and unstructured.
 * However, the original schedule domain space may be named and/or
 * structured, so we have to take this possibility into account
 * while performing the transformations.
 */
__isl_give isl_ast_build *isl_ast_build_insert_dim(
        __isl_take isl_ast_build *build, int pos)
{
        isl_ctx *ctx;
        isl_space *space, *ma_space;
        isl_id *id;
        isl_multi_aff *ma;

        build = isl_ast_build_cow(build);
        if (!build)
                return NULL;

        ctx = isl_ast_build_get_ctx(build);
        id = isl_id_alloc(ctx, "", NULL);
        space = isl_ast_build_get_space(build, 1);
        build->iterators = isl_id_list_insert(build->iterators, pos, id);
        build->domain = isl_set_insert_dims(build->domain,
                                                isl_dim_set, pos, 1);
        build->generated = isl_set_insert_dims(build->generated,
                                                isl_dim_set, pos, 1);
        build->pending = isl_set_insert_dims(build->pending,
                                                isl_dim_set, pos, 1);
        build->strides = isl_vec_insert_els(build->strides, pos, 1);
        build->strides = isl_vec_set_element_si(build->strides, pos, 1);
        ma_space = isl_space_params(isl_multi_aff_get_space(build->offsets));
        ma_space = isl_space_set_from_params(ma_space);
        ma_space = isl_space_add_dims(ma_space, isl_dim_set, 1);
        ma_space = isl_space_map_from_set(ma_space);
        ma = isl_multi_aff_zero(isl_space_copy(ma_space));
        build->offsets = isl_multi_aff_splice(build->offsets, pos, pos, ma);
        ma = isl_multi_aff_identity(ma_space);
        build->values = isl_multi_aff_splice(build->values, pos, pos, ma);
        build->options = options_insert_dim(build->options, space, pos);

        if (!build->iterators || !build->domain || !build->generated ||
            !build->pending || !build->values ||
            !build->strides || !build->offsets || !build->options)
                return isl_ast_build_free(build);

        return build;
}

/* Scale down the current dimension by a factor of "m".
 * "umap" is an isl_union_map that implements the scaling down.
 * That is, it is of the form
 *
 *      { [.... i ....] -> [.... i' ....] : i = m i' }
 *
 * This function is called right after the strides have been
 * detected, but before any constraints on the current dimension
 * have been included in build->domain.
 * We therefore only need to update stride, offset and the options.
 */
__isl_give isl_ast_build *isl_ast_build_scale_down(
        __isl_take isl_ast_build *build, __isl_take isl_val *m,
        __isl_take isl_union_map *umap)
{
        isl_aff *aff;
        isl_val *v;
        int depth;

        build = isl_ast_build_cow(build);
        if (!build || !umap || !m)
                goto error;

        depth = build->depth;

        v = isl_vec_get_element_val(build->strides, depth);
        v = isl_val_div(v, isl_val_copy(m));
        build->strides = isl_vec_set_element_val(build->strides, depth, v);

        aff = isl_multi_aff_get_aff(build->offsets, depth);
        aff = isl_aff_scale_down_val(aff, m);
        build->offsets = isl_multi_aff_set_aff(build->offsets, depth, aff);
        build->options = isl_union_map_apply_domain(build->options, umap);
        if (!build->strides || !build->offsets || !build->options)
                return isl_ast_build_free(build);

        return build;
error:
        isl_val_free(m);
        isl_union_map_free(umap);
        return isl_ast_build_free(build);
}

/* Return a list of "n" isl_ids called "c%d", with "%d" starting at "first".
 * If an isl_id with such a name already appears among the parameters
 * in build->domain, then adjust the name to "c%d_%d".
 */
static __isl_give isl_id_list *generate_names(isl_ctx *ctx, int n, int first,
        __isl_keep isl_ast_build *build)
{
        int i;
        isl_id_list *names;

        names = isl_id_list_alloc(ctx, n);
        for (i = 0; i < n; ++i) {
                isl_id *id;

                id = generate_name(ctx, first + i, build);
                names = isl_id_list_add(names, id);
        }

        return names;
}

/* Embed "options" into the given isl_ast_build space.
 *
 * This function is called from within a nested call to
 * isl_ast_build_ast_from_schedule.
 * "options" refers to the additional schedule,
 * while space refers to both the space of the outer isl_ast_build and
 * that of the additional schedule.
 * Specifically, space is of the form
 *
 *      [I -> S]
 *
 * while options lives in the space(s)
 *
 *      S -> *
 *
 * We compute
 *
 *      [I -> S] -> S
 *
 * and compose this with options, to obtain the new options
 * living in the space(s)
 *
 *      [I -> S] -> *
 */
static __isl_give isl_union_map *embed_options(
        __isl_take isl_union_map *options, __isl_take isl_space *space)
{
        isl_map *map;

        map = isl_map_universe(isl_space_unwrap(space));
        map = isl_map_range_map(map);

        options = isl_union_map_apply_range(
                                isl_union_map_from_map(map), options);

        return options;
}

/* Update "build" for use in a (possibly nested) code generation.  That is,
 * extend "build" from an AST build on some domain O to an AST build
 * on domain [O -> S], with S corresponding to "space".
 * If the original domain is a parameter domain, then the new domain is
 * simply S.
 * "iterators" is a list of iterators for S, but the number of elements
 * may be smaller or greater than the number of set dimensions of S.
 * If "keep_iterators" is set, then any extra ids in build->iterators
 * are reused for S.  Otherwise, these extra ids are dropped.
 *
 * We first update build->outer_pos to the current depth.
 * This depth is zero in case this is the outermost code generation.
 *
 * We then add additional ids such that the number of iterators is at least
 * equal to the dimension of the new build domain.
 *
 * If the original domain is parametric, then we are constructing
 * an isl_ast_build for the outer code generation and we pass control
 * to isl_ast_build_init.
 *
 * Otherwise, we adjust the fields of "build" to include "space".
 */
__isl_give isl_ast_build *isl_ast_build_product(
        __isl_take isl_ast_build *build, __isl_take isl_space *space)
{
        isl_ctx *ctx;
        isl_vec *strides;
        isl_set *set;
        isl_multi_aff *embedding;
        int dim, n_it;

        build = isl_ast_build_cow(build);
        if (!build)
                goto error;

        build->outer_pos = build->depth;

        ctx = isl_ast_build_get_ctx(build);
        dim = isl_set_dim(build->domain, isl_dim_set);
        dim += isl_space_dim(space, isl_dim_set);
        n_it = isl_id_list_n_id(build->iterators);
        if (n_it < dim) {
                isl_id_list *l;
                l = generate_names(ctx, dim - n_it, n_it, build);
                build->iterators = isl_id_list_concat(build->iterators, l);
        }

        if (isl_set_is_params(build->domain))
                return isl_ast_build_init(build, space);

        set = isl_set_universe(isl_space_copy(space));
        build->domain = isl_set_product(build->domain, isl_set_copy(set));
        build->pending = isl_set_product(build->pending, isl_set_copy(set));
        build->generated = isl_set_product(build->generated, set);

        strides = isl_vec_alloc(ctx, isl_space_dim(space, isl_dim_set));
        strides = isl_vec_set_si(strides, 1);
        build->strides = isl_vec_concat(build->strides, strides);

        space = isl_space_map_from_set(space);
        build->offsets = isl_multi_aff_align_params(build->offsets,
                                                    isl_space_copy(space));
        build->offsets = isl_multi_aff_product(build->offsets,
                                isl_multi_aff_zero(isl_space_copy(space)));
        build->values = isl_multi_aff_align_params(build->values,
                                                    isl_space_copy(space));
        embedding = isl_multi_aff_identity(space);
        build->values = isl_multi_aff_product(build->values, embedding);

        space = isl_ast_build_get_space(build, 1);
        build->options = embed_options(build->options, space);

        if (!build->iterators || !build->domain || !build->generated ||
            !build->pending || !build->values ||
            !build->strides || !build->offsets || !build->options)
                return isl_ast_build_free(build);

        return build;
error:
        isl_ast_build_free(build);
        isl_space_free(space);
        return NULL;
}

/* Does "aff" only attain non-negative values over build->domain?
 * That is, does it not attain any negative values?
 */
int isl_ast_build_aff_is_nonneg(__isl_keep isl_ast_build *build,
        __isl_keep isl_aff *aff)
{
        isl_set *test;
        int empty;

        if (!build)
                return -1;

        aff = isl_aff_copy(aff);
        test = isl_set_from_basic_set(isl_aff_neg_basic_set(aff));
        test = isl_set_intersect(test, isl_set_copy(build->domain));
        empty = isl_set_is_empty(test);
        isl_set_free(test);

        return empty;
}

/* Does the dimension at (internal) position "pos" have a non-trivial stride?
 */
int isl_ast_build_has_stride(__isl_keep isl_ast_build *build, int pos)
{
        isl_val *v;
        int has_stride;

        if (!build)
                return -1;

        v = isl_vec_get_element_val(build->strides, pos);
        if (!v)
                return -1;
        has_stride = !isl_val_is_one(v);
        isl_val_free(v);

        return has_stride;
}

/* Given that the dimension at position "pos" takes on values
 *
 *      f + s a
 *
 * with a an integer, return s through *stride.
 */
__isl_give isl_val *isl_ast_build_get_stride(__isl_keep isl_ast_build *build,
        int pos)
{
        if (!build)
                return NULL;

        return isl_vec_get_element_val(build->strides, pos);
}

/* Given that the dimension at position "pos" takes on values
 *
 *      f + s a
 *
 * with a an integer, return f.
 */
__isl_give isl_aff *isl_ast_build_get_offset(
        __isl_keep isl_ast_build *build, int pos)
{
        if (!build)
                return NULL;

        return isl_multi_aff_get_aff(build->offsets, pos);
}

/* Is the dimension at position "pos" known to attain only a single
 * value that, moreover, can be described by a single affine expression
 * in terms of the outer dimensions and parameters?
 *
 * If not, then the correponding affine expression in build->values
 * is set to be equal to the same input dimension.
 * Otherwise, it is set to the requested expression in terms of
 * outer dimensions and parameters.
 */
int isl_ast_build_has_affine_value(__isl_keep isl_ast_build *build,
        int pos)
{
        isl_aff *aff;
        int involves;

        if (!build)
                return -1;

        aff = isl_multi_aff_get_aff(build->values, pos);
        involves = isl_aff_involves_dims(aff, isl_dim_in, pos, 1);
        isl_aff_free(aff);

        if (involves < 0)
                return -1;

        return !involves;
}

/* Plug in the known values (fixed affine expressions in terms of
 * parameters and outer loop iterators) of all loop iterators
 * in the domain of "umap".
 *
 * We simply precompose "umap" with build->values.
 */
__isl_give isl_union_map *isl_ast_build_substitute_values_union_map_domain(
        __isl_keep isl_ast_build *build, __isl_take isl_union_map *umap)
{
        isl_multi_aff *values;

        if (!build)
                return isl_union_map_free(umap);

        values = isl_multi_aff_copy(build->values);
        umap = isl_union_map_preimage_domain_multi_aff(umap, values);

        return umap;
}

/* Is the current dimension known to attain only a single value?
 */
int isl_ast_build_has_value(__isl_keep isl_ast_build *build)
{
        if (!build)
                return -1;

        return build->value != NULL;
}

/* Simplify the basic set "bset" based on what we know about
 * the iterators of already generated loops.
 *
 * "bset" is assumed to live in the (internal) schedule domain.
 */
__isl_give isl_basic_set *isl_ast_build_compute_gist_basic_set(
        __isl_keep isl_ast_build *build, __isl_take isl_basic_set *bset)
{
        if (!build)
                goto error;

        bset = isl_basic_set_preimage_multi_aff(bset,
                                        isl_multi_aff_copy(build->values));
        bset = isl_basic_set_gist(bset,
                        isl_set_simple_hull(isl_set_copy(build->domain)));

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

/* Simplify the set "set" based on what we know about
 * the iterators of already generated loops.
 *
 * "set" is assumed to live in the (internal) schedule domain.
 */
__isl_give isl_set *isl_ast_build_compute_gist(
        __isl_keep isl_ast_build *build, __isl_take isl_set *set)
{
        if (!build)
                goto error;

        set = isl_set_preimage_multi_aff(set,
                                        isl_multi_aff_copy(build->values));
        set = isl_set_gist(set, isl_set_copy(build->domain));

        return set;
error:
        isl_set_free(set);
        return NULL;
}

/* Include information about what we know about the iterators of
 * already generated loops to "set".
 *
 * We currently only plug in the known affine values of outer loop
 * iterators.
 * In principle we could also introduce equalities or even other
 * constraints implied by the intersection of "set" and build->domain.
 */
__isl_give isl_set *isl_ast_build_specialize(__isl_keep isl_ast_build *build,
        __isl_take isl_set *set)
{
        if (!build)
                return isl_set_free(set);

        return isl_set_preimage_multi_aff(set,
                                        isl_multi_aff_copy(build->values));
}

/* Simplify the map "map" based on what we know about
 * the iterators of already generated loops.
 *
 * The domain of "map" is assumed to live in the (internal) schedule domain.
 */
__isl_give isl_map *isl_ast_build_compute_gist_map_domain(
        __isl_keep isl_ast_build *build, __isl_take isl_map *map)
{
        if (!build)
                goto error;

        map = isl_map_gist_domain(map, isl_set_copy(build->domain));

        return map;
error:
        isl_map_free(map);
        return NULL;
}

/* Simplify the affine expression "aff" based on what we know about
 * the iterators of already generated loops.
 *
 * The domain of "aff" is assumed to live in the (internal) schedule domain.
 */
__isl_give isl_aff *isl_ast_build_compute_gist_aff(
        __isl_keep isl_ast_build *build, __isl_take isl_aff *aff)
{
        if (!build)
                goto error;

        aff = isl_aff_gist(aff, isl_set_copy(build->domain));

        return aff;
error:
        isl_aff_free(aff);
        return NULL;
}

/* Simplify the piecewise affine expression "aff" based on what we know about
 * the iterators of already generated loops.
 *
 * The domain of "pa" is assumed to live in the (internal) schedule domain.
 */
__isl_give isl_pw_aff *isl_ast_build_compute_gist_pw_aff(
        __isl_keep isl_ast_build *build, __isl_take isl_pw_aff *pa)
{
        if (!build)
                goto error;

        if (!isl_set_is_params(build->domain))
                pa = isl_pw_aff_pullback_multi_aff(pa,
                                        isl_multi_aff_copy(build->values));
        pa = isl_pw_aff_gist(pa, isl_set_copy(build->domain));

        return pa;
error:
        isl_pw_aff_free(pa);
        return NULL;
}

/* Simplify the piecewise multi-affine expression "aff" based on what
 * we know about the iterators of already generated loops.
 *
 * The domain of "pma" is assumed to live in the (internal) schedule domain.
 */
__isl_give isl_pw_multi_aff *isl_ast_build_compute_gist_pw_multi_aff(
        __isl_keep isl_ast_build *build, __isl_take isl_pw_multi_aff *pma)
{
        if (!build)
                goto error;

        pma = isl_pw_multi_aff_pullback_multi_aff(pma,
                                        isl_multi_aff_copy(build->values));
        pma = isl_pw_multi_aff_gist(pma, isl_set_copy(build->domain));

        return pma;
error:
        isl_pw_multi_aff_free(pma);
        return NULL;
}

/* Extract the schedule domain of the given type from build->options
 * at the current depth.
 *
 * In particular, find the subset of build->options that is of
 * the following form
 *
 *      schedule_domain -> type[depth]
 *
 * and return the corresponding domain, after eliminating inner dimensions
 * and divs that depend on the current dimension.
 *
 * Note that the domain of build->options has been reformulated
 * in terms of the internal build space in embed_options,
 * but the position is still that within the current code generation.
 */
__isl_give isl_set *isl_ast_build_get_option_domain(
        __isl_keep isl_ast_build *build,
        enum isl_ast_build_domain_type type)
{
        const char *name;
        isl_space *space;
        isl_map *option;
        isl_set *domain;
        int local_pos;

        if (!build)
                return NULL;

        name = option_str[type];
        local_pos = build->depth - build->outer_pos;

        space = isl_ast_build_get_space(build, 1);
        space = isl_space_from_domain(space);
        space = isl_space_add_dims(space, isl_dim_out, 1);
        space = isl_space_set_tuple_name(space, isl_dim_out, name);

        option = isl_union_map_extract_map(build->options, space);
        option = isl_map_fix_si(option, isl_dim_out, 0, local_pos);

        domain = isl_map_domain(option);
        domain = isl_ast_build_eliminate(build, domain);

        return domain;
}

/* Extract the separation class mapping at the current depth.
 *
 * In particular, find and return the subset of build->options that is of
 * the following form
 *
 *      schedule_domain -> separation_class[[depth] -> [class]]
 *
 * The caller is expected to eliminate inner dimensions from the domain.
 *
 * Note that the domain of build->options has been reformulated
 * in terms of the internal build space in embed_options,
 * but the position is still that within the current code generation.
 */
__isl_give isl_map *isl_ast_build_get_separation_class(
        __isl_keep isl_ast_build *build)
{
        isl_ctx *ctx;
        isl_space *space_sep, *space;
        isl_map *res;
        int local_pos;

        if (!build)
                return NULL;

        local_pos = build->depth - build->outer_pos;
        ctx = isl_ast_build_get_ctx(build);
        space_sep = isl_space_alloc(ctx, 0, 1, 1);
        space_sep = isl_space_wrap(space_sep);
        space_sep = isl_space_set_tuple_name(space_sep, isl_dim_set,
                                                "separation_class");
        space = isl_ast_build_get_space(build, 1);
        space_sep = isl_space_align_params(space_sep, isl_space_copy(space));
        space = isl_space_map_from_domain_and_range(space, space_sep);

        res = isl_union_map_extract_map(build->options, space);
        res = isl_map_fix_si(res, isl_dim_out, 0, local_pos);
        res = isl_map_coalesce(res);

        return res;
}

/* Eliminate dimensions inner to the current dimension.
 */
__isl_give isl_set *isl_ast_build_eliminate_inner(
        __isl_keep isl_ast_build *build, __isl_take isl_set *set)
{
        int dim;
        int depth;

        if (!build)
                return isl_set_free(set);

        dim = isl_set_dim(set, isl_dim_set);
        depth = build->depth;
        set = isl_set_detect_equalities(set);
        set = isl_set_eliminate(set, isl_dim_set, depth + 1, dim - (depth + 1));

        return set;
}

/* Eliminate unknown divs and divs that depend on the current dimension.
 *
 * Note that during the elimination of unknown divs, we may discover
 * an explicit representation of some other unknown divs, which may
 * depend on the current dimension.  We therefore need to eliminate
 * unknown divs first.
 */
__isl_give isl_set *isl_ast_build_eliminate_divs(
        __isl_keep isl_ast_build *build, __isl_take isl_set *set)
{
        int depth;

        if (!build)
                return isl_set_free(set);

        set = isl_set_remove_unknown_divs(set);
        depth = build->depth;
        set = isl_set_remove_divs_involving_dims(set, isl_dim_set, depth, 1);

        return set;
}

/* Eliminate dimensions inner to the current dimension as well as
 * unknown divs and divs that depend on the current dimension.
 * The result then consists only of constraints that are independent
 * of the current dimension and upper and lower bounds on the current
 * dimension.
 */
__isl_give isl_set *isl_ast_build_eliminate(
        __isl_keep isl_ast_build *build, __isl_take isl_set *domain)
{
        domain = isl_ast_build_eliminate_inner(build, domain);
        domain = isl_ast_build_eliminate_divs(build, domain);
        return domain;
}

/* Replace build->single_valued by "sv".
 */
__isl_give isl_ast_build *isl_ast_build_set_single_valued(
        __isl_take isl_ast_build *build, int sv)
{
        if (!build)
                return build;
        if (build->single_valued == sv)
                return build;
        build = isl_ast_build_cow(build);
        if (!build)
                return build;
        build->single_valued = sv;

        return build;
}