isl_map_transitive_closure: prepare for the construction of general paths

[isl.git] / isl_map.c

/*
 * Copyright 2008-2009 Katholieke Universiteit Leuven
 * Copyright 2010      INRIA Saclay
 *
 * Use of this software is governed by the GNU LGPLv2.1 license
 *
 * Written by Sven Verdoolaege, K.U.Leuven, Departement
 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France 
 */

#include <string.h>
#include <strings.h>
#include "isl_ctx.h"
#include "isl_blk.h"
#include "isl_dim.h"
#include "isl_equalities.h"
#include "isl_list.h"
#include "isl_lp.h"
#include "isl_seq.h"
#include "isl_set.h"
#include "isl_map.h"
#include "isl_map_private.h"
#include "isl_map_piplib.h"
#include "isl_sample.h"
#include "isl_tab.h"
#include "isl_vec.h"

/* Maps dst positions to src positions */
struct isl_dim_map {
        unsigned len;
        int pos[1];
};

static struct isl_dim_map *isl_dim_map_alloc(struct isl_ctx *ctx, unsigned len)
{
        int i;
        struct isl_dim_map *dim_map;
        dim_map = isl_alloc(ctx, struct isl_dim_map,
                                sizeof(struct isl_dim_map) + len * sizeof(int));
        if (!dim_map)
                return NULL;
        dim_map->len = 1 + len;
        dim_map->pos[0] = 0;
        for (i = 0; i < len; ++i)
                dim_map->pos[1 + i] = -1;
        return dim_map;
}

static unsigned n(struct isl_dim *dim, enum isl_dim_type type)
{
        switch (type) {
        case isl_dim_param:     return dim->nparam;
        case isl_dim_in:        return dim->n_in;
        case isl_dim_out:       return dim->n_out;
        case isl_dim_all:       return dim->nparam + dim->n_in + dim->n_out;
        }
}

static unsigned pos(struct isl_dim *dim, enum isl_dim_type type)
{
        switch (type) {
        case isl_dim_param:     return 1;
        case isl_dim_in:        return 1 + dim->nparam;
        case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
        }
}

static void isl_dim_map_dim_range(struct isl_dim_map *dim_map,
        struct isl_dim *dim, enum isl_dim_type type,
        unsigned first, unsigned n, unsigned dst_pos)
{
        int i;
        unsigned src_pos;

        if (!dim_map || !dim)
                return;
        
        src_pos = pos(dim, type);
        for (i = 0; i < n; ++i)
                dim_map->pos[1 + dst_pos + i] = src_pos + first + i;
}

static void isl_dim_map_dim(struct isl_dim_map *dim_map, struct isl_dim *dim,
                enum isl_dim_type type, unsigned dst_pos)
{
        isl_dim_map_dim_range(dim_map, dim, type, 0, n(dim, type), dst_pos);
}

static void isl_dim_map_div(struct isl_dim_map *dim_map,
                struct isl_basic_map *bmap, unsigned dst_pos)
{
        int i;
        unsigned src_pos;

        if (!dim_map || !bmap)
                return;
        
        src_pos = 1 + isl_dim_total(bmap->dim);
        for (i = 0; i < bmap->n_div; ++i)
                dim_map->pos[1 + dst_pos + i] = src_pos + i;
}

static void isl_dim_map_dump(struct isl_dim_map *dim_map)
{
        int i;

        for (i = 0; i < dim_map->len; ++i)
                fprintf(stderr, "%d -> %d; ", i, dim_map->pos[i]);
        fprintf(stderr, "\n");
}

unsigned isl_basic_map_dim(const struct isl_basic_map *bmap,
                                enum isl_dim_type type)
{
        switch (type) {
        case isl_dim_param:
        case isl_dim_in:
        case isl_dim_out:       return isl_dim_size(bmap->dim, type);
        case isl_dim_div:       return bmap->n_div;
        case isl_dim_all:       return isl_basic_map_total_dim(bmap);
        }
}

unsigned isl_map_dim(const struct isl_map *map, enum isl_dim_type type)
{
        return map ? n(map->dim, type) : 0;
}

unsigned isl_set_dim(const struct isl_set *set, enum isl_dim_type type)
{
        return set ? n(set->dim, type) : 0;
}

unsigned isl_basic_map_offset(struct isl_basic_map *bmap,
                                        enum isl_dim_type type)
{
        struct isl_dim *dim = bmap->dim;
        switch (type) {
        case isl_dim_param:     return 1;
        case isl_dim_in:        return 1 + dim->nparam;
        case isl_dim_out:       return 1 + dim->nparam + dim->n_in;
        case isl_dim_div:       return 1 + dim->nparam + dim->n_in + dim->n_out;
        }
}

static unsigned map_offset(struct isl_map *map, enum isl_dim_type type)
{
        return pos(map->dim, type);
}

unsigned isl_basic_set_dim(const struct isl_basic_set *bset,
                                enum isl_dim_type type)
{
        return isl_basic_map_dim((const struct isl_basic_map*)bset, type);
}

unsigned isl_basic_set_n_dim(const struct isl_basic_set *bset)
{
        return bset->dim->n_out;
}

unsigned isl_basic_set_n_param(const struct isl_basic_set *bset)
{
        return bset->dim->nparam;
}

unsigned isl_basic_set_total_dim(const struct isl_basic_set *bset)
{
        return isl_dim_total(bset->dim) + bset->n_div;
}

unsigned isl_set_n_dim(const struct isl_set *set)
{
        return set->dim->n_out;
}

unsigned isl_set_n_param(const struct isl_set *set)
{
        return set->dim->nparam;
}

unsigned isl_basic_map_n_in(const struct isl_basic_map *bmap)
{
        return bmap->dim->n_in;
}

unsigned isl_basic_map_n_out(const struct isl_basic_map *bmap)
{
        return bmap->dim->n_out;
}

unsigned isl_basic_map_n_param(const struct isl_basic_map *bmap)
{
        return bmap->dim->nparam;
}

unsigned isl_basic_map_n_div(const struct isl_basic_map *bmap)
{
        return bmap->n_div;
}

unsigned isl_basic_map_total_dim(const struct isl_basic_map *bmap)
{
        return isl_dim_total(bmap->dim) + bmap->n_div;
}

unsigned isl_map_n_in(const struct isl_map *map)
{
        return map->dim->n_in;
}

unsigned isl_map_n_out(const struct isl_map *map)
{
        return map->dim->n_out;
}

unsigned isl_map_n_param(const struct isl_map *map)
{
        return map->dim->nparam;
}

int isl_map_compatible_domain(struct isl_map *map, struct isl_set *set)
{
        return map->dim->n_in == set->dim->n_out &&
               map->dim->nparam == set->dim->nparam;
}

int isl_basic_map_compatible_domain(struct isl_basic_map *bmap,
                struct isl_basic_set *bset)
{
        return bmap->dim->n_in == bset->dim->n_out &&
               bmap->dim->nparam == bset->dim->nparam;
}

int isl_basic_map_compatible_range(struct isl_basic_map *bmap,
                struct isl_basic_set *bset)
{
        return bmap->dim->n_out == bset->dim->n_out &&
               bmap->dim->nparam == bset->dim->nparam;
}

struct isl_dim *isl_basic_map_get_dim(struct isl_basic_map *bmap)
{
        if (!bmap)
                return NULL;
        return isl_dim_copy(bmap->dim);
}

struct isl_dim *isl_basic_set_get_dim(struct isl_basic_set *bset)
{
        if (!bset)
                return NULL;
        return isl_dim_copy(bset->dim);
}

struct isl_dim *isl_map_get_dim(struct isl_map *map)
{
        if (!map)
                return NULL;
        return isl_dim_copy(map->dim);
}

struct isl_dim *isl_set_get_dim(struct isl_set *set)
{
        if (!set)
                return NULL;
        return isl_dim_copy(set->dim);
}

static struct isl_basic_map *basic_map_init(struct isl_ctx *ctx,
                struct isl_basic_map *bmap, unsigned extra,
                unsigned n_eq, unsigned n_ineq)
{
        int i;
        size_t row_size = 1 + isl_dim_total(bmap->dim) + extra;

        bmap->block = isl_blk_alloc(ctx, (n_ineq + n_eq) * row_size);
        if (isl_blk_is_error(bmap->block)) {
                free(bmap);
                return NULL;
        }

        bmap->ineq = isl_alloc_array(ctx, isl_int *, n_ineq + n_eq);
        if (!bmap->ineq) {
                isl_blk_free(ctx, bmap->block);
                free(bmap);
                return NULL;
        }

        if (extra == 0) {
                bmap->block2 = isl_blk_empty();
                bmap->div = NULL;
        } else {
                bmap->block2 = isl_blk_alloc(ctx, extra * (1 + row_size));
                if (isl_blk_is_error(bmap->block2)) {
                        free(bmap->ineq);
                        isl_blk_free(ctx, bmap->block);
                        free(bmap);
                        return NULL;
                }

                bmap->div = isl_alloc_array(ctx, isl_int *, extra);
                if (!bmap->div) {
                        isl_blk_free(ctx, bmap->block2);
                        free(bmap->ineq);
                        isl_blk_free(ctx, bmap->block);
                        free(bmap);
                        return NULL;
                }
        }

        for (i = 0; i < n_ineq + n_eq; ++i)
                bmap->ineq[i] = bmap->block.data + i * row_size;

        for (i = 0; i < extra; ++i)
                bmap->div[i] = bmap->block2.data + i * (1 + row_size);

        bmap->ctx = ctx;
        isl_ctx_ref(ctx);
        bmap->ref = 1;
        bmap->flags = 0;
        bmap->c_size = n_eq + n_ineq;
        bmap->eq = bmap->ineq + n_ineq;
        bmap->extra = extra;
        bmap->n_eq = 0;
        bmap->n_ineq = 0;
        bmap->n_div = 0;
        bmap->sample = NULL;

        return bmap;
error:
        isl_basic_map_free(bmap);
        return NULL;
}

struct isl_basic_set *isl_basic_set_alloc(struct isl_ctx *ctx,
                unsigned nparam, unsigned dim, unsigned extra,
                unsigned n_eq, unsigned n_ineq)
{
        struct isl_basic_map *bmap;
        bmap = isl_basic_map_alloc(ctx, nparam, 0, dim, extra, n_eq, n_ineq);
        return (struct isl_basic_set *)bmap;
}

struct isl_basic_set *isl_basic_set_alloc_dim(struct isl_dim *dim,
                unsigned extra, unsigned n_eq, unsigned n_ineq)
{
        struct isl_basic_map *bmap;
        if (!dim)
                return NULL;
        isl_assert(dim->ctx, dim->n_in == 0, return NULL);
        bmap = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
        return (struct isl_basic_set *)bmap;
}

struct isl_basic_map *isl_basic_map_alloc_dim(struct isl_dim *dim,
                unsigned extra, unsigned n_eq, unsigned n_ineq)
{
        struct isl_basic_map *bmap;

        if (!dim)
                return NULL;
        bmap = isl_alloc_type(dim->ctx, struct isl_basic_map);
        if (!bmap)
                goto error;
        bmap->dim = dim;

        return basic_map_init(dim->ctx, bmap, extra, n_eq, n_ineq);
error:
        isl_dim_free(dim);
        return NULL;
}

struct isl_basic_map *isl_basic_map_alloc(struct isl_ctx *ctx,
                unsigned nparam, unsigned in, unsigned out, unsigned extra,
                unsigned n_eq, unsigned n_ineq)
{
        struct isl_basic_map *bmap;
        struct isl_dim *dim;

        dim = isl_dim_alloc(ctx, nparam, in, out);
        if (!dim)
                return NULL;

        bmap = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
        return bmap;
}

static void dup_constraints(
                struct isl_basic_map *dst, struct isl_basic_map *src)
{
        int i;
        unsigned total = isl_basic_map_total_dim(src);

        for (i = 0; i < src->n_eq; ++i) {
                int j = isl_basic_map_alloc_equality(dst);
                isl_seq_cpy(dst->eq[j], src->eq[i], 1+total);
        }

        for (i = 0; i < src->n_ineq; ++i) {
                int j = isl_basic_map_alloc_inequality(dst);
                isl_seq_cpy(dst->ineq[j], src->ineq[i], 1+total);
        }

        for (i = 0; i < src->n_div; ++i) {
                int j = isl_basic_map_alloc_div(dst);
                isl_seq_cpy(dst->div[j], src->div[i], 1+1+total);
        }
        ISL_F_SET(dst, ISL_BASIC_SET_FINAL);
}

struct isl_basic_map *isl_basic_map_dup(struct isl_basic_map *bmap)
{
        struct isl_basic_map *dup;

        if (!bmap)
                return NULL;
        dup = isl_basic_map_alloc_dim(isl_dim_copy(bmap->dim),
                        bmap->n_div, bmap->n_eq, bmap->n_ineq);
        if (!dup)
                return NULL;
        dup_constraints(dup, bmap);
        dup->flags = bmap->flags;
        dup->sample = isl_vec_copy(bmap->sample);
        return dup;
}

struct isl_basic_set *isl_basic_set_dup(struct isl_basic_set *bset)
{
        struct isl_basic_map *dup;

        dup = isl_basic_map_dup((struct isl_basic_map *)bset);
        return (struct isl_basic_set *)dup;
}

struct isl_basic_set *isl_basic_set_copy(struct isl_basic_set *bset)
{
        if (!bset)
                return NULL;

        if (ISL_F_ISSET(bset, ISL_BASIC_SET_FINAL)) {
                bset->ref++;
                return bset;
        }
        return isl_basic_set_dup(bset);
}

struct isl_set *isl_set_copy(struct isl_set *set)
{
        if (!set)
                return NULL;

        set->ref++;
        return set;
}

struct isl_basic_map *isl_basic_map_copy(struct isl_basic_map *bmap)
{
        if (!bmap)
                return NULL;

        if (ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL)) {
                bmap->ref++;
                return bmap;
        }
        return isl_basic_map_dup(bmap);
}

struct isl_map *isl_map_copy(struct isl_map *map)
{
        if (!map)
                return NULL;

        map->ref++;
        return map;
}

void isl_basic_map_free(struct isl_basic_map *bmap)
{
        if (!bmap)
                return;

        if (--bmap->ref > 0)
                return;

        isl_ctx_deref(bmap->ctx);
        free(bmap->div);
        isl_blk_free(bmap->ctx, bmap->block2);
        free(bmap->ineq);
        isl_blk_free(bmap->ctx, bmap->block);
        isl_vec_free(bmap->sample);
        isl_dim_free(bmap->dim);
        free(bmap);
}

void isl_basic_set_free(struct isl_basic_set *bset)
{
        isl_basic_map_free((struct isl_basic_map *)bset);
}

static int room_for_con(struct isl_basic_map *bmap, unsigned n)
{
        return bmap->n_eq + bmap->n_ineq + n <= bmap->c_size;
}

int isl_basic_map_alloc_equality(struct isl_basic_map *bmap)
{
        struct isl_ctx *ctx;
        if (!bmap)
                return -1;
        ctx = bmap->ctx;
        isl_assert(ctx, room_for_con(bmap, 1), return -1);
        isl_assert(ctx, (bmap->eq - bmap->ineq) + bmap->n_eq <= bmap->c_size,
                        return -1);
        ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
        ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
        ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
        ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
        if ((bmap->eq - bmap->ineq) + bmap->n_eq == bmap->c_size) {
                isl_int *t;
                int j = isl_basic_map_alloc_inequality(bmap);
                if (j < 0)
                        return -1;
                t = bmap->ineq[j];
                bmap->ineq[j] = bmap->ineq[bmap->n_ineq - 1];
                bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
                bmap->eq[-1] = t;
                bmap->n_eq++;
                bmap->n_ineq--;
                bmap->eq--;
                return 0;
        }
        isl_seq_clr(bmap->eq[bmap->n_eq] + 1 + isl_basic_map_total_dim(bmap),
                      bmap->extra - bmap->n_div);
        return bmap->n_eq++;
}

int isl_basic_set_alloc_equality(struct isl_basic_set *bset)
{
        return isl_basic_map_alloc_equality((struct isl_basic_map *)bset);
}

int isl_basic_map_free_equality(struct isl_basic_map *bmap, unsigned n)
{
        if (!bmap)
                return -1;
        isl_assert(bmap->ctx, n <= bmap->n_eq, return -1);
        bmap->n_eq -= n;
        return 0;
}

int isl_basic_set_free_equality(struct isl_basic_set *bset, unsigned n)
{
        return isl_basic_map_free_equality((struct isl_basic_map *)bset, n);
}

int isl_basic_map_drop_equality(struct isl_basic_map *bmap, unsigned pos)
{
        isl_int *t;
        if (!bmap)
                return -1;
        isl_assert(bmap->ctx, pos < bmap->n_eq, return -1);

        if (pos != bmap->n_eq - 1) {
                t = bmap->eq[pos];
                bmap->eq[pos] = bmap->eq[bmap->n_eq - 1];
                bmap->eq[bmap->n_eq - 1] = t;
        }
        bmap->n_eq--;
        return 0;
}

int isl_basic_set_drop_equality(struct isl_basic_set *bset, unsigned pos)
{
        return isl_basic_map_drop_equality((struct isl_basic_map *)bset, pos);
}

void isl_basic_map_inequality_to_equality(
                struct isl_basic_map *bmap, unsigned pos)
{
        isl_int *t;

        t = bmap->ineq[pos];
        bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
        bmap->ineq[bmap->n_ineq - 1] = bmap->eq[-1];
        bmap->eq[-1] = t;
        bmap->n_eq++;
        bmap->n_ineq--;
        bmap->eq--;
        ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
        ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
        ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
}

static int room_for_ineq(struct isl_basic_map *bmap, unsigned n)
{
        return bmap->n_ineq + n <= bmap->eq - bmap->ineq;
}

int isl_basic_map_alloc_inequality(struct isl_basic_map *bmap)
{
        struct isl_ctx *ctx;
        if (!bmap)
                return -1;
        ctx = bmap->ctx;
        isl_assert(ctx, room_for_ineq(bmap, 1), return -1);
        ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
        ISL_F_CLR(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
        ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        ISL_F_CLR(bmap, ISL_BASIC_MAP_ALL_EQUALITIES);
        isl_seq_clr(bmap->ineq[bmap->n_ineq] +
                      1 + isl_basic_map_total_dim(bmap),
                      bmap->extra - bmap->n_div);
        return bmap->n_ineq++;
}

int isl_basic_set_alloc_inequality(struct isl_basic_set *bset)
{
        return isl_basic_map_alloc_inequality((struct isl_basic_map *)bset);
}

int isl_basic_map_free_inequality(struct isl_basic_map *bmap, unsigned n)
{
        if (!bmap)
                return -1;
        isl_assert(bmap->ctx, n <= bmap->n_ineq, return -1);
        bmap->n_ineq -= n;
        return 0;
}

int isl_basic_set_free_inequality(struct isl_basic_set *bset, unsigned n)
{
        return isl_basic_map_free_inequality((struct isl_basic_map *)bset, n);
}

int isl_basic_map_drop_inequality(struct isl_basic_map *bmap, unsigned pos)
{
        isl_int *t;
        if (!bmap)
                return -1;
        isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);

        if (pos != bmap->n_ineq - 1) {
                t = bmap->ineq[pos];
                bmap->ineq[pos] = bmap->ineq[bmap->n_ineq - 1];
                bmap->ineq[bmap->n_ineq - 1] = t;
                ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        }
        bmap->n_ineq--;
        return 0;
}

int isl_basic_set_drop_inequality(struct isl_basic_set *bset, unsigned pos)
{
        return isl_basic_map_drop_inequality((struct isl_basic_map *)bset, pos);
}

__isl_give isl_basic_map *isl_basic_map_add_eq(__isl_take isl_basic_map *bmap,
        isl_int *eq)
{
        int k;

        bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
        if (!bmap)
                return NULL;
        k = isl_basic_map_alloc_equality(bmap);
        if (k < 0)
                goto error;
        isl_seq_cpy(bmap->eq[k], eq, 1 + isl_basic_map_total_dim(bmap));
        return bmap;
error:
        isl_basic_map_free(bmap);
        return NULL;
}

__isl_give isl_basic_set *isl_basic_set_add_eq(__isl_take isl_basic_set *bset,
        isl_int *eq)
{
        return (isl_basic_set *)
                isl_basic_map_add_eq((isl_basic_map *)bset, eq);
}

__isl_give isl_basic_map *isl_basic_map_add_ineq(__isl_take isl_basic_map *bmap,
        isl_int *ineq)
{
        int k;

        bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
        if (!bmap)
                return NULL;
        k = isl_basic_map_alloc_inequality(bmap);
        if (k < 0)
                goto error;
        isl_seq_cpy(bmap->ineq[k], ineq, 1 + isl_basic_map_total_dim(bmap));
        return bmap;
error:
        isl_basic_map_free(bmap);
        return NULL;
}

__isl_give isl_basic_set *isl_basic_set_add_ineq(__isl_take isl_basic_set *bset,
        isl_int *ineq)
{
        return (isl_basic_set *)
                isl_basic_map_add_ineq((isl_basic_map *)bset, ineq);
}

int isl_basic_map_alloc_div(struct isl_basic_map *bmap)
{
        if (!bmap)
                return -1;
        isl_assert(bmap->ctx, bmap->n_div < bmap->extra, return -1);
        isl_seq_clr(bmap->div[bmap->n_div] +
                      1 + 1 + isl_basic_map_total_dim(bmap),
                      bmap->extra - bmap->n_div);
        ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED_DIVS);
        return bmap->n_div++;
}

int isl_basic_set_alloc_div(struct isl_basic_set *bset)
{
        return isl_basic_map_alloc_div((struct isl_basic_map *)bset);
}

int isl_basic_map_free_div(struct isl_basic_map *bmap, unsigned n)
{
        if (!bmap)
                return -1;
        isl_assert(bmap->ctx, n <= bmap->n_div, return -1);
        bmap->n_div -= n;
        return 0;
}

int isl_basic_set_free_div(struct isl_basic_set *bset, unsigned n)
{
        return isl_basic_map_free_div((struct isl_basic_map *)bset, n);
}

/* Copy constraint from src to dst, putting the vars of src at offset
 * dim_off in dst and the divs of src at offset div_off in dst.
 * If both sets are actually map, then dim_off applies to the input
 * variables.
 */
static void copy_constraint(struct isl_basic_map *dst_map, isl_int *dst,
                            struct isl_basic_map *src_map, isl_int *src,
                            unsigned in_off, unsigned out_off, unsigned div_off)
{
        unsigned src_nparam = isl_basic_map_n_param(src_map);
        unsigned dst_nparam = isl_basic_map_n_param(dst_map);
        unsigned src_in = isl_basic_map_n_in(src_map);
        unsigned dst_in = isl_basic_map_n_in(dst_map);
        unsigned src_out = isl_basic_map_n_out(src_map);
        unsigned dst_out = isl_basic_map_n_out(dst_map);
        isl_int_set(dst[0], src[0]);
        isl_seq_cpy(dst+1, src+1, isl_min(dst_nparam, src_nparam));
        if (dst_nparam > src_nparam)
                isl_seq_clr(dst+1+src_nparam,
                                dst_nparam - src_nparam);
        isl_seq_clr(dst+1+dst_nparam, in_off);
        isl_seq_cpy(dst+1+dst_nparam+in_off,
                    src+1+src_nparam,
                    isl_min(dst_in-in_off, src_in));
        if (dst_in-in_off > src_in)
                isl_seq_clr(dst+1+dst_nparam+in_off+src_in,
                                dst_in - in_off - src_in);
        isl_seq_clr(dst+1+dst_nparam+dst_in, out_off);
        isl_seq_cpy(dst+1+dst_nparam+dst_in+out_off,
                    src+1+src_nparam+src_in,
                    isl_min(dst_out-out_off, src_out));
        if (dst_out-out_off > src_out)
                isl_seq_clr(dst+1+dst_nparam+dst_in+out_off+src_out,
                                dst_out - out_off - src_out);
        isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out, div_off);
        isl_seq_cpy(dst+1+dst_nparam+dst_in+dst_out+div_off,
                    src+1+src_nparam+src_in+src_out,
                    isl_min(dst_map->extra-div_off, src_map->n_div));
        if (dst_map->n_div-div_off > src_map->n_div)
                isl_seq_clr(dst+1+dst_nparam+dst_in+dst_out+
                                div_off+src_map->n_div,
                                dst_map->n_div - div_off - src_map->n_div);
}

static void copy_div(struct isl_basic_map *dst_map, isl_int *dst,
                     struct isl_basic_map *src_map, isl_int *src,
                     unsigned in_off, unsigned out_off, unsigned div_off)
{
        isl_int_set(dst[0], src[0]);
        copy_constraint(dst_map, dst+1, src_map, src+1, in_off, out_off, div_off);
}

static struct isl_basic_map *add_constraints(struct isl_basic_map *bmap1,
                struct isl_basic_map *bmap2, unsigned i_pos, unsigned o_pos)
{
        int i;
        unsigned div_off;

        if (!bmap1 || !bmap2)
                goto error;

        div_off = bmap1->n_div;

        for (i = 0; i < bmap2->n_eq; ++i) {
                int i1 = isl_basic_map_alloc_equality(bmap1);
                if (i1 < 0)
                        goto error;
                copy_constraint(bmap1, bmap1->eq[i1], bmap2, bmap2->eq[i],
                                i_pos, o_pos, div_off);
        }

        for (i = 0; i < bmap2->n_ineq; ++i) {
                int i1 = isl_basic_map_alloc_inequality(bmap1);
                if (i1 < 0)
                        goto error;
                copy_constraint(bmap1, bmap1->ineq[i1], bmap2, bmap2->ineq[i],
                                i_pos, o_pos, div_off);
        }

        for (i = 0; i < bmap2->n_div; ++i) {
                int i1 = isl_basic_map_alloc_div(bmap1);
                if (i1 < 0)
                        goto error;
                copy_div(bmap1, bmap1->div[i1], bmap2, bmap2->div[i],
                         i_pos, o_pos, div_off);
        }

        isl_basic_map_free(bmap2);

        return bmap1;

error:
        isl_basic_map_free(bmap1);
        isl_basic_map_free(bmap2);
        return NULL;
}

static void copy_constraint_dim_map(isl_int *dst, isl_int *src,
                                        struct isl_dim_map *dim_map)
{
        int i;

        for (i = 0; i < dim_map->len; ++i) {
                if (dim_map->pos[i] < 0)
                        isl_int_set_si(dst[i], 0);
                else
                        isl_int_set(dst[i], src[dim_map->pos[i]]);
        }
}

static void copy_div_dim_map(isl_int *dst, isl_int *src,
                                        struct isl_dim_map *dim_map)
{
        isl_int_set(dst[0], src[0]);
        copy_constraint_dim_map(dst+1, src+1, dim_map);
}

static struct isl_basic_map *add_constraints_dim_map(struct isl_basic_map *dst,
                struct isl_basic_map *src, struct isl_dim_map *dim_map)
{
        int i;

        if (!src || !dst || !dim_map)
                goto error;

        for (i = 0; i < src->n_eq; ++i) {
                int i1 = isl_basic_map_alloc_equality(dst);
                if (i1 < 0)
                        goto error;
                copy_constraint_dim_map(dst->eq[i1], src->eq[i], dim_map);
        }

        for (i = 0; i < src->n_ineq; ++i) {
                int i1 = isl_basic_map_alloc_inequality(dst);
                if (i1 < 0)
                        goto error;
                copy_constraint_dim_map(dst->ineq[i1], src->ineq[i], dim_map);
        }

        for (i = 0; i < src->n_div; ++i) {
                int i1 = isl_basic_map_alloc_div(dst);
                if (i1 < 0)
                        goto error;
                copy_div_dim_map(dst->div[i1], src->div[i], dim_map);
        }

        free(dim_map);
        isl_basic_map_free(src);

        return dst;
error:
        free(dim_map);
        isl_basic_map_free(src);
        isl_basic_map_free(dst);
        return NULL;
}

struct isl_basic_set *isl_basic_set_add_constraints(struct isl_basic_set *bset1,
                struct isl_basic_set *bset2, unsigned pos)
{
        return (struct isl_basic_set *)
                add_constraints((struct isl_basic_map *)bset1,
                                (struct isl_basic_map *)bset2, 0, pos);
}

struct isl_basic_map *isl_basic_map_extend_dim(struct isl_basic_map *base,
                struct isl_dim *dim, unsigned extra,
                unsigned n_eq, unsigned n_ineq)
{
        struct isl_basic_map *ext;
        unsigned flags;
        int dims_ok;

        if (!dim)
                goto error;

        if (!base)
                goto error;

        dims_ok = isl_dim_equal(base->dim, dim) &&
                  base->extra >= base->n_div + extra;

        if (dims_ok && room_for_con(base, n_eq + n_ineq) &&
                       room_for_ineq(base, n_ineq)) {
                isl_dim_free(dim);
                return base;
        }

        isl_assert(base->ctx, base->dim->nparam <= dim->nparam, goto error);
        isl_assert(base->ctx, base->dim->n_in <= dim->n_in, goto error);
        isl_assert(base->ctx, base->dim->n_out <= dim->n_out, goto error);
        extra += base->extra;
        n_eq += base->n_eq;
        n_ineq += base->n_ineq;

        ext = isl_basic_map_alloc_dim(dim, extra, n_eq, n_ineq);
        dim = NULL;
        if (!ext)
                goto error;

        if (dims_ok)
                ext->sample = isl_vec_copy(base->sample);
        flags = base->flags;
        ext = add_constraints(ext, base, 0, 0);
        if (ext) {
                ext->flags = flags;
                ISL_F_CLR(ext, ISL_BASIC_SET_FINAL);
        }

        return ext;

error:
        isl_dim_free(dim);
        isl_basic_map_free(base);
        return NULL;
}

struct isl_basic_set *isl_basic_set_extend_dim(struct isl_basic_set *base,
                struct isl_dim *dim, unsigned extra,
                unsigned n_eq, unsigned n_ineq)
{
        return (struct isl_basic_set *)
                isl_basic_map_extend_dim((struct isl_basic_map *)base, dim,
                                                        extra, n_eq, n_ineq);
}

struct isl_basic_map *isl_basic_map_extend_constraints(
                struct isl_basic_map *base, unsigned n_eq, unsigned n_ineq)
{
        if (!base)
                return NULL;
        return isl_basic_map_extend_dim(base, isl_dim_copy(base->dim),
                                        0, n_eq, n_ineq);
}

struct isl_basic_map *isl_basic_map_extend(struct isl_basic_map *base,
                unsigned nparam, unsigned n_in, unsigned n_out, unsigned extra,
                unsigned n_eq, unsigned n_ineq)
{
        struct isl_basic_map *bmap;
        struct isl_dim *dim;

        if (!base)
                return NULL;
        dim = isl_dim_alloc(base->ctx, nparam, n_in, n_out);
        if (!dim)
                return NULL;

        bmap = isl_basic_map_extend_dim(base, dim, extra, n_eq, n_ineq);
        return bmap;
}

struct isl_basic_set *isl_basic_set_extend(struct isl_basic_set *base,
                unsigned nparam, unsigned dim, unsigned extra,
                unsigned n_eq, unsigned n_ineq)
{
        return (struct isl_basic_set *)
                isl_basic_map_extend((struct isl_basic_map *)base,
                                        nparam, 0, dim, extra, n_eq, n_ineq);
}

struct isl_basic_set *isl_basic_set_extend_constraints(
                struct isl_basic_set *base, unsigned n_eq, unsigned n_ineq)
{
        return (struct isl_basic_set *)
                isl_basic_map_extend_constraints((struct isl_basic_map *)base,
                                                    n_eq, n_ineq);
}

struct isl_basic_set *isl_basic_set_cow(struct isl_basic_set *bset)
{
        return (struct isl_basic_set *)
                isl_basic_map_cow((struct isl_basic_map *)bset);
}

struct isl_basic_map *isl_basic_map_cow(struct isl_basic_map *bmap)
{
        if (!bmap)
                return NULL;

        if (bmap->ref > 1) {
                bmap->ref--;
                bmap = isl_basic_map_dup(bmap);
        }
        ISL_F_CLR(bmap, ISL_BASIC_SET_FINAL);
        return bmap;
}

struct isl_set *isl_set_cow(struct isl_set *set)
{
        if (!set)
                return NULL;

        if (set->ref == 1)
                return set;
        set->ref--;
        return isl_set_dup(set);
}

struct isl_map *isl_map_cow(struct isl_map *map)
{
        if (!map)
                return NULL;

        if (map->ref == 1)
                return map;
        map->ref--;
        return isl_map_dup(map);
}

static void swap_vars(struct isl_blk blk, isl_int *a,
                        unsigned a_len, unsigned b_len)
{
        isl_seq_cpy(blk.data, a+a_len, b_len);
        isl_seq_cpy(blk.data+b_len, a, a_len);
        isl_seq_cpy(a, blk.data, b_len+a_len);
}

struct isl_basic_set *isl_basic_set_swap_vars(
                struct isl_basic_set *bset, unsigned n)
{
        int i;
        struct isl_blk blk;
        unsigned dim;
        unsigned nparam;

        if (!bset)
                goto error;

        nparam = isl_basic_set_n_param(bset);
        dim = isl_basic_set_n_dim(bset);
        isl_assert(bset->ctx, n <= dim, goto error);

        if (n == dim)
                return bset;

        bset = isl_basic_set_cow(bset);
        if (!bset)
                return NULL;

        blk = isl_blk_alloc(bset->ctx, dim);
        if (isl_blk_is_error(blk))
                goto error;

        for (i = 0; i < bset->n_eq; ++i)
                swap_vars(blk,
                          bset->eq[i]+1+nparam, n, dim - n);

        for (i = 0; i < bset->n_ineq; ++i)
                swap_vars(blk,
                          bset->ineq[i]+1+nparam, n, dim - n);

        for (i = 0; i < bset->n_div; ++i)
                swap_vars(blk,
                          bset->div[i]+1+1+nparam, n, dim - n);

        isl_blk_free(bset->ctx, blk);

        ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
        return isl_basic_set_gauss(bset, NULL);
error:
        isl_basic_set_free(bset);
        return NULL;
}

struct isl_set *isl_set_swap_vars(struct isl_set *set, unsigned n)
{
        int i;
        set = isl_set_cow(set);
        if (!set)
                return NULL;

        for (i = 0; i < set->n; ++i) {
                set->p[i] = isl_basic_set_swap_vars(set->p[i], n);
                if (!set->p[i]) {
                        isl_set_free(set);
                        return NULL;
                }
        }
        ISL_F_CLR(set, ISL_SET_NORMALIZED);
        return set;
}

struct isl_basic_map *isl_basic_map_set_to_empty(struct isl_basic_map *bmap)
{
        int i = 0;
        unsigned total;
        if (!bmap)
                goto error;
        total = isl_basic_map_total_dim(bmap);
        isl_basic_map_free_div(bmap, bmap->n_div);
        isl_basic_map_free_inequality(bmap, bmap->n_ineq);
        if (bmap->n_eq > 0)
                isl_basic_map_free_equality(bmap, bmap->n_eq-1);
        else {
                isl_basic_map_alloc_equality(bmap);
                if (i < 0)
                        goto error;
        }
        isl_int_set_si(bmap->eq[i][0], 1);
        isl_seq_clr(bmap->eq[i]+1, total);
        ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);
        isl_vec_free(bmap->sample);
        bmap->sample = NULL;
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_map_free(bmap);
        return NULL;
}

struct isl_basic_set *isl_basic_set_set_to_empty(struct isl_basic_set *bset)
{
        return (struct isl_basic_set *)
                isl_basic_map_set_to_empty((struct isl_basic_map *)bset);
}

void isl_basic_map_swap_div(struct isl_basic_map *bmap, int a, int b)
{
        int i;
        unsigned off = isl_dim_total(bmap->dim);
        isl_int *t = bmap->div[a];
        bmap->div[a] = bmap->div[b];
        bmap->div[b] = t;

        for (i = 0; i < bmap->n_eq; ++i)
                isl_int_swap(bmap->eq[i][1+off+a], bmap->eq[i][1+off+b]);

        for (i = 0; i < bmap->n_ineq; ++i)
                isl_int_swap(bmap->ineq[i][1+off+a], bmap->ineq[i][1+off+b]);

        for (i = 0; i < bmap->n_div; ++i)
                isl_int_swap(bmap->div[i][1+1+off+a], bmap->div[i][1+1+off+b]);
        ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
}

/* Eliminate the specified n dimensions starting at first from the
 * constraints using Fourier-Motzkin, The dimensions themselves
 * are not removed.
 */
struct isl_set *isl_set_eliminate_dims(struct isl_set *set,
        unsigned first, unsigned n)
{
        int i;
        unsigned nparam;

        if (!set)
                return NULL;
        if (n == 0)
                return set;

        set = isl_set_cow(set);
        if (!set)
                return NULL;
        isl_assert(set->ctx, first+n <= isl_set_n_dim(set), goto error);
        nparam = isl_set_n_param(set);
        
        for (i = 0; i < set->n; ++i) {
                set->p[i] = isl_basic_set_eliminate_vars(set->p[i],
                                                            nparam + first, n);
                if (!set->p[i])
                        goto error;
        }
        return set;
error:
        isl_set_free(set);
        return NULL;
}

/* Project out n dimensions starting at first using Fourier-Motzkin */
struct isl_set *isl_set_remove_dims(struct isl_set *set,
        unsigned first, unsigned n)
{
        set = isl_set_eliminate_dims(set, first, n);
        set = isl_set_drop_dims(set, first, n);
        return set;
}

struct isl_basic_set *isl_basic_set_remove_divs(struct isl_basic_set *bset)
{
        bset = isl_basic_set_eliminate_vars(bset, isl_dim_total(bset->dim),
                                                bset->n_div);
        if (!bset)
                return NULL;
        bset->n_div = 0;
        return bset;
}

struct isl_set *isl_set_remove_divs(struct isl_set *set)
{
        int i;

        if (!set)
                return NULL;
        if (set->n == 0)
                return set;

        set = isl_set_cow(set);
        if (!set)
                return NULL;
        
        for (i = 0; i < set->n; ++i) {
                set->p[i] = isl_basic_set_remove_divs(set->p[i]);
                if (!set->p[i])
                        goto error;
        }
        return set;
error:
        isl_set_free(set);
        return NULL;
}

struct isl_basic_map *isl_basic_map_remove(struct isl_basic_map *bmap,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        if (!bmap)
                return NULL;
        isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
                        goto error);
        if (n == 0)
                return bmap;
        bmap = isl_basic_map_eliminate_vars(bmap,
                        isl_basic_map_offset(bmap, type) - 1 + first, n);
        if (!bmap)
                return bmap;
        if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY) && type == isl_dim_div)
                return bmap;
        bmap = isl_basic_map_drop(bmap, type, first, n);
        return bmap;
error:
        isl_basic_map_free(bmap);
        return NULL;
}

__isl_give isl_basic_set *isl_basic_set_remove(__isl_take isl_basic_set *bset,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        return (isl_basic_set *)
                isl_basic_map_remove((isl_basic_map *)bset, type, first, n);
}

struct isl_map *isl_map_remove(struct isl_map *map,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        int i;

        if (n == 0)
                return map;

        map = isl_map_cow(map);
        if (!map)
                return NULL;
        isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);
        
        for (i = 0; i < map->n; ++i) {
                map->p[i] = isl_basic_map_eliminate_vars(map->p[i],
                        isl_basic_map_offset(map->p[i], type) - 1 + first, n);
                if (!map->p[i])
                        goto error;
        }
        map = isl_map_drop(map, type, first, n);
        return map;
error:
        isl_map_free(map);
        return NULL;
}

__isl_give isl_set *isl_set_remove(__isl_take isl_set *bset,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        return (isl_set *)isl_map_remove((isl_map *)bset, type, first, n);
}

/* Project out n inputs starting at first using Fourier-Motzkin */
struct isl_map *isl_map_remove_inputs(struct isl_map *map,
        unsigned first, unsigned n)
{
        return isl_map_remove(map, isl_dim_in, first, n);
}

/* Project out n dimensions starting at first using Fourier-Motzkin */
struct isl_basic_set *isl_basic_set_remove_dims(struct isl_basic_set *bset,
        unsigned first, unsigned n)
{
        unsigned nparam = isl_basic_set_n_param(bset);
        bset = isl_basic_set_eliminate_vars(bset, nparam + first, n);
        bset = isl_basic_set_drop_dims(bset, first, n);
        return bset;
}

static void dump_term(struct isl_basic_map *bmap,
                        isl_int c, int pos, FILE *out)
{
        const char *name;
        unsigned in = isl_basic_map_n_in(bmap);
        unsigned dim = in + isl_basic_map_n_out(bmap);
        unsigned nparam = isl_basic_map_n_param(bmap);
        if (!pos)
                isl_int_print(out, c, 0);
        else {
                if (!isl_int_is_one(c))
                        isl_int_print(out, c, 0);
                if (pos < 1 + nparam) {
                        name = isl_dim_get_name(bmap->dim,
                                                isl_dim_param, pos - 1);
                        if (name)
                                fprintf(out, "%s", name);
                        else
                                fprintf(out, "p%d", pos - 1);
                } else if (pos < 1 + nparam + in)
                        fprintf(out, "i%d", pos - 1 - nparam);
                else if (pos < 1 + nparam + dim)
                        fprintf(out, "o%d", pos - 1 - nparam - in);
                else
                        fprintf(out, "e%d", pos - 1 - nparam - dim);
        }
}

static void dump_constraint_sign(struct isl_basic_map *bmap, isl_int *c,
                                int sign, FILE *out)
{
        int i;
        int first;
        unsigned len = 1 + isl_basic_map_total_dim(bmap);
        isl_int v;

        isl_int_init(v);
        for (i = 0, first = 1; i < len; ++i) {
                if (isl_int_sgn(c[i]) * sign <= 0)
                        continue;
                if (!first)
                        fprintf(out, " + ");
                first = 0;
                isl_int_abs(v, c[i]);
                dump_term(bmap, v, i, out);
        }
        isl_int_clear(v);
        if (first)
                fprintf(out, "0");
}

static void dump_constraint(struct isl_basic_map *bmap, isl_int *c,
                                const char *op, FILE *out, int indent)
{
        int i;

        fprintf(out, "%*s", indent, "");

        dump_constraint_sign(bmap, c, 1, out);
        fprintf(out, " %s ", op);
        dump_constraint_sign(bmap, c, -1, out);

        fprintf(out, "\n");

        for (i = bmap->n_div; i < bmap->extra; ++i) {
                if (isl_int_is_zero(c[1+isl_dim_total(bmap->dim)+i]))
                        continue;
                fprintf(out, "%*s", indent, "");
                fprintf(out, "ERROR: unused div coefficient not zero\n");
                abort();
        }
}

static void dump_constraints(struct isl_basic_map *bmap,
                                isl_int **c, unsigned n,
                                const char *op, FILE *out, int indent)
{
        int i;

        for (i = 0; i < n; ++i)
                dump_constraint(bmap, c[i], op, out, indent);
}

static void dump_affine(struct isl_basic_map *bmap, isl_int *exp, FILE *out)
{
        int j;
        int first = 1;
        unsigned total = isl_basic_map_total_dim(bmap);

        for (j = 0; j < 1 + total; ++j) {
                if (isl_int_is_zero(exp[j]))
                        continue;
                if (!first && isl_int_is_pos(exp[j]))
                        fprintf(out, "+");
                dump_term(bmap, exp[j], j, out);
                first = 0;
        }
}

static void dump(struct isl_basic_map *bmap, FILE *out, int indent)
{
        int i;

        dump_constraints(bmap, bmap->eq, bmap->n_eq, "=", out, indent);
        dump_constraints(bmap, bmap->ineq, bmap->n_ineq, ">=", out, indent);

        for (i = 0; i < bmap->n_div; ++i) {
                fprintf(out, "%*s", indent, "");
                fprintf(out, "e%d = [(", i);
                dump_affine(bmap, bmap->div[i]+1, out);
                fprintf(out, ")/");
                isl_int_print(out, bmap->div[i][0], 0);
                fprintf(out, "]\n");
        }
}

void isl_basic_set_dump(struct isl_basic_set *bset, FILE *out, int indent)
{
        if (!bset) {
                fprintf(out, "null basic set\n");
                return;
        }

        fprintf(out, "%*s", indent, "");
        fprintf(out, "ref: %d, nparam: %d, dim: %d, extra: %d, flags: %x\n",
                        bset->ref, bset->dim->nparam, bset->dim->n_out,
                        bset->extra, bset->flags);
        dump((struct isl_basic_map *)bset, out, indent);
}

void isl_basic_map_dump(struct isl_basic_map *bmap, FILE *out, int indent)
{
        if (!bmap) {
                fprintf(out, "null basic map\n");
                return;
        }

        fprintf(out, "%*s", indent, "");
        fprintf(out, "ref: %d, nparam: %d, in: %d, out: %d, extra: %d, "
                        "flags: %x, n_name: %d\n",
                bmap->ref,
                bmap->dim->nparam, bmap->dim->n_in, bmap->dim->n_out,
                bmap->extra, bmap->flags, bmap->dim->n_name);
        dump(bmap, out, indent);
}

int isl_inequality_negate(struct isl_basic_map *bmap, unsigned pos)
{
        unsigned total;
        if (!bmap)
                return -1;
        total = isl_basic_map_total_dim(bmap);
        isl_assert(bmap->ctx, pos < bmap->n_ineq, return -1);
        isl_seq_neg(bmap->ineq[pos], bmap->ineq[pos], 1 + total);
        isl_int_sub_ui(bmap->ineq[pos][0], bmap->ineq[pos][0], 1);
        ISL_F_CLR(bmap, ISL_BASIC_MAP_NORMALIZED);
        return 0;
}

struct isl_set *isl_set_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
{
        struct isl_set *set;

        if (!dim)
                return NULL;
        isl_assert(dim->ctx, dim->n_in == 0, return NULL);
        isl_assert(dim->ctx, n >= 0, return NULL);
        set = isl_alloc(dim->ctx, struct isl_set,
                        sizeof(struct isl_set) +
                        (n - 1) * sizeof(struct isl_basic_set *));
        if (!set)
                goto error;

        set->ctx = dim->ctx;
        isl_ctx_ref(set->ctx);
        set->ref = 1;
        set->size = n;
        set->n = 0;
        set->dim = dim;
        set->flags = flags;
        return set;
error:
        isl_dim_free(dim);
        return NULL;
}

struct isl_set *isl_set_alloc(struct isl_ctx *ctx,
                unsigned nparam, unsigned dim, int n, unsigned flags)
{
        struct isl_set *set;
        struct isl_dim *dims;

        dims = isl_dim_alloc(ctx, nparam, 0, dim);
        if (!dims)
                return NULL;

        set = isl_set_alloc_dim(dims, n, flags);
        return set;
}

/* Make sure "map" has room for at least "n" more basic maps.
 */
struct isl_map *isl_map_grow(struct isl_map *map, int n)
{
        int i;
        struct isl_map *grown = NULL;

        if (!map)
                return NULL;
        isl_assert(map->ctx, n >= 0, goto error);
        if (map->n + n <= map->size)
                return map;
        grown = isl_map_alloc_dim(isl_map_get_dim(map), map->n + n, map->flags);
        if (!grown)
                goto error;
        for (i = 0; i < map->n; ++i) {
                grown->p[i] = isl_basic_map_copy(map->p[i]);
                if (!grown->p[i])
                        goto error;
                grown->n++;
        }
        isl_map_free(map);
        return grown;
error:
        isl_map_free(grown);
        isl_map_free(map);
        return NULL;
}

/* Make sure "set" has room for at least "n" more basic sets.
 */
struct isl_set *isl_set_grow(struct isl_set *set, int n)
{
        return (struct isl_set *)isl_map_grow((struct isl_map *)set, n);
}

struct isl_set *isl_set_dup(struct isl_set *set)
{
        int i;
        struct isl_set *dup;

        if (!set)
                return NULL;

        dup = isl_set_alloc_dim(isl_dim_copy(set->dim), set->n, set->flags);
        if (!dup)
                return NULL;
        for (i = 0; i < set->n; ++i)
                dup = isl_set_add_basic_set(dup, isl_basic_set_copy(set->p[i]));
        return dup;
}

struct isl_set *isl_set_from_basic_set(struct isl_basic_set *bset)
{
        struct isl_set *set;

        if (!bset)
                return NULL;

        set = isl_set_alloc_dim(isl_dim_copy(bset->dim), 1, ISL_MAP_DISJOINT);
        if (!set) {
                isl_basic_set_free(bset);
                return NULL;
        }
        return isl_set_add_basic_set(set, bset);
}

struct isl_map *isl_map_from_basic_map(struct isl_basic_map *bmap)
{
        struct isl_map *map;

        if (!bmap)
                return NULL;

        map = isl_map_alloc_dim(isl_dim_copy(bmap->dim), 1, ISL_MAP_DISJOINT);
        if (!map) {
                isl_basic_map_free(bmap);
                return NULL;
        }
        return isl_map_add_basic_map(map, bmap);
}

__isl_give isl_set *isl_set_add_basic_set(__isl_take isl_set *set,
                                                __isl_take isl_basic_set *bset)
{
        return (struct isl_set *)isl_map_add_basic_map((struct isl_map *)set,
                                                (struct isl_basic_map *)bset);
}

void isl_set_free(struct isl_set *set)
{
        int i;

        if (!set)
                return;

        if (--set->ref > 0)
                return;

        isl_ctx_deref(set->ctx);
        for (i = 0; i < set->n; ++i)
                isl_basic_set_free(set->p[i]);
        isl_dim_free(set->dim);
        free(set);
}

void isl_set_dump(struct isl_set *set, FILE *out, int indent)
{
        int i;

        if (!set) {
                fprintf(out, "null set\n");
                return;
        }

        fprintf(out, "%*s", indent, "");
        fprintf(out, "ref: %d, n: %d, nparam: %d, dim: %d, flags: %x\n",
                        set->ref, set->n, set->dim->nparam, set->dim->n_out,
                        set->flags);
        for (i = 0; i < set->n; ++i) {
                fprintf(out, "%*s", indent, "");
                fprintf(out, "basic set %d:\n", i);
                isl_basic_set_dump(set->p[i], out, indent+4);
        }
}

void isl_map_dump(struct isl_map *map, FILE *out, int indent)
{
        int i;

        if (!map) {
                fprintf(out, "null map\n");
                return;
        }

        fprintf(out, "%*s", indent, "");
        fprintf(out, "ref: %d, n: %d, nparam: %d, in: %d, out: %d, "
                     "flags: %x, n_name: %d\n",
                        map->ref, map->n, map->dim->nparam, map->dim->n_in,
                        map->dim->n_out, map->flags, map->dim->n_name);
        for (i = 0; i < map->n; ++i) {
                fprintf(out, "%*s", indent, "");
                fprintf(out, "basic map %d:\n", i);
                isl_basic_map_dump(map->p[i], out, indent+4);
        }
}

struct isl_basic_map *isl_basic_map_intersect_domain(
                struct isl_basic_map *bmap, struct isl_basic_set *bset)
{
        struct isl_basic_map *bmap_domain;
        struct isl_dim *dim;

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

        isl_assert(bset->ctx, isl_dim_match(bmap->dim, isl_dim_param,
                                        bset->dim, isl_dim_param), goto error);

        if (isl_dim_size(bset->dim, isl_dim_set) != 0)
                isl_assert(bset->ctx,
                    isl_basic_map_compatible_domain(bmap, bset), goto error);

        bmap = isl_basic_map_cow(bmap);
        bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
                        bset->n_div, bset->n_eq, bset->n_ineq);
        if (!bmap)
                goto error;
        dim = isl_dim_reverse(isl_dim_copy(bset->dim));
        bmap_domain = isl_basic_map_from_basic_set(bset, dim);
        bmap = add_constraints(bmap, bmap_domain, 0, 0);

        bmap = isl_basic_map_simplify(bmap);
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_map_free(bmap);
        isl_basic_set_free(bset);
        return NULL;
}

struct isl_basic_map *isl_basic_map_intersect_range(
                struct isl_basic_map *bmap, struct isl_basic_set *bset)
{
        struct isl_basic_map *bmap_range;

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

        isl_assert(bset->ctx, isl_dim_match(bmap->dim, isl_dim_param,
                                        bset->dim, isl_dim_param), goto error);

        if (isl_dim_size(bset->dim, isl_dim_set) != 0)
                isl_assert(bset->ctx,
                    isl_basic_map_compatible_range(bmap, bset), goto error);

        bmap = isl_basic_map_cow(bmap);
        bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
                        bset->n_div, bset->n_eq, bset->n_ineq);
        if (!bmap)
                goto error;
        bmap_range = isl_basic_map_from_basic_set(bset, isl_dim_copy(bset->dim));
        bmap = add_constraints(bmap, bmap_range, 0, 0);

        bmap = isl_basic_map_simplify(bmap);
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_map_free(bmap);
        isl_basic_set_free(bset);
        return NULL;
}

int isl_basic_map_contains(struct isl_basic_map *bmap, struct isl_vec *vec)
{
        int i;
        unsigned total;
        isl_int s;

        total = 1 + isl_basic_map_total_dim(bmap);
        if (total != vec->size)
                return -1;

        isl_int_init(s);

        for (i = 0; i < bmap->n_eq; ++i) {
                isl_seq_inner_product(vec->el, bmap->eq[i], total, &s);
                if (!isl_int_is_zero(s)) {
                        isl_int_clear(s);
                        return 0;
                }
        }

        for (i = 0; i < bmap->n_ineq; ++i) {
                isl_seq_inner_product(vec->el, bmap->ineq[i], total, &s);
                if (isl_int_is_neg(s)) {
                        isl_int_clear(s);
                        return 0;
                }
        }

        isl_int_clear(s);

        return 1;
}

int isl_basic_set_contains(struct isl_basic_set *bset, struct isl_vec *vec)
{
        return isl_basic_map_contains((struct isl_basic_map *)bset, vec);
}

struct isl_basic_map *isl_basic_map_intersect(
                struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
{
        struct isl_vec *sample = NULL;

        if (!bmap1 || !bmap2)
                goto error;

        isl_assert(bmap1->ctx, isl_dim_match(bmap1->dim, isl_dim_param,
                                     bmap2->dim, isl_dim_param), goto error);
        if (isl_dim_total(bmap1->dim) ==
                                isl_dim_size(bmap1->dim, isl_dim_param) &&
            isl_dim_total(bmap2->dim) !=
                                isl_dim_size(bmap2->dim, isl_dim_param))
                return isl_basic_map_intersect(bmap2, bmap1);

        if (isl_dim_total(bmap2->dim) !=
                                        isl_dim_size(bmap2->dim, isl_dim_param))
                isl_assert(bmap1->ctx,
                            isl_dim_equal(bmap1->dim, bmap2->dim), goto error);

        if (bmap1->sample &&
            isl_basic_map_contains(bmap1, bmap1->sample) > 0 &&
            isl_basic_map_contains(bmap2, bmap1->sample) > 0)
                sample = isl_vec_copy(bmap1->sample);
        else if (bmap2->sample &&
            isl_basic_map_contains(bmap1, bmap2->sample) > 0 &&
            isl_basic_map_contains(bmap2, bmap2->sample) > 0)
                sample = isl_vec_copy(bmap2->sample);

        bmap1 = isl_basic_map_cow(bmap1);
        bmap1 = isl_basic_map_extend_dim(bmap1, isl_dim_copy(bmap1->dim),
                        bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
        if (!bmap1)
                goto error;
        bmap1 = add_constraints(bmap1, bmap2, 0, 0);

        if (sample) {
                isl_vec_free(bmap1->sample);
                bmap1->sample = sample;
        }

        bmap1 = isl_basic_map_simplify(bmap1);
        return isl_basic_map_finalize(bmap1);
error:
        if (sample)
                isl_vec_free(sample);
        isl_basic_map_free(bmap1);
        isl_basic_map_free(bmap2);
        return NULL;
}

struct isl_basic_set *isl_basic_set_intersect(
                struct isl_basic_set *bset1, struct isl_basic_set *bset2)
{
        return (struct isl_basic_set *)
                isl_basic_map_intersect(
                        (struct isl_basic_map *)bset1,
                        (struct isl_basic_map *)bset2);
}

/* Special case of isl_map_intersect, where both map1 and map2
 * are convex, without any divs and such that either map1 or map2
 * contains a single constraint.  This constraint is then simply
 * added to the other map.
 */
static __isl_give isl_map *map_intersect_add_constraint(
        __isl_take isl_map *map1, __isl_take isl_map *map2)
{
        struct isl_basic_map *bmap1;
        struct isl_basic_map *bmap2;

        isl_assert(map1->ctx, map1->n == 1, goto error);
        isl_assert(map2->ctx, map1->n == 1, goto error);
        isl_assert(map1->ctx, map1->p[0]->n_div == 0, goto error);
        isl_assert(map2->ctx, map1->p[0]->n_div == 0, goto error);

        if (map2->p[0]->n_eq + map2->p[0]->n_ineq != 1)
                return isl_map_intersect(map2, map1);

        isl_assert(map2->ctx,
                    map2->p[0]->n_eq + map2->p[0]->n_ineq == 1, goto error);

        map1 = isl_map_cow(map1);
        if (!map1)
                goto error;
        map1->p[0] = isl_basic_map_cow(map1->p[0]);
        if (map2->p[0]->n_eq == 1)
                map1->p[0] = isl_basic_map_add_eq(map1->p[0], map2->p[0]->eq[0]);
        else
                map1->p[0] = isl_basic_map_add_ineq(map1->p[0],
                                                        map2->p[0]->ineq[0]);

        map1->p[0] = isl_basic_map_simplify(map1->p[0]);
        map1->p[0] = isl_basic_map_finalize(map1->p[0]);
        if (!map1->p[0])
                goto error;

        isl_map_free(map2);

        return map1;
error:
        isl_map_free(map1);
        isl_map_free(map2);
        return NULL;
}

struct isl_map *isl_map_intersect(struct isl_map *map1, struct isl_map *map2)
{
        unsigned flags = 0;
        struct isl_map *result;
        int i, j;

        if (!map1 || !map2)
                goto error;

        if (map1->n == 1 && map2->n == 1 &&
            map1->p[0]->n_div == 0 && map2->p[0]->n_div == 0 &&
            isl_dim_equal(map1->dim, map2->dim) &&
            (map1->p[0]->n_eq + map1->p[0]->n_ineq == 1 ||
             map2->p[0]->n_eq + map2->p[0]->n_ineq == 1))
                return map_intersect_add_constraint(map1, map2);
        isl_assert(map1->ctx, isl_dim_match(map1->dim, isl_dim_param,
                                         map2->dim, isl_dim_param), goto error);
        if (isl_dim_total(map1->dim) ==
                                isl_dim_size(map1->dim, isl_dim_param) &&
            isl_dim_total(map2->dim) != isl_dim_size(map2->dim, isl_dim_param))
                return isl_map_intersect(map2, map1);

        if (isl_dim_total(map2->dim) != isl_dim_size(map2->dim, isl_dim_param))
                isl_assert(map1->ctx,
                            isl_dim_equal(map1->dim, map2->dim), goto error);

        if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
            ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
                ISL_FL_SET(flags, ISL_MAP_DISJOINT);

        result = isl_map_alloc_dim(isl_dim_copy(map1->dim),
                                map1->n * map2->n, flags);
        if (!result)
                goto error;
        for (i = 0; i < map1->n; ++i)
                for (j = 0; j < map2->n; ++j) {
                        struct isl_basic_map *part;
                        part = isl_basic_map_intersect(
                                    isl_basic_map_copy(map1->p[i]),
                                    isl_basic_map_copy(map2->p[j]));
                        if (isl_basic_map_is_empty(part))
                                isl_basic_map_free(part);
                        else
                                result = isl_map_add_basic_map(result, part);
                        if (!result)
                                goto error;
                }
        isl_map_free(map1);
        isl_map_free(map2);
        return result;
error:
        isl_map_free(map1);
        isl_map_free(map2);
        return NULL;
}

struct isl_set *isl_set_intersect(struct isl_set *set1, struct isl_set *set2)
{
        return (struct isl_set *)
                isl_map_intersect((struct isl_map *)set1,
                                  (struct isl_map *)set2);
}

struct isl_basic_map *isl_basic_map_reverse(struct isl_basic_map *bmap)
{
        struct isl_dim *dim;
        struct isl_basic_set *bset;
        unsigned in;

        if (!bmap)
                return NULL;
        bmap = isl_basic_map_cow(bmap);
        if (!bmap)
                return NULL;
        dim = isl_dim_reverse(isl_dim_copy(bmap->dim));
        in = isl_basic_map_n_in(bmap);
        bset = isl_basic_set_from_basic_map(bmap);
        bset = isl_basic_set_swap_vars(bset, in);
        return isl_basic_map_from_basic_set(bset, dim);
}

__isl_give isl_basic_map *isl_basic_map_add(__isl_take isl_basic_map *bmap,
                enum isl_dim_type type, unsigned n)
{
        struct isl_dim *res_dim;
        struct isl_basic_map *res;
        struct isl_dim_map *dim_map;
        unsigned total, pos;

        if (n == 0)
                return bmap;

        if (!bmap)
                return NULL;

        res_dim = isl_dim_add(isl_basic_map_get_dim(bmap), type, n);

        total = isl_basic_map_total_dim(bmap) + n;
        dim_map = isl_dim_map_alloc(bmap->ctx, total);
        pos = 0;
        isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos);
        pos += isl_dim_size(res_dim, isl_dim_param);
        isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos);
        pos += isl_dim_size(res_dim, isl_dim_in);
        isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos);
        pos += isl_dim_size(res_dim, isl_dim_out);
        isl_dim_map_div(dim_map, bmap, pos);

        res = isl_basic_map_alloc_dim(res_dim,
                        bmap->n_div, bmap->n_eq, bmap->n_ineq);
        res = add_constraints_dim_map(res, bmap, dim_map);
        res = isl_basic_map_simplify(res);
        return isl_basic_map_finalize(res);
}

__isl_give isl_basic_set *isl_basic_set_add(__isl_take isl_basic_set *bset,
                enum isl_dim_type type, unsigned n)
{
        if (!bset)
                return NULL;
        isl_assert(bset->ctx, type != isl_dim_in, goto error);
        return (isl_basic_set *)isl_basic_map_add((isl_basic_map *)bset, type, n);
error:
        isl_basic_set_free(bset);
        return NULL;
}

__isl_give isl_map *isl_map_add(__isl_take isl_map *map,
                enum isl_dim_type type, unsigned n)
{
        int i;

        if (n == 0)
                return map;

        map = isl_map_cow(map);
        if (!map)
                return NULL;

        map->dim = isl_dim_add(map->dim, type, n);
        if (!map->dim)
                goto error;

        for (i = 0; i < map->n; ++i) {
                map->p[i] = isl_basic_map_add(map->p[i], type, n);
                if (!map->p[i])
                        goto error;
        }

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

__isl_give isl_set *isl_set_add(__isl_take isl_set *set,
                enum isl_dim_type type, unsigned n)
{
        if (!set)
                return NULL;
        isl_assert(set->ctx, type != isl_dim_in, goto error);
        return (isl_set *)isl_map_add((isl_map *)set, type, n);
error:
        isl_set_free(set);
        return NULL;
}

/* Move the specified dimensions to the last columns right before
 * the divs.  Don't change the dimension specification of bmap.
 * That's the responsibility of the caller.
 */
static __isl_give isl_basic_map *move_last(__isl_take isl_basic_map *bmap,
        enum isl_dim_type type, unsigned first, unsigned n)
{
        struct isl_dim_map *dim_map;
        struct isl_basic_map *res;
        enum isl_dim_type t;
        unsigned total, off;

        if (!bmap)
                return NULL;
        if (pos(bmap->dim, type) + first + n == 1 + isl_dim_total(bmap->dim))
                return bmap;

        total = isl_basic_map_total_dim(bmap);
        dim_map = isl_dim_map_alloc(bmap->ctx, total);

        off = 0;
        for (t = isl_dim_param; t <= isl_dim_out; ++t) {
                unsigned size = isl_dim_size(bmap->dim, t);
                if (t == type) {
                        isl_dim_map_dim_range(dim_map, bmap->dim, t,
                                            0, first, off);
                        off += first;
                        isl_dim_map_dim_range(dim_map, bmap->dim, t,
                                            first, n, total - bmap->n_div - n);
                        isl_dim_map_dim_range(dim_map, bmap->dim, t,
                                            first + n, size - (first + n), off);
                        off += size - (first + n);
                } else {
                        isl_dim_map_dim(dim_map, bmap->dim, t, off);
                        off += size;
                }
        }
        isl_dim_map_div(dim_map, bmap, off + n);

        res = isl_basic_map_alloc_dim(isl_basic_map_get_dim(bmap),
                        bmap->n_div, bmap->n_eq, bmap->n_ineq);
        res = add_constraints_dim_map(res, bmap, dim_map);
        return res;
}

/* Turn the n dimensions of type type, starting at first
 * into existentially quantified variables.
 */
__isl_give isl_basic_map *isl_basic_map_project_out(
                __isl_take isl_basic_map *bmap,
                enum isl_dim_type type, unsigned first, unsigned n)
{
        int i;
        size_t row_size;
        isl_int **new_div;
        isl_int *old;

        if (n == 0)
                return bmap;

        if (!bmap)
                return NULL;

        if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
                return isl_basic_map_remove(bmap, type, first, n);

        isl_assert(bmap->ctx, first + n <= isl_basic_map_dim(bmap, type),
                        goto error);

        bmap = move_last(bmap, type, first, n);
        bmap = isl_basic_map_cow(bmap);

        row_size = 1 + isl_dim_total(bmap->dim) + bmap->extra;
        old = bmap->block2.data;
        bmap->block2 = isl_blk_extend(bmap->ctx, bmap->block2,
                                        (bmap->extra + n) * (1 + row_size));
        if (!bmap->block2.data)
                goto error;
        new_div = isl_alloc_array(ctx, isl_int *, bmap->extra + n);
        if (!new_div)
                goto error;
        for (i = 0; i < n; ++i) {
                new_div[i] = bmap->block2.data +
                                (bmap->extra + i) * (1 + row_size);
                isl_seq_clr(new_div[i], 1 + row_size);
        }
        for (i = 0; i < bmap->extra; ++i)
                new_div[n + i] = bmap->block2.data + (bmap->div[i] - old);
        free(bmap->div);
        bmap->div = new_div;
        bmap->n_div += n;
        bmap->extra += n;

        bmap->dim = isl_dim_drop(bmap->dim, type, first, n);
        if (!bmap->dim)
                goto error;
        bmap = isl_basic_map_simplify(bmap);
        bmap = isl_basic_map_drop_redundant_divs(bmap);
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_map_free(bmap);
        return NULL;
}

/* Turn the n dimensions of type type, starting at first
 * into existentially quantified variables.
 */
struct isl_basic_set *isl_basic_set_project_out(struct isl_basic_set *bset,
                enum isl_dim_type type, unsigned first, unsigned n)
{
        return (isl_basic_set *)isl_basic_map_project_out(
                        (isl_basic_map *)bset, type, first, n);
}

/* Turn the n dimensions of type type, starting at first
 * into existentially quantified variables.
 */
__isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
                enum isl_dim_type type, unsigned first, unsigned n)
{
        int i;

        if (!map)
                return NULL;

        if (n == 0)
                return map;

        isl_assert(map->ctx, first + n <= isl_map_dim(map, type), goto error);

        map = isl_map_cow(map);
        if (!map)
                return NULL;

        map->dim = isl_dim_drop(map->dim, type, first, n);
        if (!map->dim)
                goto error;

        for (i = 0; i < map->n; ++i) {
                map->p[i] = isl_basic_map_project_out(map->p[i], type, first, n);
                if (!map->p[i])
                        goto error;
        }

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

/* Turn the n dimensions of type type, starting at first
 * into existentially quantified variables.
 */
__isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
                enum isl_dim_type type, unsigned first, unsigned n)
{
        return (isl_set *)isl_map_project_out((isl_map *)set, type, first, n);
}

static struct isl_basic_map *add_divs(struct isl_basic_map *bmap, unsigned n)
{
        int i, j;

        for (i = 0; i < n; ++i) {
                j = isl_basic_map_alloc_div(bmap);
                if (j < 0)
                        goto error;
                isl_seq_clr(bmap->div[j], 1+1+isl_basic_map_total_dim(bmap));
        }
        return bmap;
error:
        isl_basic_map_free(bmap);
        return NULL;
}

struct isl_basic_map *isl_basic_map_apply_range(
                struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
{
        struct isl_dim *dim_result = NULL;
        struct isl_basic_map *bmap;
        unsigned n_in, n_out, n, nparam, total, pos;
        struct isl_dim_map *dim_map1, *dim_map2;

        if (!bmap1 || !bmap2)
                goto error;

        dim_result = isl_dim_join(isl_dim_copy(bmap1->dim),
                                  isl_dim_copy(bmap2->dim));

        n_in = isl_basic_map_n_in(bmap1);
        n_out = isl_basic_map_n_out(bmap2);
        n = isl_basic_map_n_out(bmap1);
        nparam = isl_basic_map_n_param(bmap1);

        total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + n;
        dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
        dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
        isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
        isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
        isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
        isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_in);
        isl_dim_map_div(dim_map1, bmap1, pos += n_out);
        isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
        isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
        isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);

        bmap = isl_basic_map_alloc_dim(dim_result,
                        bmap1->n_div + bmap2->n_div + n,
                        bmap1->n_eq + bmap2->n_eq,
                        bmap1->n_ineq + bmap2->n_ineq);
        bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
        bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
        bmap = add_divs(bmap, n);
        bmap = isl_basic_map_simplify(bmap);
        bmap = isl_basic_map_drop_redundant_divs(bmap);
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_map_free(bmap1);
        isl_basic_map_free(bmap2);
        return NULL;
}

struct isl_basic_set *isl_basic_set_apply(
                struct isl_basic_set *bset, struct isl_basic_map *bmap)
{
        if (!bset || !bmap)
                goto error;

        isl_assert(bset->ctx, isl_basic_map_compatible_domain(bmap, bset),
                    goto error);

        return (struct isl_basic_set *)
                isl_basic_map_apply_range((struct isl_basic_map *)bset, bmap);
error:
        isl_basic_set_free(bset);
        isl_basic_map_free(bmap);
        return NULL;
}

struct isl_basic_map *isl_basic_map_apply_domain(
                struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
{
        if (!bmap1 || !bmap2)
                goto error;

        isl_assert(bmap1->ctx,
            isl_basic_map_n_in(bmap1) == isl_basic_map_n_in(bmap2), goto error);
        isl_assert(bmap1->ctx,
            isl_basic_map_n_param(bmap1) == isl_basic_map_n_param(bmap2),
            goto error);

        bmap1 = isl_basic_map_reverse(bmap1);
        bmap1 = isl_basic_map_apply_range(bmap1, bmap2);
        return isl_basic_map_reverse(bmap1);
error:
        isl_basic_map_free(bmap1);
        isl_basic_map_free(bmap2);
        return NULL;
}

/* Given two basic maps A -> f(A) and B -> g(B), construct a basic map
 * A \cap B -> f(A) + f(B)
 */
struct isl_basic_map *isl_basic_map_sum(
                struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
{
        unsigned n_in, n_out, nparam, total, pos;
        struct isl_basic_map *bmap = NULL;
        struct isl_dim_map *dim_map1, *dim_map2;
        int i;

        if (!bmap1 || !bmap2)
                goto error;

        isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim),
                goto error);

        nparam = isl_basic_map_n_param(bmap1);
        n_in = isl_basic_map_n_in(bmap1);
        n_out = isl_basic_map_n_out(bmap1);

        total = nparam + n_in + n_out + bmap1->n_div + bmap2->n_div + 2 * n_out;
        dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
        dim_map2 = isl_dim_map_alloc(bmap2->ctx, total);
        isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
        isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos);
        isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
        isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos);
        isl_dim_map_div(dim_map1, bmap1, pos += n_in + n_out);
        isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);
        isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += bmap2->n_div);
        isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += n_out);

        bmap = isl_basic_map_alloc_dim(isl_dim_copy(bmap1->dim),
                        bmap1->n_div + bmap2->n_div + 2 * n_out,
                        bmap1->n_eq + bmap2->n_eq + n_out,
                        bmap1->n_ineq + bmap2->n_ineq);
        for (i = 0; i < n_out; ++i) {
                int j = isl_basic_map_alloc_equality(bmap);
                if (j < 0)
                        goto error;
                isl_seq_clr(bmap->eq[j], 1+total);
                isl_int_set_si(bmap->eq[j][1+nparam+n_in+i], -1);
                isl_int_set_si(bmap->eq[j][1+pos+i], 1);
                isl_int_set_si(bmap->eq[j][1+pos-n_out+i], 1);
        }
        bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
        bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
        bmap = add_divs(bmap, 2 * n_out);

        bmap = isl_basic_map_simplify(bmap);
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_map_free(bmap);
        isl_basic_map_free(bmap1);
        isl_basic_map_free(bmap2);
        return NULL;
}

/* Given two maps A -> f(A) and B -> g(B), construct a map
 * A \cap B -> f(A) + f(B)
 */
struct isl_map *isl_map_sum(struct isl_map *map1, struct isl_map *map2)
{
        struct isl_map *result;
        int i, j;

        if (!map1 || !map2)
                goto error;

        isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);

        result = isl_map_alloc_dim(isl_dim_copy(map1->dim),
                                map1->n * map2->n, 0);
        if (!result)
                goto error;
        for (i = 0; i < map1->n; ++i)
                for (j = 0; j < map2->n; ++j) {
                        struct isl_basic_map *part;
                        part = isl_basic_map_sum(
                                    isl_basic_map_copy(map1->p[i]),
                                    isl_basic_map_copy(map2->p[j]));
                        if (isl_basic_map_is_empty(part))
                                isl_basic_map_free(part);
                        else
                                result = isl_map_add_basic_map(result, part);
                        if (!result)
                                goto error;
                }
        isl_map_free(map1);
        isl_map_free(map2);
        return result;
error:
        isl_map_free(map1);
        isl_map_free(map2);
        return NULL;
}

/* Given a basic map A -> f(A), construct A -> -f(A).
 */
struct isl_basic_map *isl_basic_map_neg(struct isl_basic_map *bmap)
{
        int i, j;
        unsigned off, n;

        bmap = isl_basic_map_cow(bmap);
        if (!bmap)
                return NULL;

        n = isl_basic_map_dim(bmap, isl_dim_out);
        off = isl_basic_map_offset(bmap, isl_dim_out);
        for (i = 0; i < bmap->n_eq; ++i)
                for (j = 0; j < n; ++j)
                        isl_int_neg(bmap->eq[i][off+j], bmap->eq[i][off+j]);
        for (i = 0; i < bmap->n_ineq; ++i)
                for (j = 0; j < n; ++j)
                        isl_int_neg(bmap->ineq[i][off+j], bmap->ineq[i][off+j]);
        for (i = 0; i < bmap->n_div; ++i)
                for (j = 0; j < n; ++j)
                        isl_int_neg(bmap->div[i][1+off+j], bmap->div[i][1+off+j]);
        return isl_basic_map_finalize(bmap);
}

/* Given a map A -> f(A), construct A -> -f(A).
 */
struct isl_map *isl_map_neg(struct isl_map *map)
{
        int i;

        map = isl_map_cow(map);
        if (!map)
                return NULL;

        for (i = 0; i < map->n; ++i) {
                map->p[i] = isl_basic_map_neg(map->p[i]);
                if (!map->p[i])
                        goto error;
        }

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

/* Given a basic map A -> f(A) and an integer d, construct a basic map
 * A -> floor(f(A)/d).
 */
struct isl_basic_map *isl_basic_map_floordiv(struct isl_basic_map *bmap,
                isl_int d)
{
        unsigned n_in, n_out, nparam, total, pos;
        struct isl_basic_map *result = NULL;
        struct isl_dim_map *dim_map;
        int i;

        if (!bmap)
                return NULL;

        nparam = isl_basic_map_n_param(bmap);
        n_in = isl_basic_map_n_in(bmap);
        n_out = isl_basic_map_n_out(bmap);

        total = nparam + n_in + n_out + bmap->n_div + n_out;
        dim_map = isl_dim_map_alloc(bmap->ctx, total);
        isl_dim_map_dim(dim_map, bmap->dim, isl_dim_param, pos = 0);
        isl_dim_map_dim(dim_map, bmap->dim, isl_dim_in, pos += nparam);
        isl_dim_map_div(dim_map, bmap, pos += n_in + n_out);
        isl_dim_map_dim(dim_map, bmap->dim, isl_dim_out, pos += bmap->n_div);

        result = isl_basic_map_alloc_dim(isl_dim_copy(bmap->dim),
                        bmap->n_div + n_out,
                        bmap->n_eq, bmap->n_ineq + 2 * n_out);
        result = add_constraints_dim_map(result, bmap, dim_map);
        result = add_divs(result, n_out);
        for (i = 0; i < n_out; ++i) {
                int j;
                j = isl_basic_map_alloc_inequality(result);
                if (j < 0)
                        goto error;
                isl_seq_clr(result->ineq[j], 1+total);
                isl_int_neg(result->ineq[j][1+nparam+n_in+i], d);
                isl_int_set_si(result->ineq[j][1+pos+i], 1);
                j = isl_basic_map_alloc_inequality(result);
                if (j < 0)
                        goto error;
                isl_seq_clr(result->ineq[j], 1+total);
                isl_int_set(result->ineq[j][1+nparam+n_in+i], d);
                isl_int_set_si(result->ineq[j][1+pos+i], -1);
                isl_int_sub_ui(result->ineq[j][0], d, 1);
        }

        result = isl_basic_map_simplify(result);
        return isl_basic_map_finalize(result);
error:
        isl_basic_map_free(result);
        return NULL;
}

/* Given a map A -> f(A) and an integer d, construct a map
 * A -> floor(f(A)/d).
 */
struct isl_map *isl_map_floordiv(struct isl_map *map, isl_int d)
{
        int i;

        map = isl_map_cow(map);
        if (!map)
                return NULL;

        ISL_F_CLR(map, ISL_MAP_DISJOINT);
        ISL_F_CLR(map, ISL_MAP_NORMALIZED);
        for (i = 0; i < map->n; ++i) {
                map->p[i] = isl_basic_map_floordiv(map->p[i], d);
                if (!map->p[i])
                        goto error;
        }

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

static struct isl_basic_map *var_equal(struct isl_basic_map *bmap, unsigned pos)
{
        int i;
        unsigned nparam;
        unsigned n_in;

        i = isl_basic_map_alloc_equality(bmap);
        if (i < 0)
                goto error;
        nparam = isl_basic_map_n_param(bmap);
        n_in = isl_basic_map_n_in(bmap);
        isl_seq_clr(bmap->eq[i], 1 + isl_basic_map_total_dim(bmap));
        isl_int_set_si(bmap->eq[i][1+nparam+pos], -1);
        isl_int_set_si(bmap->eq[i][1+nparam+n_in+pos], 1);
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_map_free(bmap);
        return NULL;
}

/* Add a constraints to "bmap" expressing i_pos < o_pos
 */
static struct isl_basic_map *var_less(struct isl_basic_map *bmap, unsigned pos)
{
        int i;
        unsigned nparam;
        unsigned n_in;

        i = isl_basic_map_alloc_inequality(bmap);
        if (i < 0)
                goto error;
        nparam = isl_basic_map_n_param(bmap);
        n_in = isl_basic_map_n_in(bmap);
        isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
        isl_int_set_si(bmap->ineq[i][0], -1);
        isl_int_set_si(bmap->ineq[i][1+nparam+pos], -1);
        isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], 1);
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_map_free(bmap);
        return NULL;
}

/* Add a constraints to "bmap" expressing i_pos > o_pos
 */
static struct isl_basic_map *var_more(struct isl_basic_map *bmap, unsigned pos)
{
        int i;
        unsigned nparam;
        unsigned n_in;

        i = isl_basic_map_alloc_inequality(bmap);
        if (i < 0)
                goto error;
        nparam = isl_basic_map_n_param(bmap);
        n_in = isl_basic_map_n_in(bmap);
        isl_seq_clr(bmap->ineq[i], 1 + isl_basic_map_total_dim(bmap));
        isl_int_set_si(bmap->ineq[i][0], -1);
        isl_int_set_si(bmap->ineq[i][1+nparam+pos], 1);
        isl_int_set_si(bmap->ineq[i][1+nparam+n_in+pos], -1);
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_map_free(bmap);
        return NULL;
}

struct isl_basic_map *isl_basic_map_equal(struct isl_dim *dim, unsigned n_equal)
{
        int i;
        struct isl_basic_map *bmap;
        bmap = isl_basic_map_alloc_dim(dim, 0, n_equal, 0);
        if (!bmap)
                return NULL;
        for (i = 0; i < n_equal && bmap; ++i)
                bmap = var_equal(bmap, i);
        return isl_basic_map_finalize(bmap);
}

/* Return a relation on pairs of sets of dimension "dim" expressing i_pos < o_pos
 */
struct isl_basic_map *isl_basic_map_less_at(struct isl_dim *dim, unsigned pos)
{
        int i;
        struct isl_basic_map *bmap;
        bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
        if (!bmap)
                return NULL;
        for (i = 0; i < pos && bmap; ++i)
                bmap = var_equal(bmap, i);
        if (bmap)
                bmap = var_less(bmap, pos);
        return isl_basic_map_finalize(bmap);
}

/* Return a relation on pairs of sets of dimension "dim" expressing i_pos > o_pos
 */
struct isl_basic_map *isl_basic_map_more_at(struct isl_dim *dim, unsigned pos)
{
        int i;
        struct isl_basic_map *bmap;
        bmap = isl_basic_map_alloc_dim(dim, 0, pos, 1);
        if (!bmap)
                return NULL;
        for (i = 0; i < pos && bmap; ++i)
                bmap = var_equal(bmap, i);
        if (bmap)
                bmap = var_more(bmap, pos);
        return isl_basic_map_finalize(bmap);
}

static __isl_give isl_map *map_lex_lte(__isl_take isl_dim *dims, int equal)
{
        struct isl_map *map;
        unsigned dim;
        int i;

        if (!dims)
                return NULL;
        dim = dims->n_out;
        map = isl_map_alloc_dim(isl_dim_copy(dims), dim + equal, ISL_MAP_DISJOINT);

        for (i = 0; i < dim; ++i)
                map = isl_map_add_basic_map(map,
                                  isl_basic_map_less_at(isl_dim_copy(dims), i));
        if (equal)
                map = isl_map_add_basic_map(map,
                                  isl_basic_map_equal(isl_dim_copy(dims), dim));

        isl_dim_free(dims);
        return map;
}

__isl_give isl_map *isl_map_lex_lt(__isl_take isl_dim *set_dim)
{
        return map_lex_lte(isl_dim_map(set_dim), 0);
}

__isl_give isl_map *isl_map_lex_le(__isl_take isl_dim *set_dim)
{
        return map_lex_lte(isl_dim_map(set_dim), 1);
}

static __isl_give isl_map *map_lex_gte(__isl_take isl_dim *dims, int equal)
{
        struct isl_map *map;
        unsigned dim;
        int i;

        if (!dims)
                return NULL;
        dim = dims->n_out;
        map = isl_map_alloc_dim(isl_dim_copy(dims), dim + equal, ISL_MAP_DISJOINT);

        for (i = 0; i < dim; ++i)
                map = isl_map_add_basic_map(map,
                                  isl_basic_map_more_at(isl_dim_copy(dims), i));
        if (equal)
                map = isl_map_add_basic_map(map,
                                  isl_basic_map_equal(isl_dim_copy(dims), dim));

        isl_dim_free(dims);
        return map;
}

__isl_give isl_map *isl_map_lex_gt(__isl_take isl_dim *set_dim)
{
        return map_lex_gte(isl_dim_map(set_dim), 0);
}

__isl_give isl_map *isl_map_lex_ge(__isl_take isl_dim *set_dim)
{
        return map_lex_gte(isl_dim_map(set_dim), 1);
}

struct isl_basic_map *isl_basic_map_from_basic_set(
                struct isl_basic_set *bset, struct isl_dim *dim)
{
        struct isl_basic_map *bmap;

        bset = isl_basic_set_cow(bset);
        if (!bset || !dim)
                goto error;

        isl_assert(bset->ctx, isl_dim_compatible(bset->dim, dim), goto error);
        isl_dim_free(bset->dim);
        bmap = (struct isl_basic_map *) bset;
        bmap->dim = dim;
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_set_free(bset);
        isl_dim_free(dim);
        return NULL;
}

struct isl_basic_set *isl_basic_set_from_basic_map(struct isl_basic_map *bmap)
{
        if (!bmap)
                goto error;
        if (bmap->dim->n_in == 0)
                return (struct isl_basic_set *)bmap;
        bmap = isl_basic_map_cow(bmap);
        if (!bmap)
                goto error;
        bmap->dim = isl_dim_cow(bmap->dim);
        if (!bmap->dim)
                goto error;
        bmap->dim->n_out += bmap->dim->n_in;
        bmap->dim->n_in = 0;
        bmap = isl_basic_map_finalize(bmap);
        return (struct isl_basic_set *)bmap;
error:
        isl_basic_map_free(bmap);
        return NULL;
}

/* For a div d = floor(f/m), add the constraints
 *
 *              f - m d >= 0
 *              -(f-(n-1)) + m d >= 0
 *
 * Note that the second constraint is the negation of
 *
 *              f - m d >= n
 */
int isl_basic_map_add_div_constraints(struct isl_basic_map *bmap, unsigned div)
{
        int i, j;
        unsigned total = isl_basic_map_total_dim(bmap);
        unsigned div_pos = 1 + total - bmap->n_div + div;

        i = isl_basic_map_alloc_inequality(bmap);
        if (i < 0)
                return -1;
        isl_seq_cpy(bmap->ineq[i], bmap->div[div]+1, 1+total);
        isl_int_neg(bmap->ineq[i][div_pos], bmap->div[div][0]);

        j = isl_basic_map_alloc_inequality(bmap);
        if (j < 0)
                return -1;
        isl_seq_neg(bmap->ineq[j], bmap->ineq[i], 1 + total);
        isl_int_add(bmap->ineq[j][0], bmap->ineq[j][0], bmap->ineq[j][div_pos]);
        isl_int_sub_ui(bmap->ineq[j][0], bmap->ineq[j][0], 1);
        return j;
}

struct isl_basic_set *isl_basic_map_underlying_set(
                struct isl_basic_map *bmap)
{
        if (!bmap)
                goto error;
        if (bmap->dim->nparam == 0 && bmap->dim->n_in == 0 && bmap->n_div == 0)
                return (struct isl_basic_set *)bmap;
        bmap = isl_basic_map_cow(bmap);
        if (!bmap)
                goto error;
        bmap->dim = isl_dim_underlying(bmap->dim, bmap->n_div);
        if (!bmap->dim)
                goto error;
        bmap->extra -= bmap->n_div;
        bmap->n_div = 0;
        bmap = isl_basic_map_finalize(bmap);
        return (struct isl_basic_set *)bmap;
error:
        return NULL;
}

__isl_give isl_basic_set *isl_basic_set_underlying_set(
                __isl_take isl_basic_set *bset)
{
        return isl_basic_map_underlying_set((isl_basic_map *)bset);
}

struct isl_basic_map *isl_basic_map_overlying_set(
        struct isl_basic_set *bset, struct isl_basic_map *like)
{
        struct isl_basic_map *bmap;
        struct isl_ctx *ctx;
        unsigned total;
        int i;

        if (!bset || !like)
                goto error;
        ctx = bset->ctx;
        isl_assert(ctx, bset->n_div == 0, goto error);
        isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
        isl_assert(ctx, bset->dim->n_out == isl_basic_map_total_dim(like),
                        goto error);
        if (isl_dim_equal(bset->dim, like->dim) && like->n_div == 0) {
                isl_basic_map_free(like);
                return (struct isl_basic_map *)bset;
        }
        bset = isl_basic_set_cow(bset);
        if (!bset)
                goto error;
        total = bset->dim->n_out + bset->extra;
        bmap = (struct isl_basic_map *)bset;
        isl_dim_free(bmap->dim);
        bmap->dim = isl_dim_copy(like->dim);
        if (!bmap->dim)
                goto error;
        bmap->n_div = like->n_div;
        bmap->extra += like->n_div;
        if (bmap->extra) {
                unsigned ltotal;
                ltotal = total - bmap->extra + like->extra;
                if (ltotal > total)
                        ltotal = total;
                bmap->block2 = isl_blk_extend(ctx, bmap->block2,
                                        bmap->extra * (1 + 1 + total));
                if (isl_blk_is_error(bmap->block2))
                        goto error;
                bmap->div = isl_realloc_array(ctx, bmap->div, isl_int *,
                                                bmap->extra);
                if (!bmap->div)
                        goto error;
                for (i = 0; i < bmap->extra; ++i)
                        bmap->div[i] = bmap->block2.data + i * (1 + 1 + total);
                for (i = 0; i < like->n_div; ++i) {
                        isl_seq_cpy(bmap->div[i], like->div[i], 1 + 1 + ltotal);
                        isl_seq_clr(bmap->div[i]+1+1+ltotal, total - ltotal);
                }
                bmap = isl_basic_map_extend_constraints(bmap, 
                                                        0, 2 * like->n_div);
                for (i = 0; i < like->n_div; ++i) {
                        if (isl_int_is_zero(bmap->div[i][0]))
                                continue;
                        if (isl_basic_map_add_div_constraints(bmap, i) < 0)
                                goto error;
                }
        }
        isl_basic_map_free(like);
        bmap = isl_basic_map_simplify(bmap);
        bmap = isl_basic_map_finalize(bmap);
        return bmap;
error:
        isl_basic_map_free(like);
        isl_basic_set_free(bset);
        return NULL;
}

struct isl_basic_set *isl_basic_set_from_underlying_set(
        struct isl_basic_set *bset, struct isl_basic_set *like)
{
        return (struct isl_basic_set *)
                isl_basic_map_overlying_set(bset, (struct isl_basic_map *)like);
}

struct isl_set *isl_set_from_underlying_set(
        struct isl_set *set, struct isl_basic_set *like)
{
        int i;

        if (!set || !like)
                goto error;
        isl_assert(set->ctx, set->dim->n_out == isl_basic_set_total_dim(like),
                    goto error);
        if (isl_dim_equal(set->dim, like->dim) && like->n_div == 0) {
                isl_basic_set_free(like);
                return set;
        }
        set = isl_set_cow(set);
        if (!set)
                goto error;
        for (i = 0; i < set->n; ++i) {
                set->p[i] = isl_basic_set_from_underlying_set(set->p[i],
                                                      isl_basic_set_copy(like));
                if (!set->p[i])
                        goto error;
        }
        isl_dim_free(set->dim);
        set->dim = isl_dim_copy(like->dim);
        if (!set->dim)
                goto error;
        isl_basic_set_free(like);
        return set;
error:
        isl_basic_set_free(like);
        isl_set_free(set);
        return NULL;
}

struct isl_set *isl_map_underlying_set(struct isl_map *map)
{
        int i;

        map = isl_map_cow(map);
        if (!map)
                return NULL;
        map->dim = isl_dim_cow(map->dim);
        if (!map->dim)
                goto error;

        for (i = 1; i < map->n; ++i)
                isl_assert(map->ctx, map->p[0]->n_div == map->p[i]->n_div,
                                goto error);
        for (i = 0; i < map->n; ++i) {
                map->p[i] = (struct isl_basic_map *)
                                isl_basic_map_underlying_set(map->p[i]);
                if (!map->p[i])
                        goto error;
        }
        if (map->n == 0)
                map->dim = isl_dim_underlying(map->dim, 0);
        else {
                isl_dim_free(map->dim);
                map->dim = isl_dim_copy(map->p[0]->dim);
        }
        if (!map->dim)
                goto error;
        return (struct isl_set *)map;
error:
        isl_map_free(map);
        return NULL;
}

struct isl_set *isl_set_to_underlying_set(struct isl_set *set)
{
        return (struct isl_set *)isl_map_underlying_set((struct isl_map *)set);
}

struct isl_basic_set *isl_basic_map_domain(struct isl_basic_map *bmap)
{
        struct isl_basic_set *domain;
        unsigned n_in;
        unsigned n_out;
        if (!bmap)
                return NULL;
        n_in = isl_basic_map_n_in(bmap);
        n_out = isl_basic_map_n_out(bmap);
        domain = isl_basic_set_from_basic_map(bmap);
        return isl_basic_set_project_out(domain, isl_dim_set, n_in, n_out);
}

struct isl_basic_set *isl_basic_map_range(struct isl_basic_map *bmap)
{
        return isl_basic_map_domain(isl_basic_map_reverse(bmap));
}

struct isl_set *isl_map_range(struct isl_map *map)
{
        int i;
        struct isl_set *set;

        if (!map)
                goto error;
        map = isl_map_cow(map);
        if (!map)
                goto error;

        set = (struct isl_set *) map;
        if (set->dim->n_in != 0) {
                set->dim = isl_dim_drop_inputs(set->dim, 0, set->dim->n_in);
                if (!set->dim)
                        goto error;
        }
        for (i = 0; i < map->n; ++i) {
                set->p[i] = isl_basic_map_range(map->p[i]);
                if (!set->p[i])
                        goto error;
        }
        ISL_F_CLR(set, ISL_MAP_DISJOINT);
        ISL_F_CLR(set, ISL_SET_NORMALIZED);
        return set;
error:
        isl_map_free(map);
        return NULL;
}

struct isl_map *isl_map_from_set(struct isl_set *set, struct isl_dim *dim)
{
        int i;
        struct isl_map *map = NULL;

        set = isl_set_cow(set);
        if (!set || !dim)
                goto error;
        isl_assert(set->ctx, isl_dim_compatible(set->dim, dim), goto error);
        map = (struct isl_map *)set;
        for (i = 0; i < set->n; ++i) {
                map->p[i] = isl_basic_map_from_basic_set(
                                set->p[i], isl_dim_copy(dim));
                if (!map->p[i])
                        goto error;
        }
        isl_dim_free(map->dim);
        map->dim = dim;
        return map;
error:
        isl_dim_free(dim);
        isl_set_free(set);
        return NULL;
}

struct isl_map *isl_map_from_range(struct isl_set *set)
{
        return (struct isl_map *)set;
}

__isl_give isl_map *isl_map_from_domain(__isl_take isl_set *set)
{
        return isl_map_reverse(isl_map_from_range(set));;
}

__isl_give isl_map *isl_map_from_domain_and_range(__isl_take isl_set *domain,
        __isl_take isl_set *range)
{
        return isl_map_product(isl_map_from_domain(domain),
                               isl_map_from_range(range));
}

struct isl_set *isl_set_from_map(struct isl_map *map)
{
        int i;
        struct isl_set *set = NULL;

        if (!map)
                return NULL;
        map = isl_map_cow(map);
        if (!map)
                return NULL;
        map->dim = isl_dim_cow(map->dim);
        if (!map->dim)
                goto error;
        map->dim->n_out += map->dim->n_in;
        map->dim->n_in = 0;
        set = (struct isl_set *)map;
        for (i = 0; i < map->n; ++i) {
                set->p[i] = isl_basic_set_from_basic_map(map->p[i]);
                if (!set->p[i])
                        goto error;
        }
        return set;
error:
        isl_map_free(map);
        return NULL;
}

struct isl_map *isl_map_alloc_dim(struct isl_dim *dim, int n, unsigned flags)
{
        struct isl_map *map;

        if (!dim)
                return NULL;
        isl_assert(dim->ctx, n >= 0, return NULL);
        map = isl_alloc(dim->ctx, struct isl_map,
                        sizeof(struct isl_map) +
                        (n - 1) * sizeof(struct isl_basic_map *));
        if (!map)
                goto error;

        map->ctx = dim->ctx;
        isl_ctx_ref(map->ctx);
        map->ref = 1;
        map->size = n;
        map->n = 0;
        map->dim = dim;
        map->flags = flags;
        return map;
error:
        isl_dim_free(dim);
        return NULL;
}

struct isl_map *isl_map_alloc(struct isl_ctx *ctx,
                unsigned nparam, unsigned in, unsigned out, int n,
                unsigned flags)
{
        struct isl_map *map;
        struct isl_dim *dims;

        dims = isl_dim_alloc(ctx, nparam, in, out);
        if (!dims)
                return NULL;

        map = isl_map_alloc_dim(dims, n, flags);
        return map;
}

struct isl_basic_map *isl_basic_map_empty(struct isl_dim *dim)
{
        struct isl_basic_map *bmap;
        bmap = isl_basic_map_alloc_dim(dim, 0, 1, 0);
        bmap = isl_basic_map_set_to_empty(bmap);
        return bmap;
}

struct isl_basic_set *isl_basic_set_empty(struct isl_dim *dim)
{
        struct isl_basic_set *bset;
        bset = isl_basic_set_alloc_dim(dim, 0, 1, 0);
        bset = isl_basic_set_set_to_empty(bset);
        return bset;
}

struct isl_basic_map *isl_basic_map_empty_like(struct isl_basic_map *model)
{
        struct isl_basic_map *bmap;
        if (!model)
                return NULL;
        bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
        bmap = isl_basic_map_set_to_empty(bmap);
        return bmap;
}

struct isl_basic_map *isl_basic_map_empty_like_map(struct isl_map *model)
{
        struct isl_basic_map *bmap;
        if (!model)
                return NULL;
        bmap = isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
        bmap = isl_basic_map_set_to_empty(bmap);
        return bmap;
}

struct isl_basic_set *isl_basic_set_empty_like(struct isl_basic_set *model)
{
        struct isl_basic_set *bset;
        if (!model)
                return NULL;
        bset = isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 1, 0);
        bset = isl_basic_set_set_to_empty(bset);
        return bset;
}

struct isl_basic_map *isl_basic_map_universe(struct isl_dim *dim)
{
        struct isl_basic_map *bmap;
        bmap = isl_basic_map_alloc_dim(dim, 0, 0, 0);
        return bmap;
}

struct isl_basic_set *isl_basic_set_universe(struct isl_dim *dim)
{
        struct isl_basic_set *bset;
        bset = isl_basic_set_alloc_dim(dim, 0, 0, 0);
        return bset;
}

__isl_give isl_basic_map *isl_basic_map_universe_like(
                __isl_keep isl_basic_map *model)
{
        if (!model)
                return NULL;
        return isl_basic_map_alloc_dim(isl_dim_copy(model->dim), 0, 0, 0);
}

struct isl_basic_set *isl_basic_set_universe_like(struct isl_basic_set *model)
{
        if (!model)
                return NULL;
        return isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 0, 0);
}

__isl_give isl_basic_set *isl_basic_set_universe_like_set(
        __isl_keep isl_set *model)
{
        if (!model)
                return NULL;
        return isl_basic_set_alloc_dim(isl_dim_copy(model->dim), 0, 0, 0);
}

struct isl_map *isl_map_empty(struct isl_dim *dim)
{
        return isl_map_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
}

struct isl_map *isl_map_empty_like(struct isl_map *model)
{
        if (!model)
                return NULL;
        return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
}

struct isl_map *isl_map_empty_like_basic_map(struct isl_basic_map *model)
{
        if (!model)
                return NULL;
        return isl_map_alloc_dim(isl_dim_copy(model->dim), 0, ISL_MAP_DISJOINT);
}

struct isl_set *isl_set_empty(struct isl_dim *dim)
{
        return isl_set_alloc_dim(dim, 0, ISL_MAP_DISJOINT);
}

struct isl_set *isl_set_empty_like(struct isl_set *model)
{
        if (!model)
                return NULL;
        return isl_set_empty(isl_dim_copy(model->dim));
}

struct isl_map *isl_map_universe(struct isl_dim *dim)
{
        struct isl_map *map;
        if (!dim)
                return NULL;
        map = isl_map_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
        map = isl_map_add_basic_map(map, isl_basic_map_universe(dim));
        return map;
}

struct isl_set *isl_set_universe(struct isl_dim *dim)
{
        struct isl_set *set;
        if (!dim)
                return NULL;
        set = isl_set_alloc_dim(isl_dim_copy(dim), 1, ISL_MAP_DISJOINT);
        set = isl_set_add_basic_set(set, isl_basic_set_universe(dim));
        return set;
}

__isl_give isl_set *isl_set_universe_like(__isl_keep isl_set *model)
{
        if (!model)
                return NULL;
        return isl_set_universe(isl_dim_copy(model->dim));
}

struct isl_map *isl_map_dup(struct isl_map *map)
{
        int i;
        struct isl_map *dup;

        if (!map)
                return NULL;
        dup = isl_map_alloc_dim(isl_dim_copy(map->dim), map->n, map->flags);
        for (i = 0; i < map->n; ++i)
                dup = isl_map_add_basic_map(dup, isl_basic_map_copy(map->p[i]));
        return dup;
}

__isl_give isl_map *isl_map_add_basic_map(__isl_take isl_map *map,
                                                __isl_take isl_basic_map *bmap)
{
        if (!bmap || !map)
                goto error;
        if (isl_basic_map_fast_is_empty(bmap)) {
                isl_basic_map_free(bmap);
                return map;
        }
        isl_assert(map->ctx, isl_dim_equal(map->dim, bmap->dim), goto error);
        isl_assert(map->ctx, map->n < map->size, goto error);
        map->p[map->n] = bmap;
        map->n++;
        ISL_F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
error:
        if (map)
                isl_map_free(map);
        if (bmap)
                isl_basic_map_free(bmap);
        return NULL;
}

void isl_map_free(struct isl_map *map)
{
        int i;

        if (!map)
                return;

        if (--map->ref > 0)
                return;

        isl_ctx_deref(map->ctx);
        for (i = 0; i < map->n; ++i)
                isl_basic_map_free(map->p[i]);
        isl_dim_free(map->dim);
        free(map);
}

struct isl_map *isl_map_extend(struct isl_map *base,
                unsigned nparam, unsigned n_in, unsigned n_out)
{
        int i;

        base = isl_map_cow(base);
        if (!base)
                return NULL;

        base->dim = isl_dim_extend(base->dim, nparam, n_in, n_out);
        if (!base->dim)
                goto error;
        for (i = 0; i < base->n; ++i) {
                base->p[i] = isl_basic_map_extend_dim(base->p[i],
                                isl_dim_copy(base->dim), 0, 0, 0);
                if (!base->p[i])
                        goto error;
        }
        return base;
error:
        isl_map_free(base);
        return NULL;
}

struct isl_set *isl_set_extend(struct isl_set *base,
                unsigned nparam, unsigned dim)
{
        return (struct isl_set *)isl_map_extend((struct isl_map *)base,
                                                        nparam, 0, dim);
}

static struct isl_basic_map *isl_basic_map_fix_pos_si(
        struct isl_basic_map *bmap, unsigned pos, int value)
{
        int j;

        bmap = isl_basic_map_cow(bmap);
        bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
        j = isl_basic_map_alloc_equality(bmap);
        if (j < 0)
                goto error;
        isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
        isl_int_set_si(bmap->eq[j][pos], -1);
        isl_int_set_si(bmap->eq[j][0], value);
        bmap = isl_basic_map_simplify(bmap);
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_map_free(bmap);
        return NULL;
}

static __isl_give isl_basic_map *isl_basic_map_fix_pos(
        __isl_take isl_basic_map *bmap, unsigned pos, isl_int value)
{
        int j;

        bmap = isl_basic_map_cow(bmap);
        bmap = isl_basic_map_extend_constraints(bmap, 1, 0);
        j = isl_basic_map_alloc_equality(bmap);
        if (j < 0)
                goto error;
        isl_seq_clr(bmap->eq[j] + 1, isl_basic_map_total_dim(bmap));
        isl_int_set_si(bmap->eq[j][pos], -1);
        isl_int_set(bmap->eq[j][0], value);
        bmap = isl_basic_map_simplify(bmap);
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_map_free(bmap);
        return NULL;
}

struct isl_basic_map *isl_basic_map_fix_si(struct isl_basic_map *bmap,
                enum isl_dim_type type, unsigned pos, int value)
{
        if (!bmap)
                return NULL;
        isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
        return isl_basic_map_fix_pos_si(bmap,
                isl_basic_map_offset(bmap, type) + pos, value);
error:
        isl_basic_map_free(bmap);
        return NULL;
}

__isl_give isl_basic_map *isl_basic_map_fix(__isl_take isl_basic_map *bmap,
                enum isl_dim_type type, unsigned pos, isl_int value)
{
        if (!bmap)
                return NULL;
        isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
        return isl_basic_map_fix_pos(bmap,
                isl_basic_map_offset(bmap, type) + pos, value);
error:
        isl_basic_map_free(bmap);
        return NULL;
}

struct isl_basic_set *isl_basic_set_fix_si(struct isl_basic_set *bset,
                enum isl_dim_type type, unsigned pos, int value)
{
        return (struct isl_basic_set *)
                isl_basic_map_fix_si((struct isl_basic_map *)bset,
                                        type, pos, value);
}

__isl_give isl_basic_set *isl_basic_set_fix(__isl_take isl_basic_set *bset,
                enum isl_dim_type type, unsigned pos, isl_int value)
{
        return (struct isl_basic_set *)
                isl_basic_map_fix((struct isl_basic_map *)bset,
                                        type, pos, value);
}

struct isl_basic_map *isl_basic_map_fix_input_si(struct isl_basic_map *bmap,
                unsigned input, int value)
{
        return isl_basic_map_fix_si(bmap, isl_dim_in, input, value);
}

struct isl_basic_set *isl_basic_set_fix_dim_si(struct isl_basic_set *bset,
                unsigned dim, int value)
{
        return (struct isl_basic_set *)
                isl_basic_map_fix_si((struct isl_basic_map *)bset,
                                        isl_dim_set, dim, value);
}

struct isl_map *isl_map_fix_si(struct isl_map *map,
                enum isl_dim_type type, unsigned pos, int value)
{
        int i;

        map = isl_map_cow(map);
        if (!map)
                return NULL;

        isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
        for (i = 0; i < map->n; ++i) {
                map->p[i] = isl_basic_map_fix_si(map->p[i], type, pos, value);
                if (!map->p[i])
                        goto error;
        }
        ISL_F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
error:
        isl_map_free(map);
        return NULL;
}

__isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
                enum isl_dim_type type, unsigned pos, int value)
{
        return (struct isl_set *)
                isl_map_fix_si((struct isl_map *)set, type, pos, value);
}

__isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
                enum isl_dim_type type, unsigned pos, isl_int value)
{
        int i;

        map = isl_map_cow(map);
        if (!map)
                return NULL;

        isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
        for (i = 0; i < map->n; ++i) {
                map->p[i] = isl_basic_map_fix(map->p[i], type, pos, value);
                if (!map->p[i])
                        goto error;
        }
        ISL_F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
error:
        isl_map_free(map);
        return NULL;
}

__isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
                enum isl_dim_type type, unsigned pos, isl_int value)
{
        return (struct isl_set *)isl_map_fix((isl_map *)set, type, pos, value);
}

struct isl_map *isl_map_fix_input_si(struct isl_map *map,
                unsigned input, int value)
{
        return isl_map_fix_si(map, isl_dim_in, input, value);
}

struct isl_set *isl_set_fix_dim_si(struct isl_set *set, unsigned dim, int value)
{
        return (struct isl_set *)
                isl_map_fix_si((struct isl_map *)set, isl_dim_set, dim, value);
}

__isl_give isl_basic_map *isl_basic_map_lower_bound_si(
                __isl_take isl_basic_map *bmap,
                enum isl_dim_type type, unsigned pos, int value)
{
        int j;

        if (!bmap)
                return NULL;
        isl_assert(bmap->ctx, pos < isl_basic_map_dim(bmap, type), goto error);
        pos += isl_basic_map_offset(bmap, type);
        bmap = isl_basic_map_cow(bmap);
        bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
        j = isl_basic_map_alloc_inequality(bmap);
        if (j < 0)
                goto error;
        isl_seq_clr(bmap->ineq[j], 1 + isl_basic_map_total_dim(bmap));
        isl_int_set_si(bmap->ineq[j][pos], 1);
        isl_int_set_si(bmap->ineq[j][0], -value);
        bmap = isl_basic_map_simplify(bmap);
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_map_free(bmap);
        return NULL;
}

struct isl_basic_set *isl_basic_set_lower_bound_dim(struct isl_basic_set *bset,
        unsigned dim, isl_int value)
{
        int j;

        bset = isl_basic_set_cow(bset);
        bset = isl_basic_set_extend_constraints(bset, 0, 1);
        j = isl_basic_set_alloc_inequality(bset);
        if (j < 0)
                goto error;
        isl_seq_clr(bset->ineq[j], 1 + isl_basic_set_total_dim(bset));
        isl_int_set_si(bset->ineq[j][1 + isl_basic_set_n_param(bset) + dim], 1);
        isl_int_neg(bset->ineq[j][0], value);
        bset = isl_basic_set_simplify(bset);
        return isl_basic_set_finalize(bset);
error:
        isl_basic_set_free(bset);
        return NULL;
}

__isl_give isl_map *isl_map_lower_bound_si(__isl_take isl_map *map,
                enum isl_dim_type type, unsigned pos, int value)
{
        int i;

        map = isl_map_cow(map);
        if (!map)
                return NULL;

        isl_assert(map->ctx, pos < isl_map_dim(map, type), goto error);
        for (i = 0; i < map->n; ++i) {
                map->p[i] = isl_basic_map_lower_bound_si(map->p[i],
                                                         type, pos, value);
                if (!map->p[i])
                        goto error;
        }
        ISL_F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
error:
        isl_map_free(map);
        return NULL;
}

struct isl_set *isl_set_lower_bound_dim(struct isl_set *set, unsigned dim,
                                        isl_int value)
{
        int i;

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

        isl_assert(set->ctx, dim < isl_set_n_dim(set), goto error);
        for (i = 0; i < set->n; ++i) {
                set->p[i] = isl_basic_set_lower_bound_dim(set->p[i], dim, value);
                if (!set->p[i])
                        goto error;
        }
        return set;
error:
        isl_set_free(set);
        return NULL;
}

struct isl_map *isl_map_reverse(struct isl_map *map)
{
        int i;

        map = isl_map_cow(map);
        if (!map)
                return NULL;

        map->dim = isl_dim_reverse(map->dim);
        if (!map->dim)
                goto error;
        for (i = 0; i < map->n; ++i) {
                map->p[i] = isl_basic_map_reverse(map->p[i]);
                if (!map->p[i])
                        goto error;
        }
        ISL_F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
error:
        isl_map_free(map);
        return NULL;
}

static struct isl_map *isl_basic_map_partial_lexopt(
                struct isl_basic_map *bmap, struct isl_basic_set *dom,
                struct isl_set **empty, int max)
{
        if (!bmap)
                goto error;
        if (bmap->ctx->opt->pip == ISL_PIP_PIP)
                return isl_pip_basic_map_lexopt(bmap, dom, empty, max);
        else
                return isl_tab_basic_map_partial_lexopt(bmap, dom, empty, max);
error:
        isl_basic_map_free(bmap);
        isl_basic_set_free(dom);
        if (empty)
                *empty = NULL;
        return NULL;
}

struct isl_map *isl_basic_map_partial_lexmax(
                struct isl_basic_map *bmap, struct isl_basic_set *dom,
                struct isl_set **empty)
{
        return isl_basic_map_partial_lexopt(bmap, dom, empty, 1);
}

struct isl_map *isl_basic_map_partial_lexmin(
                struct isl_basic_map *bmap, struct isl_basic_set *dom,
                struct isl_set **empty)
{
        return isl_basic_map_partial_lexopt(bmap, dom, empty, 0);
}

struct isl_set *isl_basic_set_partial_lexmin(
                struct isl_basic_set *bset, struct isl_basic_set *dom,
                struct isl_set **empty)
{
        return (struct isl_set *)
                isl_basic_map_partial_lexmin((struct isl_basic_map *)bset,
                        dom, empty);
}

struct isl_set *isl_basic_set_partial_lexmax(
                struct isl_basic_set *bset, struct isl_basic_set *dom,
                struct isl_set **empty)
{
        return (struct isl_set *)
                isl_basic_map_partial_lexmax((struct isl_basic_map *)bset,
                        dom, empty);
}

/* Given a basic map "bmap", compute the lexicograhically minimal
 * (or maximal) image element for each domain element in dom.
 * Set *empty to those elements in dom that do not have an image element.
 *
 * We first make sure the basic sets in dom are disjoint and then
 * simply collect the results over each of the basic sets separately.
 * We could probably improve the efficiency a bit by moving the union
 * domain down into the parametric integer programming.
 */
static __isl_give isl_map *basic_map_partial_lexopt(
                __isl_take isl_basic_map *bmap, __isl_take isl_set *dom,
                __isl_give isl_set **empty, int max)
{
        int i;
        struct isl_map *res;

        dom = isl_set_make_disjoint(dom);
        if (!dom)
                goto error;

        if (isl_set_fast_is_empty(dom)) {
                res = isl_map_empty_like_basic_map(bmap);
                *empty = isl_set_empty_like(dom);
                isl_set_free(dom);
                isl_basic_map_free(bmap);
                return res;
        }

        res = isl_basic_map_partial_lexopt(isl_basic_map_copy(bmap),
                        isl_basic_set_copy(dom->p[0]), empty, max);
                
        for (i = 1; i < dom->n; ++i) {
                struct isl_map *res_i;
                struct isl_set *empty_i;

                res_i = isl_basic_map_partial_lexopt(isl_basic_map_copy(bmap),
                                isl_basic_set_copy(dom->p[i]), &empty_i, max);

                res = isl_map_union_disjoint(res, res_i);
                *empty = isl_set_union_disjoint(*empty, empty_i);
        }

        isl_set_free(dom);
        isl_basic_map_free(bmap);
        return res;
error:
        *empty = NULL;
        isl_set_free(dom);
        isl_basic_map_free(bmap);
        return NULL;
}

/* Given a map "map", compute the lexicograhically minimal
 * (or maximal) image element for each domain element in dom.
 * Set *empty to those elements in dom that do not have an image element.
 *
 * We first compute the lexicographically minimal or maximal element
 * in the first basic map.  This results in a partial solution "res"
 * and a subset "todo" of dom that still need to be handled.
 * We then consider each of the remaining maps in "map" and successively
 * improve both "res" and "todo".
 *
 * Let res^k and todo^k be the results after k steps and let i = k + 1.
 * Assume we are computing the lexicographical maximum.
 * We first intersect basic map i with a relation that maps elements
 * to elements that are lexicographically larger than the image elements
 * in res^k and the compute the maximum image element of this intersection.
 * The result ("better") corresponds to those image elements in basic map i
 * that are better than what we had before.  The remainder ("keep") are the
 * domain elements for which the image element in res_k was better.
 * We also compute the lexicographical maximum of basic map i in todo^k.
 * res^i is the result of the operation + better + those elements in
 *              res^k that we should keep
 * todo^i is the remainder of the maximum operation on todo^k.
 */
static __isl_give isl_map *isl_map_partial_lexopt(
                __isl_take isl_map *map, __isl_take isl_set *dom,
                __isl_give isl_set **empty, int max)
{
        int i;
        struct isl_map *res;
        struct isl_set *todo;

        if (!map || !dom)
                goto error;

        if (isl_map_fast_is_empty(map)) {
                if (empty)
                        *empty = dom;
                else
                        isl_set_free(dom);
                return map;
        }

        res = basic_map_partial_lexopt(isl_basic_map_copy(map->p[0]),
                                        isl_set_copy(dom), &todo, max);

        for (i = 1; i < map->n; ++i) {
                struct isl_map *lt;
                struct isl_map *better;
                struct isl_set *keep;
                struct isl_map *res_i;
                struct isl_set *todo_i;
                struct isl_dim *dim = isl_map_get_dim(res);

                dim = isl_dim_range(dim);
                if (max)
                        lt = isl_map_lex_lt(dim);
                else
                        lt = isl_map_lex_gt(dim);
                lt = isl_map_apply_range(isl_map_copy(res), lt);
                lt = isl_map_intersect(lt,
                        isl_map_from_basic_map(isl_basic_map_copy(map->p[i])));
                better = isl_map_partial_lexopt(lt,
                        isl_map_domain(isl_map_copy(res)),
                        &keep, max);

                res_i = basic_map_partial_lexopt(isl_basic_map_copy(map->p[i]),
                                                todo, &todo_i, max);

                res = isl_map_intersect_domain(res, keep);
                res = isl_map_union_disjoint(res, res_i);
                res = isl_map_union_disjoint(res, better);
                todo = todo_i;
        }

        isl_set_free(dom);
        isl_map_free(map);

        if (empty)
                *empty = todo;
        else
                isl_set_free(todo);

        return res;
error:
        if (empty)
                *empty = NULL;
        isl_set_free(dom);
        isl_map_free(map);
        return NULL;
}

__isl_give isl_map *isl_map_partial_lexmax(
                __isl_take isl_map *map, __isl_take isl_set *dom,
                __isl_give isl_set **empty)
{
        return isl_map_partial_lexopt(map, dom, empty, 1);
}

__isl_give isl_map *isl_map_partial_lexmin(
                __isl_take isl_map *map, __isl_take isl_set *dom,
                __isl_give isl_set **empty)
{
        return isl_map_partial_lexopt(map, dom, empty, 0);
}

__isl_give isl_set *isl_set_partial_lexmin(
                __isl_take isl_set *set, __isl_take isl_set *dom,
                __isl_give isl_set **empty)
{
        return (struct isl_set *)
                isl_map_partial_lexmin((struct isl_map *)set,
                        dom, empty);
}

__isl_give isl_set *isl_set_partial_lexmax(
                __isl_take isl_set *set, __isl_take isl_set *dom,
                __isl_give isl_set **empty)
{
        return (struct isl_set *)
                isl_map_partial_lexmax((struct isl_map *)set,
                        dom, empty);
}

__isl_give isl_map *isl_basic_map_lexopt(__isl_take isl_basic_map *bmap, int max)
{
        struct isl_basic_set *dom = NULL;
        struct isl_dim *dom_dim;

        if (!bmap)
                goto error;
        dom_dim = isl_dim_domain(isl_dim_copy(bmap->dim));
        dom = isl_basic_set_universe(dom_dim);
        return isl_basic_map_partial_lexopt(bmap, dom, NULL, max);
error:
        isl_basic_map_free(bmap);
        return NULL;
}

__isl_give isl_map *isl_basic_map_lexmin(__isl_take isl_basic_map *bmap)
{
        return isl_basic_map_lexopt(bmap, 0);
}

__isl_give isl_map *isl_basic_map_lexmax(__isl_take isl_basic_map *bmap)
{
        return isl_basic_map_lexopt(bmap, 1);
}

__isl_give isl_set *isl_basic_set_lexmin(__isl_take isl_basic_set *bset)
{
        return (isl_set *)isl_basic_map_lexmin((isl_basic_map *)bset);
}

__isl_give isl_set *isl_basic_set_lexmax(__isl_take isl_basic_set *bset)
{
        return (isl_set *)isl_basic_map_lexmax((isl_basic_map *)bset);
}

__isl_give isl_map *isl_map_lexopt(__isl_take isl_map *map, int max)
{
        struct isl_set *dom = NULL;
        struct isl_dim *dom_dim;

        if (!map)
                goto error;
        dom_dim = isl_dim_domain(isl_dim_copy(map->dim));
        dom = isl_set_universe(dom_dim);
        return isl_map_partial_lexopt(map, dom, NULL, max);
error:
        isl_map_free(map);
        return NULL;
}

__isl_give isl_map *isl_map_lexmin(__isl_take isl_map *map)
{
        return isl_map_lexopt(map, 0);
}

__isl_give isl_map *isl_map_lexmax(__isl_take isl_map *map)
{
        return isl_map_lexopt(map, 1);
}

__isl_give isl_set *isl_set_lexmin(__isl_take isl_set *set)
{
        return (isl_set *)isl_map_lexmin((isl_map *)set);
}

__isl_give isl_set *isl_set_lexmax(__isl_take isl_set *set)
{
        return (isl_set *)isl_map_lexmax((isl_map *)set);
}

static struct isl_map *isl_map_reset_dim(struct isl_map *map,
        struct isl_dim *dim)
{
        int i;

        if (!map || !dim)
                goto error;

        for (i = 0; i < map->n; ++i) {
                isl_dim_free(map->p[i]->dim);
                map->p[i]->dim = isl_dim_copy(dim);
        }
        isl_dim_free(map->dim);
        map->dim = dim;

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

static struct isl_set *isl_set_reset_dim(struct isl_set *set,
        struct isl_dim *dim)
{
        return (struct isl_set *) isl_map_reset_dim((struct isl_map *)set, dim);
}

/* Apply a preimage specified by "mat" on the parameters of "bset".
 * bset is assumed to have only parameters and divs.
 */
static struct isl_basic_set *basic_set_parameter_preimage(
        struct isl_basic_set *bset, struct isl_mat *mat)
{
        unsigned nparam;

        if (!bset || !mat)
                goto error;

        bset->dim = isl_dim_cow(bset->dim);
        if (!bset->dim)
                goto error;

        nparam = isl_basic_set_dim(bset, isl_dim_param);

        isl_assert(bset->ctx, mat->n_row == 1 + nparam, goto error);

        bset->dim->nparam = 0;
        bset->dim->n_out = nparam;
        bset = isl_basic_set_preimage(bset, mat);
        if (bset) {
                bset->dim->nparam = bset->dim->n_out;
                bset->dim->n_out = 0;
        }
        return bset;
error:
        isl_mat_free(mat);
        isl_basic_set_free(bset);
        return NULL;
}

/* Apply a preimage specified by "mat" on the parameters of "set".
 * set is assumed to have only parameters and divs.
 */
static struct isl_set *set_parameter_preimage(
        struct isl_set *set, struct isl_mat *mat)
{
        struct isl_dim *dim = NULL;
        unsigned nparam;

        if (!set || !mat)
                goto error;

        dim = isl_dim_copy(set->dim);
        dim = isl_dim_cow(dim);
        if (!dim)
                goto error;

        nparam = isl_set_dim(set, isl_dim_param);

        isl_assert(set->ctx, mat->n_row == 1 + nparam, goto error);

        dim->nparam = 0;
        dim->n_out = nparam;
        isl_set_reset_dim(set, dim);
        set = isl_set_preimage(set, mat);
        if (!set)
                goto error2;
        dim = isl_dim_copy(set->dim);
        dim = isl_dim_cow(dim);
        if (!dim)
                goto error2;
        dim->nparam = dim->n_out;
        dim->n_out = 0;
        isl_set_reset_dim(set, dim);
        return set;
error:
        isl_dim_free(dim);
        isl_mat_free(mat);
error2:
        isl_set_free(set);
        return NULL;
}

/* Intersect the basic set "bset" with the affine space specified by the
 * equalities in "eq".
 */
static struct isl_basic_set *basic_set_append_equalities(
        struct isl_basic_set *bset, struct isl_mat *eq)
{
        int i, k;
        unsigned len;

        if (!bset || !eq)
                goto error;

        bset = isl_basic_set_extend_dim(bset, isl_dim_copy(bset->dim), 0,
                                        eq->n_row, 0);
        if (!bset)
                goto error;

        len = 1 + isl_dim_total(bset->dim) + bset->extra;
        for (i = 0; i < eq->n_row; ++i) {
                k = isl_basic_set_alloc_equality(bset);
                if (k < 0)
                        goto error;
                isl_seq_cpy(bset->eq[k], eq->row[i], eq->n_col);
                isl_seq_clr(bset->eq[k] + eq->n_col, len - eq->n_col);
        }
        isl_mat_free(eq);

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

/* Intersect the set "set" with the affine space specified by the
 * equalities in "eq".
 */
static struct isl_set *set_append_equalities(struct isl_set *set,
        struct isl_mat *eq)
{
        int i;

        if (!set || !eq)
                goto error;

        for (i = 0; i < set->n; ++i) {
                set->p[i] = basic_set_append_equalities(set->p[i],
                                        isl_mat_copy(eq));
                if (!set->p[i])
                        goto error;
        }
        isl_mat_free(eq);
        return set;
error:
        isl_mat_free(eq);
        isl_set_free(set);
        return NULL;
}

/* Project the given basic set onto its parameter domain, possibly introducing
 * new, explicit, existential variables in the constraints.
 * The input has parameters and (possibly implicit) existential variables.
 * The output has the same parameters, but only
 * explicit existentially quantified variables.
 *
 * The actual projection is performed by pip, but pip doesn't seem
 * to like equalities very much, so we first remove the equalities
 * among the parameters by performing a variable compression on
 * the parameters.  Afterward, an inverse transformation is performed
 * and the equalities among the parameters are inserted back in.
 */
static struct isl_set *parameter_compute_divs(struct isl_basic_set *bset)
{
        int i, j;
        struct isl_mat *eq;
        struct isl_mat *T, *T2;
        struct isl_set *set;
        unsigned nparam, n_div;

        bset = isl_basic_set_cow(bset);
        if (!bset)
                return NULL;

        if (bset->n_eq == 0)
                return isl_basic_set_lexmin(bset);

        isl_basic_set_gauss(bset, NULL);

        nparam = isl_basic_set_dim(bset, isl_dim_param);
        n_div = isl_basic_set_dim(bset, isl_dim_div);

        for (i = 0, j = n_div - 1; i < bset->n_eq && j >= 0; --j) {
                if (!isl_int_is_zero(bset->eq[i][1 + nparam + j]))
                        ++i;
        }
        if (i == bset->n_eq)
                return isl_basic_set_lexmin(bset);

        eq = isl_mat_sub_alloc(bset->ctx, bset->eq, i, bset->n_eq - i,
                0, 1 + nparam);
        eq = isl_mat_cow(eq);
        T = isl_mat_variable_compression(isl_mat_copy(eq), &T2);
        bset = basic_set_parameter_preimage(bset, T);

        set = isl_basic_set_lexmin(bset);
        set = set_parameter_preimage(set, T2);
        set = set_append_equalities(set, eq);
        return set;
}

/* Compute an explicit representation for all the existentially
 * quantified variables.
 * The input and output dimensions are first turned into parameters.
 * compute_divs then returns a map with the same parameters and
 * no input or output dimensions and the dimension specification
 * is reset to that of the input.
 */
static struct isl_map *compute_divs(struct isl_basic_map *bmap)
{
        struct isl_basic_set *bset;
        struct isl_set *set;
        struct isl_map *map;
        struct isl_dim *dim, *orig_dim = NULL;
        unsigned         nparam;
        unsigned         n_in;
        unsigned         n_out;

        bmap = isl_basic_map_cow(bmap);
        if (!bmap)
                return NULL;

        nparam = isl_basic_map_dim(bmap, isl_dim_param);
        n_in = isl_basic_map_dim(bmap, isl_dim_in);
        n_out = isl_basic_map_dim(bmap, isl_dim_out);
        dim = isl_dim_set_alloc(bmap->ctx, nparam + n_in + n_out, 0);
        if (!dim)
                goto error;

        orig_dim = bmap->dim;
        bmap->dim = dim;
        bset = (struct isl_basic_set *)bmap;

        set = parameter_compute_divs(bset);
        map = (struct isl_map *)set;
        map = isl_map_reset_dim(map, orig_dim);

        return map;
error:
        isl_basic_map_free(bmap);
        return NULL;
}

static int basic_map_divs_known(__isl_keep isl_basic_map *bmap)
{
        int i;
        unsigned off;

        if (!bmap)
                return -1;

        off = isl_dim_total(bmap->dim);
        for (i = 0; i < bmap->n_div; ++i) {
                if (isl_int_is_zero(bmap->div[i][0]))
                        return 0;
                isl_assert(bmap->ctx, isl_int_is_zero(bmap->div[i][1+1+off+i]),
                                return -1);
        }
        return 1;
}

static int map_divs_known(__isl_keep isl_map *map)
{
        int i;

        if (!map)
                return -1;

        for (i = 0; i < map->n; ++i) {
                int known = basic_map_divs_known(map->p[i]);
                if (known <= 0)
                        return known;
        }

        return 1;
}

/* If bmap contains any unknown divs, then compute explicit
 * expressions for them.  However, this computation may be
 * quite expensive, so first try to remove divs that aren't
 * strictly needed.
 */
struct isl_map *isl_basic_map_compute_divs(struct isl_basic_map *bmap)
{
        int i;
        int known;
        struct isl_map *map;

        known = basic_map_divs_known(bmap);
        if (known < 0)
                goto error;
        if (known)
                return isl_map_from_basic_map(bmap);

        bmap = isl_basic_map_drop_redundant_divs(bmap);

        known = basic_map_divs_known(bmap);
        if (known < 0)
                goto error;
        if (known)
                return isl_map_from_basic_map(bmap);

        map = compute_divs(bmap);
        return map;
error:
        isl_basic_map_free(bmap);
        return NULL;
}

struct isl_map *isl_map_compute_divs(struct isl_map *map)
{
        int i;
        int known;
        struct isl_map *res;

        if (!map)
                return NULL;
        if (map->n == 0)
                return map;

        known = map_divs_known(map);
        if (known < 0) {
                isl_map_free(map);
                return NULL;
        }
        if (known)
                return map;

        res = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[0]));
        for (i = 1 ; i < map->n; ++i) {
                struct isl_map *r2;
                r2 = isl_basic_map_compute_divs(isl_basic_map_copy(map->p[i]));
                if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
                        res = isl_map_union_disjoint(res, r2);
                else
                        res = isl_map_union(res, r2);
        }
        isl_map_free(map);

        return res;
}

struct isl_set *isl_basic_set_compute_divs(struct isl_basic_set *bset)
{
        return (struct isl_set *)
                isl_basic_map_compute_divs((struct isl_basic_map *)bset);
}

struct isl_set *isl_set_compute_divs(struct isl_set *set)
{
        return (struct isl_set *)
                isl_map_compute_divs((struct isl_map *)set);
}

struct isl_set *isl_map_domain(struct isl_map *map)
{
        int i;
        struct isl_set *set;

        if (!map)
                goto error;

        map = isl_map_cow(map);
        if (!map)
                return NULL;

        set = (struct isl_set *)map;
        set->dim = isl_dim_domain(set->dim);
        if (!set->dim)
                goto error;
        for (i = 0; i < map->n; ++i) {
                set->p[i] = isl_basic_map_domain(map->p[i]);
                if (!set->p[i])
                        goto error;
        }
        ISL_F_CLR(set, ISL_MAP_DISJOINT);
        ISL_F_CLR(set, ISL_SET_NORMALIZED);
        return set;
error:
        isl_map_free(map);
        return NULL;
}

struct isl_map *isl_map_union_disjoint(
                        struct isl_map *map1, struct isl_map *map2)
{
        int i;
        unsigned flags = 0;
        struct isl_map *map = NULL;

        if (!map1 || !map2)
                goto error;

        if (map1->n == 0) {
                isl_map_free(map1);
                return map2;
        }
        if (map2->n == 0) {
                isl_map_free(map2);
                return map1;
        }

        isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);

        if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
            ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
                ISL_FL_SET(flags, ISL_MAP_DISJOINT);

        map = isl_map_alloc_dim(isl_dim_copy(map1->dim),
                                map1->n + map2->n, flags);
        if (!map)
                goto error;
        for (i = 0; i < map1->n; ++i) {
                map = isl_map_add_basic_map(map,
                                  isl_basic_map_copy(map1->p[i]));
                if (!map)
                        goto error;
        }
        for (i = 0; i < map2->n; ++i) {
                map = isl_map_add_basic_map(map,
                                  isl_basic_map_copy(map2->p[i]));
                if (!map)
                        goto error;
        }
        isl_map_free(map1);
        isl_map_free(map2);
        return map;
error:
        isl_map_free(map);
        isl_map_free(map1);
        isl_map_free(map2);
        return NULL;
}

struct isl_map *isl_map_union(struct isl_map *map1, struct isl_map *map2)
{
        map1 = isl_map_union_disjoint(map1, map2);
        if (!map1)
                return NULL;
        if (map1->n > 1)
                ISL_F_CLR(map1, ISL_MAP_DISJOINT);
        return map1;
}

struct isl_set *isl_set_union_disjoint(
                        struct isl_set *set1, struct isl_set *set2)
{
        return (struct isl_set *)
                isl_map_union_disjoint(
                        (struct isl_map *)set1, (struct isl_map *)set2);
}

struct isl_set *isl_set_union(struct isl_set *set1, struct isl_set *set2)
{
        return (struct isl_set *)
                isl_map_union((struct isl_map *)set1, (struct isl_map *)set2);
}

struct isl_map *isl_map_intersect_range(
                struct isl_map *map, struct isl_set *set)
{
        unsigned flags = 0;
        struct isl_map *result;
        int i, j;

        if (!map || !set)
                goto error;

        if (ISL_F_ISSET(map, ISL_MAP_DISJOINT) &&
            ISL_F_ISSET(set, ISL_MAP_DISJOINT))
                ISL_FL_SET(flags, ISL_MAP_DISJOINT);

        result = isl_map_alloc_dim(isl_dim_copy(map->dim),
                                        map->n * set->n, flags);
        if (!result)
                goto error;
        for (i = 0; i < map->n; ++i)
                for (j = 0; j < set->n; ++j) {
                        result = isl_map_add_basic_map(result,
                            isl_basic_map_intersect_range(
                                isl_basic_map_copy(map->p[i]),
                                isl_basic_set_copy(set->p[j])));
                        if (!result)
                                goto error;
                }
        isl_map_free(map);
        isl_set_free(set);
        return result;
error:
        isl_map_free(map);
        isl_set_free(set);
        return NULL;
}

struct isl_map *isl_map_intersect_domain(
                struct isl_map *map, struct isl_set *set)
{
        return isl_map_reverse(
                isl_map_intersect_range(isl_map_reverse(map), set));
}

struct isl_map *isl_map_apply_domain(
                struct isl_map *map1, struct isl_map *map2)
{
        if (!map1 || !map2)
                goto error;
        map1 = isl_map_reverse(map1);
        map1 = isl_map_apply_range(map1, map2);
        return isl_map_reverse(map1);
error:
        isl_map_free(map1);
        isl_map_free(map2);
        return NULL;
}

struct isl_map *isl_map_apply_range(
                struct isl_map *map1, struct isl_map *map2)
{
        struct isl_dim *dim_result;
        struct isl_map *result;
        int i, j;

        if (!map1 || !map2)
                goto error;

        dim_result = isl_dim_join(isl_dim_copy(map1->dim),
                                  isl_dim_copy(map2->dim));

        result = isl_map_alloc_dim(dim_result, map1->n * map2->n, 0);
        if (!result)
                goto error;
        for (i = 0; i < map1->n; ++i)
                for (j = 0; j < map2->n; ++j) {
                        result = isl_map_add_basic_map(result,
                            isl_basic_map_apply_range(
                                isl_basic_map_copy(map1->p[i]),
                                isl_basic_map_copy(map2->p[j])));
                        if (!result)
                                goto error;
                }
        isl_map_free(map1);
        isl_map_free(map2);
        if (result && result->n <= 1)
                ISL_F_SET(result, ISL_MAP_DISJOINT);
        return result;
error:
        isl_map_free(map1);
        isl_map_free(map2);
        return NULL;
}

/*
 * returns range - domain
 */
struct isl_basic_set *isl_basic_map_deltas(struct isl_basic_map *bmap)
{
        struct isl_basic_set *bset;
        unsigned dim;
        unsigned nparam;
        int i;

        if (!bmap)
                goto error;
        dim = isl_basic_map_n_in(bmap);
        nparam = isl_basic_map_n_param(bmap);
        isl_assert(bmap->ctx, dim == isl_basic_map_n_out(bmap), goto error);
        bset = isl_basic_set_from_basic_map(bmap);
        bset = isl_basic_set_cow(bset);
        bset = isl_basic_set_extend(bset, nparam, 3*dim, 0, dim, 0);
        bset = isl_basic_set_swap_vars(bset, 2*dim);
        for (i = 0; i < dim; ++i) {
                int j = isl_basic_map_alloc_equality(
                                            (struct isl_basic_map *)bset);
                if (j < 0)
                        goto error;
                isl_seq_clr(bset->eq[j], 1 + isl_basic_set_total_dim(bset));
                isl_int_set_si(bset->eq[j][1+nparam+i], 1);
                isl_int_set_si(bset->eq[j][1+nparam+dim+i], 1);
                isl_int_set_si(bset->eq[j][1+nparam+2*dim+i], -1);
        }
        return isl_basic_set_project_out(bset, isl_dim_set, dim, 2*dim);
error:
        isl_basic_map_free(bmap);
        return NULL;
}

/*
 * returns range - domain
 */
struct isl_set *isl_map_deltas(struct isl_map *map)
{
        int i;
        struct isl_set *result;

        if (!map)
                return NULL;

        isl_assert(map->ctx, isl_map_n_in(map) == isl_map_n_out(map), goto error);
        result = isl_set_alloc(map->ctx, isl_map_n_param(map),
                                        isl_map_n_in(map), map->n, map->flags);
        if (!result)
                goto error;
        for (i = 0; i < map->n; ++i)
                result = isl_set_add_basic_set(result,
                          isl_basic_map_deltas(isl_basic_map_copy(map->p[i])));
        isl_map_free(map);
        return result;
error:
        isl_map_free(map);
        return NULL;
}

static struct isl_basic_map *basic_map_identity(struct isl_dim *dims)
{
        struct isl_basic_map *bmap;
        unsigned nparam;
        unsigned dim;
        int i;

        if (!dims)
                return NULL;

        nparam = dims->nparam;
        dim = dims->n_out;
        bmap = isl_basic_map_alloc_dim(dims, 0, dim, 0);
        if (!bmap)
                goto error;

        for (i = 0; i < dim; ++i) {
                int j = isl_basic_map_alloc_equality(bmap);
                if (j < 0)
                        goto error;
                isl_seq_clr(bmap->eq[j], 1 + isl_basic_map_total_dim(bmap));
                isl_int_set_si(bmap->eq[j][1+nparam+i], 1);
                isl_int_set_si(bmap->eq[j][1+nparam+dim+i], -1);
        }
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_map_free(bmap);
        return NULL;
}

struct isl_basic_map *isl_basic_map_identity(struct isl_dim *set_dim)
{
        struct isl_dim *dim = isl_dim_map(set_dim);
        if (!dim)
                return NULL;
        return basic_map_identity(dim);
}

struct isl_basic_map *isl_basic_map_identity_like(struct isl_basic_map *model)
{
        if (!model || !model->dim)
                return NULL;
        isl_assert(model->ctx,
                        model->dim->n_in == model->dim->n_out, return NULL);
        return basic_map_identity(isl_dim_copy(model->dim));
}

static struct isl_map *map_identity(struct isl_dim *dim)
{
        struct isl_map *map = isl_map_alloc_dim(dim, 1, ISL_MAP_DISJOINT);
        return isl_map_add_basic_map(map, basic_map_identity(isl_dim_copy(dim)));
}

struct isl_map *isl_map_identity(struct isl_dim *set_dim)
{
        struct isl_dim *dim = isl_dim_map(set_dim);
        if (!dim)
                return NULL;
        return map_identity(dim);
}

struct isl_map *isl_map_identity_like(struct isl_map *model)
{
        if (!model || !model->dim)
                return NULL;
        isl_assert(model->ctx,
                        model->dim->n_in == model->dim->n_out, return NULL);
        return map_identity(isl_dim_copy(model->dim));
}

struct isl_map *isl_map_identity_like_basic_map(struct isl_basic_map *model)
{
        if (!model || !model->dim)
                return NULL;
        isl_assert(model->ctx,
                        model->dim->n_in == model->dim->n_out, return NULL);
        return map_identity(isl_dim_copy(model->dim));
}

/* Construct a basic set with all set dimensions having only non-negative
 * values.
 */
struct isl_basic_set *isl_basic_set_positive_orthant(struct isl_dim *dims)
{
        int i;
        unsigned nparam;
        unsigned dim;
        struct isl_basic_set *bset;

        if (!dims)
                return NULL;
        nparam = dims->nparam;
        dim = dims->n_out;
        bset = isl_basic_set_alloc_dim(dims, 0, 0, dim);
        if (!bset)
                return NULL;
        for (i = 0; i < dim; ++i) {
                int k = isl_basic_set_alloc_inequality(bset);
                if (k < 0)
                        goto error;
                isl_seq_clr(bset->ineq[k], 1 + isl_basic_set_total_dim(bset));
                isl_int_set_si(bset->ineq[k][1 + nparam + i], 1);
        }
        return bset;
error:
        isl_basic_set_free(bset);
        return NULL;
}

int isl_set_is_equal(struct isl_set *set1, struct isl_set *set2)
{
        return isl_map_is_equal((struct isl_map *)set1, (struct isl_map *)set2);
}

int isl_basic_map_is_subset(
                struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
{
        int is_subset;
        struct isl_map *map1;
        struct isl_map *map2;

        if (!bmap1 || !bmap2)
                return -1;

        map1 = isl_map_from_basic_map(isl_basic_map_copy(bmap1));
        map2 = isl_map_from_basic_map(isl_basic_map_copy(bmap2));

        is_subset = isl_map_is_subset(map1, map2);

        isl_map_free(map1);
        isl_map_free(map2);

        return is_subset;
}

int isl_basic_map_is_equal(
                struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
{
        int is_subset;

        if (!bmap1 || !bmap2)
                return -1;
        is_subset = isl_basic_map_is_subset(bmap1, bmap2);
        if (is_subset != 1)
                return is_subset;
        is_subset = isl_basic_map_is_subset(bmap2, bmap1);
        return is_subset;
}

int isl_basic_set_is_equal(
                struct isl_basic_set *bset1, struct isl_basic_set *bset2)
{
        return isl_basic_map_is_equal(
                (struct isl_basic_map *)bset1, (struct isl_basic_map *)bset2);
}

int isl_map_is_empty(struct isl_map *map)
{
        int i;
        int is_empty;

        if (!map)
                return -1;
        for (i = 0; i < map->n; ++i) {
                is_empty = isl_basic_map_is_empty(map->p[i]);
                if (is_empty < 0)
                        return -1;
                if (!is_empty)
                        return 0;
        }
        return 1;
}

int isl_map_fast_is_empty(struct isl_map *map)
{
        return map->n == 0;
}

int isl_set_fast_is_empty(struct isl_set *set)
{
        return set->n == 0;
}

int isl_set_is_empty(struct isl_set *set)
{
        return isl_map_is_empty((struct isl_map *)set);
}

int isl_map_is_equal(struct isl_map *map1, struct isl_map *map2)
{
        int is_subset;

        if (!map1 || !map2)
                return -1;
        is_subset = isl_map_is_subset(map1, map2);
        if (is_subset != 1)
                return is_subset;
        is_subset = isl_map_is_subset(map2, map1);
        return is_subset;
}

int isl_basic_map_is_strict_subset(
                struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
{
        int is_subset;

        if (!bmap1 || !bmap2)
                return -1;
        is_subset = isl_basic_map_is_subset(bmap1, bmap2);
        if (is_subset != 1)
                return is_subset;
        is_subset = isl_basic_map_is_subset(bmap2, bmap1);
        if (is_subset == -1)
                return is_subset;
        return !is_subset;
}

int isl_map_is_strict_subset(struct isl_map *map1, struct isl_map *map2)
{
        int is_subset;

        if (!map1 || !map2)
                return -1;
        is_subset = isl_map_is_subset(map1, map2);
        if (is_subset != 1)
                return is_subset;
        is_subset = isl_map_is_subset(map2, map1);
        if (is_subset == -1)
                return is_subset;
        return !is_subset;
}

int isl_set_is_strict_subset(__isl_keep isl_set *set1, __isl_keep isl_set *set2)
{
        return isl_map_is_strict_subset((isl_map *)set1, (isl_map *)set2);
}

int isl_basic_map_is_universe(struct isl_basic_map *bmap)
{
        if (!bmap)
                return -1;
        return bmap->n_eq == 0 && bmap->n_ineq == 0;
}

int isl_basic_set_is_universe(struct isl_basic_set *bset)
{
        if (!bset)
                return -1;
        return bset->n_eq == 0 && bset->n_ineq == 0;
}

int isl_map_fast_is_universe(__isl_keep isl_map *map)
{
        if (!map)
                return -1;

        return map->n == 1 && isl_basic_map_is_universe(map->p[0]);
}

int isl_basic_map_is_empty(struct isl_basic_map *bmap)
{
        struct isl_basic_set *bset = NULL;
        struct isl_vec *sample = NULL;
        int empty;
        unsigned total;

        if (!bmap)
                return -1;

        if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
                return 1;

        if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
                struct isl_basic_map *copy = isl_basic_map_copy(bmap);
                copy = isl_basic_map_convex_hull(copy);
                empty = ISL_F_ISSET(copy, ISL_BASIC_MAP_EMPTY);
                isl_basic_map_free(copy);
                return empty;
        }

        total = 1 + isl_basic_map_total_dim(bmap);
        if (bmap->sample && bmap->sample->size == total) {
                int contains = isl_basic_map_contains(bmap, bmap->sample);
                if (contains < 0)
                        return -1;
                if (contains)
                        return 0;
        }
        isl_vec_free(bmap->sample);
        bmap->sample = NULL;
        bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
        if (!bset)
                return -1;
        sample = isl_basic_set_sample_vec(bset);
        if (!sample)
                return -1;
        empty = sample->size == 0;
        isl_vec_free(bmap->sample);
        bmap->sample = sample;
        if (empty)
                ISL_F_SET(bmap, ISL_BASIC_MAP_EMPTY);

        return empty;
}

int isl_basic_map_fast_is_empty(struct isl_basic_map *bmap)
{
        if (!bmap)
                return -1;
        return ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY);
}

int isl_basic_set_fast_is_empty(struct isl_basic_set *bset)
{
        if (!bset)
                return -1;
        return ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY);
}

int isl_basic_set_is_empty(struct isl_basic_set *bset)
{
        return isl_basic_map_is_empty((struct isl_basic_map *)bset);
}

struct isl_map *isl_basic_map_union(
        struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
{
        struct isl_map *map;
        if (!bmap1 || !bmap2)
                return NULL;

        isl_assert(bmap1->ctx, isl_dim_equal(bmap1->dim, bmap2->dim), goto error);

        map = isl_map_alloc_dim(isl_dim_copy(bmap1->dim), 2, 0);
        if (!map)
                goto error;
        map = isl_map_add_basic_map(map, bmap1);
        map = isl_map_add_basic_map(map, bmap2);
        return map;
error:
        isl_basic_map_free(bmap1);
        isl_basic_map_free(bmap2);
        return NULL;
}

struct isl_set *isl_basic_set_union(
                struct isl_basic_set *bset1, struct isl_basic_set *bset2)
{
        return (struct isl_set *)isl_basic_map_union(
                                            (struct isl_basic_map *)bset1,
                                            (struct isl_basic_map *)bset2);
}

/* Order divs such that any div only depends on previous divs */
struct isl_basic_map *isl_basic_map_order_divs(struct isl_basic_map *bmap)
{
        int i;
        unsigned off = isl_dim_total(bmap->dim);

        for (i = 0; i < bmap->n_div; ++i) {
                int pos;
                if (isl_int_is_zero(bmap->div[i][0]))
                        continue;
                pos = isl_seq_first_non_zero(bmap->div[i]+1+1+off+i,
                                                            bmap->n_div-i);
                if (pos == -1)
                        continue;
                isl_basic_map_swap_div(bmap, i, i + pos);
                --i;
        }
        return bmap;
}

struct isl_basic_set *isl_basic_set_order_divs(struct isl_basic_set *bset)
{
        return (struct isl_basic_set *)
                isl_basic_map_order_divs((struct isl_basic_map *)bset);
}

/* Look for a div in dst that corresponds to the div "div" in src.
 * The divs before "div" in src and dst are assumed to be the same.
 * 
 * Returns -1 if no corresponding div was found and the position
 * of the corresponding div in dst otherwise.
 */
static int find_div(struct isl_basic_map *dst,
                        struct isl_basic_map *src, unsigned div)
{
        int i;

        unsigned total = isl_dim_total(src->dim);

        isl_assert(dst->ctx, div <= dst->n_div, return -1);
        for (i = div; i < dst->n_div; ++i)
                if (isl_seq_eq(dst->div[i], src->div[div], 1+1+total+div) &&
                    isl_seq_first_non_zero(dst->div[i]+1+1+total+div,
                                                dst->n_div - div) == -1)
                        return i;
        return -1;
}

struct isl_basic_map *isl_basic_map_align_divs(
                struct isl_basic_map *dst, struct isl_basic_map *src)
{
        int i;
        unsigned total = isl_dim_total(src->dim);

        if (!dst || !src)
                goto error;

        if (src->n_div == 0)
                return dst;

        for (i = 0; i < src->n_div; ++i)
                isl_assert(src->ctx, !isl_int_is_zero(src->div[i][0]), goto error);

        src = isl_basic_map_order_divs(src);
        dst = isl_basic_map_cow(dst);
        dst = isl_basic_map_extend_dim(dst, isl_dim_copy(dst->dim),
                        src->n_div, 0, 2 * src->n_div);
        if (!dst)
                return NULL;
        for (i = 0; i < src->n_div; ++i) {
                int j = find_div(dst, src, i);
                if (j < 0) {
                        j = isl_basic_map_alloc_div(dst);
                        if (j < 0)
                                goto error;
                        isl_seq_cpy(dst->div[j], src->div[i], 1+1+total+i);
                        isl_seq_clr(dst->div[j]+1+1+total+i, dst->n_div - i);
                        if (isl_basic_map_add_div_constraints(dst, j) < 0)
                                goto error;
                }
                if (j != i)
                        isl_basic_map_swap_div(dst, i, j);
        }
        return dst;
error:
        isl_basic_map_free(dst);
        return NULL;
}

struct isl_basic_set *isl_basic_set_align_divs(
                struct isl_basic_set *dst, struct isl_basic_set *src)
{
        return (struct isl_basic_set *)isl_basic_map_align_divs(
                (struct isl_basic_map *)dst, (struct isl_basic_map *)src);
}

struct isl_map *isl_map_align_divs(struct isl_map *map)
{
        int i;

        if (!map)
                return NULL;
        if (map->n == 0)
                return map;
        map = isl_map_compute_divs(map);
        map = isl_map_cow(map);
        if (!map)
                return NULL;

        for (i = 1; i < map->n; ++i)
                map->p[0] = isl_basic_map_align_divs(map->p[0], map->p[i]);
        for (i = 1; i < map->n; ++i)
                map->p[i] = isl_basic_map_align_divs(map->p[i], map->p[0]);

        ISL_F_CLR(map, ISL_MAP_NORMALIZED);
        return map;
}

struct isl_set *isl_set_align_divs(struct isl_set *set)
{
        return (struct isl_set *)isl_map_align_divs((struct isl_map *)set);
}

struct isl_set *isl_set_apply(struct isl_set *set, struct isl_map *map)
{
        if (!set || !map)
                goto error;
        isl_assert(set->ctx, isl_map_compatible_domain(map, set), goto error);
        map = isl_map_intersect_domain(map, set);
        set = isl_map_range(map);
        return set;
error:
        isl_set_free(set);
        isl_map_free(map);
        return NULL;
}

/* There is no need to cow as removing empty parts doesn't change
 * the meaning of the set.
 */
struct isl_map *isl_map_remove_empty_parts(struct isl_map *map)
{
        int i;

        if (!map)
                return NULL;

        for (i = map->n-1; i >= 0; --i) {
                if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_EMPTY))
                        continue;
                isl_basic_map_free(map->p[i]);
                if (i != map->n-1) {
                        ISL_F_CLR(map, ISL_MAP_NORMALIZED);
                        map->p[i] = map->p[map->n-1];
                }
                map->n--;
        }

        return map;
}

struct isl_set *isl_set_remove_empty_parts(struct isl_set *set)
{
        return (struct isl_set *)
                isl_map_remove_empty_parts((struct isl_map *)set);
}

struct isl_basic_map *isl_map_copy_basic_map(struct isl_map *map)
{
        struct isl_basic_map *bmap;
        if (!map || map->n == 0)
                return NULL;
        bmap = map->p[map->n-1];
        isl_assert(map->ctx, ISL_F_ISSET(bmap, ISL_BASIC_SET_FINAL), return NULL);
        return isl_basic_map_copy(bmap);
}

struct isl_basic_set *isl_set_copy_basic_set(struct isl_set *set)
{
        return (struct isl_basic_set *)
                isl_map_copy_basic_map((struct isl_map *)set);
}

__isl_give isl_map *isl_map_drop_basic_map(__isl_take isl_map *map,
                                                __isl_keep isl_basic_map *bmap)
{
        int i;

        if (!map || !bmap)
                goto error;
        for (i = map->n-1; i >= 0; --i) {
                if (map->p[i] != bmap)
                        continue;
                map = isl_map_cow(map);
                if (!map)
                        goto error;
                isl_basic_map_free(map->p[i]);
                if (i != map->n-1) {
                        ISL_F_CLR(map, ISL_SET_NORMALIZED);
                        map->p[i] = map->p[map->n-1];
                }
                map->n--;
                return map;
        }
        return map;
error:
        isl_map_free(map);
        return NULL;
}

struct isl_set *isl_set_drop_basic_set(struct isl_set *set,
                                                struct isl_basic_set *bset)
{
        return (struct isl_set *)isl_map_drop_basic_map((struct isl_map *)set,
                                                (struct isl_basic_map *)bset);
}

/* Given two basic sets bset1 and bset2, compute the maximal difference
 * between the values of dimension pos in bset1 and those in bset2
 * for any common value of the parameters and dimensions preceding pos.
 */
static enum isl_lp_result basic_set_maximal_difference_at(
        __isl_keep isl_basic_set *bset1, __isl_keep isl_basic_set *bset2,
        int pos, isl_int *opt)
{
        struct isl_dim *dims;
        struct isl_basic_map *bmap1 = NULL;
        struct isl_basic_map *bmap2 = NULL;
        struct isl_ctx *ctx;
        struct isl_vec *obj;
        unsigned total;
        unsigned nparam;
        unsigned dim1, dim2;
        enum isl_lp_result res;

        if (!bset1 || !bset2)
                return isl_lp_error;

        nparam = isl_basic_set_n_param(bset1);
        dim1 = isl_basic_set_n_dim(bset1);
        dim2 = isl_basic_set_n_dim(bset2);
        dims = isl_dim_alloc(bset1->ctx, nparam, pos, dim1 - pos);
        bmap1 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset1), dims);
        dims = isl_dim_alloc(bset2->ctx, nparam, pos, dim2 - pos);
        bmap2 = isl_basic_map_from_basic_set(isl_basic_set_copy(bset2), dims);
        if (!bmap1 || !bmap2)
                goto error;
        bmap1 = isl_basic_map_cow(bmap1);
        bmap1 = isl_basic_map_extend(bmap1, nparam,
                        pos, (dim1 - pos) + (dim2 - pos),
                        bmap2->n_div, bmap2->n_eq, bmap2->n_ineq);
        bmap1 = add_constraints(bmap1, bmap2, 0, dim1 - pos);
        if (!bmap1)
                goto error;
        total = isl_basic_map_total_dim(bmap1);
        ctx = bmap1->ctx;
        obj = isl_vec_alloc(ctx, 1 + total);
        isl_seq_clr(obj->block.data, 1 + total);
        isl_int_set_si(obj->block.data[1+nparam+pos], 1);
        isl_int_set_si(obj->block.data[1+nparam+pos+(dim1-pos)], -1);
        if (!obj)
                goto error;
        res = isl_basic_map_solve_lp(bmap1, 1, obj->block.data, ctx->one,
                                        opt, NULL, NULL);
        isl_basic_map_free(bmap1);
        isl_vec_free(obj);
        return res;
error:
        isl_basic_map_free(bmap1);
        isl_basic_map_free(bmap2);
        return isl_lp_error;
}

/* Given two _disjoint_ basic sets bset1 and bset2, check whether
 * for any common value of the parameters and dimensions preceding pos
 * in both basic sets, the values of dimension pos in bset1 are
 * smaller or larger than those in bset2.
 *
 * Returns
 *       1 if bset1 follows bset2
 *      -1 if bset1 precedes bset2
 *       0 if bset1 and bset2 are incomparable
 *      -2 if some error occurred.
 */
int isl_basic_set_compare_at(struct isl_basic_set *bset1,
        struct isl_basic_set *bset2, int pos)
{
        isl_int opt;
        enum isl_lp_result res;
        int cmp;

        isl_int_init(opt);

        res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);

        if (res == isl_lp_empty)
                cmp = 0;
        else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
                  res == isl_lp_unbounded)
                cmp = 1;
        else if (res == isl_lp_ok && isl_int_is_neg(opt))
                cmp = -1;
        else
                cmp = -2;

        isl_int_clear(opt);
        return cmp;
}

/* Given two basic sets bset1 and bset2, check whether
 * for any common value of the parameters and dimensions preceding pos
 * there is a value of dimension pos in bset1 that is larger
 * than a value of the same dimension in bset2.
 *
 * Return
 *       1 if there exists such a pair
 *       0 if there is no such pair, but there is a pair of equal values
 *      -1 otherwise
 *      -2 if some error occurred.
 */
int isl_basic_set_follows_at(__isl_keep isl_basic_set *bset1,
        __isl_keep isl_basic_set *bset2, int pos)
{
        isl_int opt;
        enum isl_lp_result res;
        int cmp;

        isl_int_init(opt);

        res = basic_set_maximal_difference_at(bset1, bset2, pos, &opt);

        if (res == isl_lp_empty)
                cmp = -1;
        else if ((res == isl_lp_ok && isl_int_is_pos(opt)) ||
                  res == isl_lp_unbounded)
                cmp = 1;
        else if (res == isl_lp_ok && isl_int_is_neg(opt))
                cmp = -1;
        else if (res == isl_lp_ok)
                cmp = 0;
        else
                cmp = -2;

        isl_int_clear(opt);
        return cmp;
}

/* Given two sets set1 and set2, check whether
 * for any common value of the parameters and dimensions preceding pos
 * there is a value of dimension pos in set1 that is larger
 * than a value of the same dimension in set2.
 *
 * Return
 *       1 if there exists such a pair
 *       0 if there is no such pair, but there is a pair of equal values
 *      -1 otherwise
 *      -2 if some error occurred.
 */
int isl_set_follows_at(__isl_keep isl_set *set1,
        __isl_keep isl_set *set2, int pos)
{
        int i, j;
        int follows = -1;

        if (!set1 || !set2)
                return -2;

        for (i = 0; i < set1->n; ++i)
                for (j = 0; j < set2->n; ++j) {
                        int f;
                        f = isl_basic_set_follows_at(set1->p[i], set2->p[j], pos);
                        if (f == 1 || f == -2)
                                return f;
                        if (f > follows)
                                follows = f;
                }

        return follows;
}

static int isl_basic_map_fast_has_fixed_var(struct isl_basic_map *bmap,
        unsigned pos, isl_int *val)
{
        int i;
        int d;
        unsigned total;

        if (!bmap)
                return -1;
        total = isl_basic_map_total_dim(bmap);
        for (i = 0, d = total-1; i < bmap->n_eq && d+1 > pos; ++i) {
                for (; d+1 > pos; --d)
                        if (!isl_int_is_zero(bmap->eq[i][1+d]))
                                break;
                if (d != pos)
                        continue;
                if (isl_seq_first_non_zero(bmap->eq[i]+1, d) != -1)
                        return 0;
                if (isl_seq_first_non_zero(bmap->eq[i]+1+d+1, total-d-1) != -1)
                        return 0;
                if (!isl_int_is_one(bmap->eq[i][1+d]))
                        return 0;
                if (val)
                        isl_int_neg(*val, bmap->eq[i][0]);
                return 1;
        }
        return 0;
}

static int isl_map_fast_has_fixed_var(struct isl_map *map,
        unsigned pos, isl_int *val)
{
        int i;
        isl_int v;
        isl_int tmp;
        int fixed;

        if (!map)
                return -1;
        if (map->n == 0)
                return 0;
        if (map->n == 1)
                return isl_basic_map_fast_has_fixed_var(map->p[0], pos, val); 
        isl_int_init(v);
        isl_int_init(tmp);
        fixed = isl_basic_map_fast_has_fixed_var(map->p[0], pos, &v); 
        for (i = 1; fixed == 1 && i < map->n; ++i) {
                fixed = isl_basic_map_fast_has_fixed_var(map->p[i], pos, &tmp); 
                if (fixed == 1 && isl_int_ne(tmp, v))
                        fixed = 0;
        }
        if (val)
                isl_int_set(*val, v);
        isl_int_clear(tmp);
        isl_int_clear(v);
        return fixed;
}

static int isl_basic_set_fast_has_fixed_var(struct isl_basic_set *bset,
        unsigned pos, isl_int *val)
{
        return isl_basic_map_fast_has_fixed_var((struct isl_basic_map *)bset,
                                                pos, val);
}

static int isl_set_fast_has_fixed_var(struct isl_set *set, unsigned pos,
        isl_int *val)
{
        return isl_map_fast_has_fixed_var((struct isl_map *)set, pos, val);
}

int isl_basic_map_fast_is_fixed(struct isl_basic_map *bmap,
        enum isl_dim_type type, unsigned pos, isl_int *val)
{
        if (pos >= isl_basic_map_dim(bmap, type))
                return -1;
        return isl_basic_map_fast_has_fixed_var(bmap,
                isl_basic_map_offset(bmap, type) - 1 + pos, val);
}

int isl_map_fast_is_fixed(struct isl_map *map,
        enum isl_dim_type type, unsigned pos, isl_int *val)
{
        if (pos >= isl_map_dim(map, type))
                return -1;
        return isl_map_fast_has_fixed_var(map,
                map_offset(map, type) - 1 + pos, val);
}

/* Check if dimension dim has fixed value and if so and if val is not NULL,
 * then return this fixed value in *val.
 */
int isl_basic_set_fast_dim_is_fixed(struct isl_basic_set *bset, unsigned dim,
        isl_int *val)
{
        return isl_basic_set_fast_has_fixed_var(bset,
                                        isl_basic_set_n_param(bset) + dim, val);
}

/* Check if dimension dim has fixed value and if so and if val is not NULL,
 * then return this fixed value in *val.
 */
int isl_set_fast_dim_is_fixed(struct isl_set *set, unsigned dim, isl_int *val)
{
        return isl_set_fast_has_fixed_var(set, isl_set_n_param(set) + dim, val);
}

/* Check if input variable in has fixed value and if so and if val is not NULL,
 * then return this fixed value in *val.
 */
int isl_map_fast_input_is_fixed(struct isl_map *map, unsigned in, isl_int *val)
{
        return isl_map_fast_has_fixed_var(map, isl_map_n_param(map) + in, val);
}

/* Check if dimension dim has an (obvious) fixed lower bound and if so
 * and if val is not NULL, then return this lower bound in *val.
 */
int isl_basic_set_fast_dim_has_fixed_lower_bound(struct isl_basic_set *bset,
        unsigned dim, isl_int *val)
{
        int i, i_eq = -1, i_ineq = -1;
        isl_int *c;
        unsigned total;
        unsigned nparam;

        if (!bset)
                return -1;
        total = isl_basic_set_total_dim(bset);
        nparam = isl_basic_set_n_param(bset);
        for (i = 0; i < bset->n_eq; ++i) {
                if (isl_int_is_zero(bset->eq[i][1+nparam+dim]))
                        continue;
                if (i_eq != -1)
                        return 0;
                i_eq = i;
        }
        for (i = 0; i < bset->n_ineq; ++i) {
                if (!isl_int_is_pos(bset->ineq[i][1+nparam+dim]))
                        continue;
                if (i_eq != -1 || i_ineq != -1)
                        return 0;
                i_ineq = i;
        }
        if (i_eq == -1 && i_ineq == -1)
                return 0;
        c = i_eq != -1 ? bset->eq[i_eq] : bset->ineq[i_ineq];
        /* The coefficient should always be one due to normalization. */
        if (!isl_int_is_one(c[1+nparam+dim]))
                return 0;
        if (isl_seq_first_non_zero(c+1, nparam+dim) != -1)
                return 0;
        if (isl_seq_first_non_zero(c+1+nparam+dim+1,
                                        total - nparam - dim - 1) != -1)
                return 0;
        if (val)
                isl_int_neg(*val, c[0]);
        return 1;
}

int isl_set_fast_dim_has_fixed_lower_bound(struct isl_set *set,
        unsigned dim, isl_int *val)
{
        int i;
        isl_int v;
        isl_int tmp;
        int fixed;

        if (!set)
                return -1;
        if (set->n == 0)
                return 0;
        if (set->n == 1)
                return isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
                                                                dim, val);
        isl_int_init(v);
        isl_int_init(tmp);
        fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[0],
                                                                dim, &v);
        for (i = 1; fixed == 1 && i < set->n; ++i) {
                fixed = isl_basic_set_fast_dim_has_fixed_lower_bound(set->p[i],
                                                                dim, &tmp);
                if (fixed == 1 && isl_int_ne(tmp, v))
                        fixed = 0;
        }
        if (val)
                isl_int_set(*val, v);
        isl_int_clear(tmp);
        isl_int_clear(v);
        return fixed;
}

struct constraint {
        unsigned        size;
        isl_int         *c;
};

static int qsort_constraint_cmp(const void *p1, const void *p2)
{
        const struct constraint *c1 = (const struct constraint *)p1;
        const struct constraint *c2 = (const struct constraint *)p2;
        unsigned size = isl_min(c1->size, c2->size);
        return isl_seq_cmp(c1->c, c2->c, size);
}

static struct isl_basic_map *isl_basic_map_sort_constraints(
        struct isl_basic_map *bmap)
{
        int i;
        struct constraint *c;
        unsigned total;

        if (!bmap)
                return NULL;
        total = isl_basic_map_total_dim(bmap);
        c = isl_alloc_array(bmap->ctx, struct constraint, bmap->n_ineq);
        if (!c)
                goto error;
        for (i = 0; i < bmap->n_ineq; ++i) {
                c[i].size = total;
                c[i].c = bmap->ineq[i];
        }
        qsort(c, bmap->n_ineq, sizeof(struct constraint), qsort_constraint_cmp);
        for (i = 0; i < bmap->n_ineq; ++i)
                bmap->ineq[i] = c[i].c;
        free(c);
        return bmap;
error:
        isl_basic_map_free(bmap);
        return NULL;
}

struct isl_basic_map *isl_basic_map_normalize(struct isl_basic_map *bmap)
{
        if (!bmap)
                return NULL;
        if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NORMALIZED))
                return bmap;
        bmap = isl_basic_map_convex_hull(bmap);
        bmap = isl_basic_map_sort_constraints(bmap);
        ISL_F_SET(bmap, ISL_BASIC_MAP_NORMALIZED);
        return bmap;
}

struct isl_basic_set *isl_basic_set_normalize(struct isl_basic_set *bset)
{
        return (struct isl_basic_set *)isl_basic_map_normalize(
                                                (struct isl_basic_map *)bset);
}

static int isl_basic_map_fast_cmp(const struct isl_basic_map *bmap1,
        const struct isl_basic_map *bmap2)
{
        int i, cmp;
        unsigned total;

        if (bmap1 == bmap2)
                return 0;
        if (isl_basic_map_n_param(bmap1) != isl_basic_map_n_param(bmap2))
                return isl_basic_map_n_param(bmap1) - isl_basic_map_n_param(bmap2);
        if (isl_basic_map_n_in(bmap1) != isl_basic_map_n_in(bmap2))
                return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
        if (isl_basic_map_n_out(bmap1) != isl_basic_map_n_out(bmap2))
                return isl_basic_map_n_out(bmap1) - isl_basic_map_n_out(bmap2);
        if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY) &&
            ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
                return 0;
        if (ISL_F_ISSET(bmap1, ISL_BASIC_MAP_EMPTY))
                return 1;
        if (ISL_F_ISSET(bmap2, ISL_BASIC_MAP_EMPTY))
                return -1;
        if (bmap1->n_eq != bmap2->n_eq)
                return bmap1->n_eq - bmap2->n_eq;
        if (bmap1->n_ineq != bmap2->n_ineq)
                return bmap1->n_ineq - bmap2->n_ineq;
        if (bmap1->n_div != bmap2->n_div)
                return bmap1->n_div - bmap2->n_div;
        total = isl_basic_map_total_dim(bmap1);
        for (i = 0; i < bmap1->n_eq; ++i) {
                cmp = isl_seq_cmp(bmap1->eq[i], bmap2->eq[i], 1+total);
                if (cmp)
                        return cmp;
        }
        for (i = 0; i < bmap1->n_ineq; ++i) {
                cmp = isl_seq_cmp(bmap1->ineq[i], bmap2->ineq[i], 1+total);
                if (cmp)
                        return cmp;
        }
        for (i = 0; i < bmap1->n_div; ++i) {
                cmp = isl_seq_cmp(bmap1->div[i], bmap2->div[i], 1+1+total);
                if (cmp)
                        return cmp;
        }
        return 0;
}

static int isl_basic_map_fast_is_equal(struct isl_basic_map *bmap1,
        struct isl_basic_map *bmap2)
{
        return isl_basic_map_fast_cmp(bmap1, bmap2) == 0;
}

static int qsort_bmap_cmp(const void *p1, const void *p2)
{
        const struct isl_basic_map *bmap1 = *(const struct isl_basic_map **)p1;
        const struct isl_basic_map *bmap2 = *(const struct isl_basic_map **)p2;

        return isl_basic_map_fast_cmp(bmap1, bmap2);
}

/* We normalize in place, but if anything goes wrong we need
 * to return NULL, so we need to make sure we don't change the
 * meaning of any possible other copies of map.
 */
struct isl_map *isl_map_normalize(struct isl_map *map)
{
        int i, j;
        struct isl_basic_map *bmap;

        if (!map)
                return NULL;
        if (ISL_F_ISSET(map, ISL_MAP_NORMALIZED))
                return map;
        for (i = 0; i < map->n; ++i) {
                bmap = isl_basic_map_normalize(isl_basic_map_copy(map->p[i]));
                if (!bmap)
                        goto error;
                isl_basic_map_free(map->p[i]);
                map->p[i] = bmap;
        }
        qsort(map->p, map->n, sizeof(struct isl_basic_map *), qsort_bmap_cmp);
        ISL_F_SET(map, ISL_MAP_NORMALIZED);
        map = isl_map_remove_empty_parts(map);
        if (!map)
                return NULL;
        for (i = map->n - 1; i >= 1; --i) {
                if (!isl_basic_map_fast_is_equal(map->p[i-1], map->p[i]))
                        continue;
                isl_basic_map_free(map->p[i-1]);
                for (j = i; j < map->n; ++j)
                        map->p[j-1] = map->p[j];
                map->n--;
        }
        return map;
error:
        isl_map_free(map);
        return NULL;

}

struct isl_set *isl_set_normalize(struct isl_set *set)
{
        return (struct isl_set *)isl_map_normalize((struct isl_map *)set);
}

int isl_map_fast_is_equal(struct isl_map *map1, struct isl_map *map2)
{
        int i;
        int equal;

        if (!map1 || !map2)
                return -1;

        if (map1 == map2)
                return 1;
        if (!isl_dim_equal(map1->dim, map2->dim))
                return 0;

        map1 = isl_map_copy(map1);
        map2 = isl_map_copy(map2);
        map1 = isl_map_normalize(map1);
        map2 = isl_map_normalize(map2);
        if (!map1 || !map2)
                goto error;
        equal = map1->n == map2->n;
        for (i = 0; equal && i < map1->n; ++i) {
                equal = isl_basic_map_fast_is_equal(map1->p[i], map2->p[i]);
                if (equal < 0)
                        goto error;
        }
        isl_map_free(map1);
        isl_map_free(map2);
        return equal;
error:
        isl_map_free(map1);
        isl_map_free(map2);
        return -1;
}

int isl_set_fast_is_equal(struct isl_set *set1, struct isl_set *set2)
{
        return isl_map_fast_is_equal((struct isl_map *)set1,
                                                (struct isl_map *)set2);
}

/* Return an interval that ranges from min to max (inclusive)
 */
struct isl_basic_set *isl_basic_set_interval(struct isl_ctx *ctx,
        isl_int min, isl_int max)
{
        int k;
        struct isl_basic_set *bset = NULL;

        bset = isl_basic_set_alloc(ctx, 0, 1, 0, 0, 2);
        if (!bset)
                goto error;

        k = isl_basic_set_alloc_inequality(bset);
        if (k < 0)
                goto error;
        isl_int_set_si(bset->ineq[k][1], 1);
        isl_int_neg(bset->ineq[k][0], min);

        k = isl_basic_set_alloc_inequality(bset);
        if (k < 0)
                goto error;
        isl_int_set_si(bset->ineq[k][1], -1);
        isl_int_set(bset->ineq[k][0], max);

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

/* Return the Cartesian product of the basic sets in list (in the given order).
 */
struct isl_basic_set *isl_basic_set_product(struct isl_basic_set_list *list)
{
        int i;
        unsigned dim;
        unsigned nparam;
        unsigned extra;
        unsigned n_eq;
        unsigned n_ineq;
        struct isl_basic_set *product = NULL;

        if (!list)
                goto error;
        isl_assert(list->ctx, list->n > 0, goto error);
        isl_assert(list->ctx, list->p[0], goto error);
        nparam = isl_basic_set_n_param(list->p[0]);
        dim = isl_basic_set_n_dim(list->p[0]);
        extra = list->p[0]->n_div;
        n_eq = list->p[0]->n_eq;
        n_ineq = list->p[0]->n_ineq;
        for (i = 1; i < list->n; ++i) {
                isl_assert(list->ctx, list->p[i], goto error);
                isl_assert(list->ctx,
                    nparam == isl_basic_set_n_param(list->p[i]), goto error);
                dim += isl_basic_set_n_dim(list->p[i]);
                extra += list->p[i]->n_div;
                n_eq += list->p[i]->n_eq;
                n_ineq += list->p[i]->n_ineq;
        }
        product = isl_basic_set_alloc(list->ctx, nparam, dim, extra,
                                        n_eq, n_ineq);
        if (!product)
                goto error;
        dim = 0;
        for (i = 0; i < list->n; ++i) {
                isl_basic_set_add_constraints(product,
                                        isl_basic_set_copy(list->p[i]), dim);
                dim += isl_basic_set_n_dim(list->p[i]);
        }
        isl_basic_set_list_free(list);
        return product;
error:
        isl_basic_set_free(product);
        isl_basic_set_list_free(list);
        return NULL;
}

struct isl_basic_map *isl_basic_map_product(
                struct isl_basic_map *bmap1, struct isl_basic_map *bmap2)
{
        struct isl_dim *dim_result = NULL;
        struct isl_basic_map *bmap;
        unsigned in1, in2, out1, out2, nparam, total, pos;
        struct isl_dim_map *dim_map1, *dim_map2;

        if (!bmap1 || !bmap2)
                goto error;

        isl_assert(bmap1->ctx, isl_dim_match(bmap1->dim, isl_dim_param,
                                     bmap2->dim, isl_dim_param), goto error);
        dim_result = isl_dim_product(isl_dim_copy(bmap1->dim),
                                                   isl_dim_copy(bmap2->dim));

        in1 = isl_basic_map_n_in(bmap1);
        in2 = isl_basic_map_n_in(bmap2);
        out1 = isl_basic_map_n_out(bmap1);
        out2 = isl_basic_map_n_out(bmap2);
        nparam = isl_basic_map_n_param(bmap1);

        total = nparam + in1 + in2 + out1 + out2 + bmap1->n_div + bmap2->n_div;
        dim_map1 = isl_dim_map_alloc(bmap1->ctx, total);
        dim_map2 = isl_dim_map_alloc(bmap1->ctx, total);
        isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_param, pos = 0);
        isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_param, pos = 0);
        isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_in, pos += nparam);
        isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_in, pos += in1);
        isl_dim_map_dim(dim_map1, bmap1->dim, isl_dim_out, pos += in2);
        isl_dim_map_dim(dim_map2, bmap2->dim, isl_dim_out, pos += out1);
        isl_dim_map_div(dim_map1, bmap1, pos += out2);
        isl_dim_map_div(dim_map2, bmap2, pos += bmap1->n_div);

        bmap = isl_basic_map_alloc_dim(dim_result,
                        bmap1->n_div + bmap2->n_div,
                        bmap1->n_eq + bmap2->n_eq,
                        bmap1->n_ineq + bmap2->n_ineq);
        bmap = add_constraints_dim_map(bmap, bmap1, dim_map1);
        bmap = add_constraints_dim_map(bmap, bmap2, dim_map2);
        bmap = isl_basic_map_simplify(bmap);
        return isl_basic_map_finalize(bmap);
error:
        isl_basic_map_free(bmap1);
        isl_basic_map_free(bmap2);
        return NULL;
}

/* Given two maps A -> B and C -> D, construct a map (A, C) -> (B, D)
 */
struct isl_map *isl_map_product(struct isl_map *map1, struct isl_map *map2)
{
        unsigned flags = 0;
        struct isl_map *result;
        int i, j;

        if (!map1 || !map2)
                goto error;

        isl_assert(map1->ctx, isl_dim_match(map1->dim, isl_dim_param,
                                         map2->dim, isl_dim_param), goto error);

        if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT) &&
            ISL_F_ISSET(map2, ISL_MAP_DISJOINT))
                ISL_FL_SET(flags, ISL_MAP_DISJOINT);

        result = isl_map_alloc_dim(isl_dim_product(isl_dim_copy(map1->dim),
                                                   isl_dim_copy(map2->dim)),
                                map1->n * map2->n, flags);
        if (!result)
                goto error;
        for (i = 0; i < map1->n; ++i)
                for (j = 0; j < map2->n; ++j) {
                        struct isl_basic_map *part;
                        part = isl_basic_map_product(
                                    isl_basic_map_copy(map1->p[i]),
                                    isl_basic_map_copy(map2->p[j]));
                        if (isl_basic_map_is_empty(part))
                                isl_basic_map_free(part);
                        else
                                result = isl_map_add_basic_map(result, part);
                        if (!result)
                                goto error;
                }
        isl_map_free(map1);
        isl_map_free(map2);
        return result;
error:
        isl_map_free(map1);
        isl_map_free(map2);
        return NULL;
}

/* Given two set A and B, construct its Cartesian product A x B.
 */
struct isl_set *isl_set_product(struct isl_set *set1, struct isl_set *set2)
{
        return (struct isl_set *)isl_map_product((struct isl_map *)set1,
                                                 (struct isl_map *)set2);
}

uint32_t isl_basic_set_get_hash(struct isl_basic_set *bset)
{
        int i;
        uint32_t hash = isl_hash_init();
        unsigned total;

        if (!bset)
                return 0;
        bset = isl_basic_set_copy(bset);
        bset = isl_basic_set_normalize(bset);
        if (!bset)
                return 0;
        total = isl_basic_set_total_dim(bset);
        isl_hash_byte(hash, bset->n_eq & 0xFF);
        for (i = 0; i < bset->n_eq; ++i) {
                uint32_t c_hash;
                c_hash = isl_seq_get_hash(bset->eq[i], 1 + total);
                isl_hash_hash(hash, c_hash);
        }
        isl_hash_byte(hash, bset->n_ineq & 0xFF);
        for (i = 0; i < bset->n_ineq; ++i) {
                uint32_t c_hash;
                c_hash = isl_seq_get_hash(bset->ineq[i], 1 + total);
                isl_hash_hash(hash, c_hash);
        }
        isl_hash_byte(hash, bset->n_div & 0xFF);
        for (i = 0; i < bset->n_div; ++i) {
                uint32_t c_hash;
                if (isl_int_is_zero(bset->div[i][0]))
                        continue;
                isl_hash_byte(hash, i & 0xFF);
                c_hash = isl_seq_get_hash(bset->div[i], 1 + 1 + total);
                isl_hash_hash(hash, c_hash);
        }
        isl_basic_set_free(bset);
        return hash;
}

uint32_t isl_set_get_hash(struct isl_set *set)
{
        int i;
        uint32_t hash;

        if (!set)
                return 0;
        set = isl_set_copy(set);
        set = isl_set_normalize(set);
        if (!set)
                return 0;

        hash = isl_hash_init();
        for (i = 0; i < set->n; ++i) {
                uint32_t bset_hash;
                bset_hash = isl_basic_set_get_hash(set->p[i]);
                isl_hash_hash(hash, bset_hash);
        }
                
        isl_set_free(set);

        return hash;
}

/* Check if the value for dimension dim is completely determined
 * by the values of the other parameters and variables.
 * That is, check if dimension dim is involved in an equality.
 */
int isl_basic_set_dim_is_unique(struct isl_basic_set *bset, unsigned dim)
{
        int i;
        unsigned nparam;

        if (!bset)
                return -1;
        nparam = isl_basic_set_n_param(bset);
        for (i = 0; i < bset->n_eq; ++i)
                if (!isl_int_is_zero(bset->eq[i][1 + nparam + dim]))
                        return 1;
        return 0;
}

/* Check if the value for dimension dim is completely determined
 * by the values of the other parameters and variables.
 * That is, check if dimension dim is involved in an equality
 * for each of the subsets.
 */
int isl_set_dim_is_unique(struct isl_set *set, unsigned dim)
{
        int i;

        if (!set)
                return -1;
        for (i = 0; i < set->n; ++i) {
                int unique;
                unique = isl_basic_set_dim_is_unique(set->p[i], dim);
                if (unique != 1)
                        return unique;
        }
        return 1;
}

int isl_map_foreach_basic_map(__isl_keep isl_map *map,
        int (*fn)(__isl_take isl_basic_map *bmap, void *user), void *user)
{
        int i;

        if (!map)
                return -1;

        for (i = 0; i < map->n; ++i)
                if (fn(isl_basic_map_copy(map->p[i]), user) < 0)
                        return -1;

        return 0;
}

int isl_set_foreach_basic_set(__isl_keep isl_set *set,
        int (*fn)(__isl_take isl_basic_set *bset, void *user), void *user)
{
        int i;

        if (!set)
                return -1;

        for (i = 0; i < set->n; ++i)
                if (fn(isl_basic_set_copy(set->p[i]), user) < 0)
                        return -1;

        return 0;
}

__isl_give isl_map *isl_set_lifting(__isl_take isl_set *set)
{
        struct isl_dim *dim;
        struct isl_basic_map *bmap;
        unsigned n_set;
        unsigned n_div;
        unsigned n_param;
        unsigned total;
        int i, k, l;

        set = isl_set_align_divs(set);

        if (!set)
                return NULL;

        dim = isl_set_get_dim(set);
        if (set->n == 0 || set->p[0]->n_div == 0) {
                isl_set_free(set);
                return isl_map_identity(dim);
        }

        n_div = set->p[0]->n_div;
        dim = isl_dim_map(dim);
        n_param = isl_dim_size(dim, isl_dim_param);
        n_set = isl_dim_size(dim, isl_dim_in);
        dim = isl_dim_extend(dim, n_param, n_set, n_set + n_div);
        bmap = isl_basic_map_alloc_dim(dim, 0, n_set, 2 * n_div);
        for (i = 0; i < n_set; ++i)
                bmap = var_equal(bmap, i);

        total = n_param + n_set + n_set + n_div;
        for (i = 0; i < n_div; ++i) {
                k = isl_basic_map_alloc_inequality(bmap);
                if (k < 0)
                        goto error;
                isl_seq_cpy(bmap->ineq[k], set->p[0]->div[i]+1, 1+n_param);
                isl_seq_clr(bmap->ineq[k]+1+n_param, n_set);
                isl_seq_cpy(bmap->ineq[k]+1+n_param+n_set,
                            set->p[0]->div[i]+1+1+n_param, n_set + n_div);
                isl_int_neg(bmap->ineq[k][1+n_param+n_set+n_set+i],
                            set->p[0]->div[i][0]);

                l = isl_basic_map_alloc_inequality(bmap);
                if (l < 0)
                        goto error;
                isl_seq_neg(bmap->ineq[l], bmap->ineq[k], 1 + total);
                isl_int_add(bmap->ineq[l][0], bmap->ineq[l][0],
                            set->p[0]->div[i][0]);
                isl_int_sub_ui(bmap->ineq[l][0], bmap->ineq[l][0], 1);
        }

        isl_set_free(set);
        return isl_map_from_basic_map(bmap);
error:
        isl_set_free(set);
        isl_basic_map_free(bmap);
        return NULL;
}

int isl_basic_set_size(__isl_keep isl_basic_set *bset)
{
        unsigned dim;
        int size = 0;

        if (!bset)
                return -1;

        dim = isl_basic_set_total_dim(bset);
        size += bset->n_eq * (1 + dim);
        size += bset->n_ineq * (1 + dim);
        size += bset->n_div * (2 + dim);

        return size;
}

int isl_set_size(__isl_keep isl_set *set)
{
        int i;
        int size = 0;

        if (!set)
                return -1;

        for (i = 0; i < set->n; ++i)
                size += isl_basic_set_size(set->p[i]);

        return size;
}