isl_*_eliminate: perform integer elimination

[isl.git] / isl_map_piplib.c

/*
 * Copyright 2008-2009 Katholieke Universiteit Leuven
 *
 * 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
 */

#include <isl_ctx_private.h>
#include <isl_map_private.h>
#include <isl/set.h>
#include <isl/map.h>
#include <isl/mat.h>
#include <isl/seq.h>
#include "isl_piplib.h"
#include "isl_map_piplib.h"

static void copy_values_from(isl_int *dst, Entier *src, unsigned n)
{
        int i;

        for (i = 0; i < n; ++i)
                entier_assign(dst[i], src[i]);
}

static void add_value(isl_int *dst, Entier *src)
{
        mpz_add(*dst, *dst, *src);
}

static void copy_constraint_from(isl_int *dst, PipVector *src,
                unsigned nparam, unsigned n_in, unsigned n_out,
                unsigned extra, int *pos)
{
        int i;

        copy_values_from(dst, src->the_vector+src->nb_elements-1, 1);
        copy_values_from(dst+1, src->the_vector, nparam+n_in);
        isl_seq_clr(dst+1+nparam+n_in, n_out);
        isl_seq_clr(dst+1+nparam+n_in+n_out, extra);
        for (i = 0; i + n_in + nparam < src->nb_elements-1; ++i) {
                int p = pos[i];
                add_value(&dst[1+nparam+n_in+n_out+p],
                          &src->the_vector[n_in+nparam+i]);
        }
}

static int add_inequality(struct isl_ctx *ctx,
                   struct isl_basic_map *bmap, int *pos, PipVector *vec)
{
        unsigned nparam = isl_basic_map_n_param(bmap);
        unsigned n_in = isl_basic_map_n_in(bmap);
        unsigned n_out = isl_basic_map_n_out(bmap);
        unsigned n_div = isl_basic_map_n_div(bmap);
        int i = isl_basic_map_alloc_inequality(bmap);
        if (i < 0)
                return -1;
        copy_constraint_from(bmap->ineq[i], vec,
            nparam, n_in, n_out, n_div, pos);

        return i;
}

/* 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
 */
static int add_div_constraints(struct isl_ctx *ctx,
        struct isl_basic_map *bmap, int *pos, PipNewparm *p, unsigned div)
{
        int i, j;
        unsigned total = isl_basic_map_total_dim(bmap);
        unsigned div_pos = 1 + total - bmap->n_div + div;

        i = add_inequality(ctx, bmap, pos, p->vector);
        if (i < 0)
                return -1;
        copy_values_from(&bmap->ineq[i][div_pos], &p->deno, 1);
        isl_int_neg(bmap->ineq[i][div_pos], bmap->ineq[i][div_pos]);

        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;
}

static int add_equality(struct isl_ctx *ctx,
                   struct isl_basic_map *bmap, int *pos,
                   unsigned var, PipVector *vec)
{
        int i;
        unsigned nparam = isl_basic_map_n_param(bmap);
        unsigned n_in = isl_basic_map_n_in(bmap);
        unsigned n_out = isl_basic_map_n_out(bmap);

        isl_assert(ctx, var < n_out, return -1);

        i = isl_basic_map_alloc_equality(bmap);
        if (i < 0)
                return -1;
        copy_constraint_from(bmap->eq[i], vec,
            nparam, n_in, n_out, bmap->extra, pos);
        isl_int_set_si(bmap->eq[i][1+nparam+n_in+var], -1);

        return i;
}

static int find_div(struct isl_ctx *ctx,
                   struct isl_basic_map *bmap, int *pos, PipNewparm *p)
{
        int i, j;
        unsigned nparam = isl_basic_map_n_param(bmap);
        unsigned n_in = isl_basic_map_n_in(bmap);
        unsigned n_out = isl_basic_map_n_out(bmap);

        i = isl_basic_map_alloc_div(bmap);
        if (i < 0)
                return -1;

        copy_constraint_from(bmap->div[i]+1, p->vector,
            nparam, n_in, n_out, bmap->extra, pos);

        copy_values_from(bmap->div[i], &p->deno, 1);
        for (j = 0; j < i; ++j)
                if (isl_seq_eq(bmap->div[i], bmap->div[j],
                                1+1+isl_basic_map_total_dim(bmap)+j)) {
                        isl_basic_map_free_div(bmap, 1);
                        return j;
                }

        if (add_div_constraints(ctx, bmap, pos, p, i) < 0)
                return -1;

        return i;
}

/* Count some properties of a quast
 * - maximal number of new parameters
 * - maximal depth
 * - total number of solutions
 * - total number of empty branches
 */
static void quast_count(PipQuast *q, int *maxnew, int depth, int *maxdepth,
                        int *sol, int *nosol)
{
        PipNewparm *p;

        for (p = q->newparm; p; p = p->next)
                if (p->rank > *maxnew)
                        *maxnew = p->rank;
        if (q->condition) {
                if (++depth > *maxdepth)
                        *maxdepth = depth;
                quast_count(q->next_else, maxnew, depth, maxdepth, sol, nosol);
                quast_count(q->next_then, maxnew, depth, maxdepth, sol, nosol);
        } else {
                if (q->list)
                        ++(*sol);
                else
                        ++(*nosol);
        }
}

/*
 * pos: array of length bmap->set.extra, mapping each of the existential
 *              variables PIP proposes to an existential variable in bmap
 * bmap: collects the currently active constraints
 * rest: collects the empty leaves of the quast (if not NULL)
 */
struct scan_data {
        struct isl_ctx                  *ctx;
        struct isl_basic_map            *bmap;
        struct isl_set                  **rest;
        int        *pos;
};

/*
 * New existentially quantified variables are places after the existing ones.
 */
static struct isl_map *scan_quast_r(struct scan_data *data, PipQuast *q,
                                    struct isl_map *map)
{
        PipNewparm *p;
        struct isl_basic_map *bmap = data->bmap;
        unsigned old_n_div = bmap->n_div;
        unsigned nparam = isl_basic_map_n_param(bmap);
        unsigned n_in = isl_basic_map_n_in(bmap);
        unsigned n_out = isl_basic_map_n_out(bmap);

        if (!map)
                goto error;

        for (p = q->newparm; p; p = p->next) {
                int pos;
                unsigned pip_param = nparam + n_in;

                pos = find_div(data->ctx, bmap, data->pos, p);
                if (pos < 0)
                        goto error;
                data->pos[p->rank - pip_param] = pos;
        }

        if (q->condition) {
                int pos = add_inequality(data->ctx, bmap, data->pos,
                                         q->condition);
                if (pos < 0)
                        goto error;
                map = scan_quast_r(data, q->next_then, map);

                if (isl_inequality_negate(bmap, pos))
                        goto error;
                map = scan_quast_r(data, q->next_else, map);

                if (isl_basic_map_free_inequality(bmap, 1))
                        goto error;
        } else if (q->list) {
                PipList *l;
                int j;
                /* if bmap->n_out is zero, we are only interested in the domains
                 * where a solution exists and not in the actual solution
                 */
                for (j = 0, l = q->list; j < n_out && l; ++j, l = l->next)
                        if (add_equality(data->ctx, bmap, data->pos, j,
                                                l->vector) < 0)
                                goto error;
                map = isl_map_add_basic_map(map, isl_basic_map_copy(bmap));
                if (isl_basic_map_free_equality(bmap, n_out))
                        goto error;
        } else if (data->rest) {
                struct isl_basic_set *bset;
                bset = isl_basic_set_from_basic_map(isl_basic_map_copy(bmap));
                bset = isl_basic_set_drop_dims(bset, n_in, n_out);
                if (!bset)
                        goto error;
                *data->rest = isl_set_add_basic_set(*data->rest, bset);
        }

        if (isl_basic_map_free_inequality(bmap, 2*(bmap->n_div - old_n_div)))
                goto error;
        if (isl_basic_map_free_div(bmap, bmap->n_div - old_n_div))
                goto error;
        return map;
error:
        isl_map_free(map);
        return NULL;
}

/*
 * Returns a map of dimension "keep_dim" with "context" as domain and
 * as range the first "isl_space_dim(keep_dim, isl_dim_out)" variables
 * in the quast lists.
 */
static struct isl_map *isl_map_from_quast(struct isl_ctx *ctx, PipQuast *q,
                isl_space *keep_dim,
                struct isl_basic_set *context,
                struct isl_set **rest)
{
        int             pip_param;
        int             nexist;
        int             max_depth;
        int             n_sol, n_nosol;
        struct scan_data        data;
        struct isl_map          *map = NULL;
        isl_space               *dims;
        unsigned                nparam;
        unsigned                dim;
        unsigned                keep;

        data.ctx = ctx;
        data.rest = rest;
        data.bmap = NULL;
        data.pos = NULL;

        if (!context || !keep_dim)
                goto error;

        dim = isl_basic_set_n_dim(context);
        nparam = isl_basic_set_n_param(context);
        keep = isl_space_dim(keep_dim, isl_dim_out);
        pip_param = nparam + dim;

        max_depth = 0;
        n_sol = 0;
        n_nosol = 0;
        nexist = pip_param-1;
        quast_count(q, &nexist, 0, &max_depth, &n_sol, &n_nosol);
        nexist -= pip_param-1;

        if (rest) {
                *rest = isl_set_alloc_space(isl_space_copy(context->dim), n_nosol,
                                        ISL_MAP_DISJOINT);
                if (!*rest)
                        goto error;
        }
        map = isl_map_alloc_space(isl_space_copy(keep_dim), n_sol,
                                ISL_MAP_DISJOINT);
        if (!map)
                goto error;

        dims = isl_space_reverse(isl_space_copy(context->dim));
        data.bmap = isl_basic_map_from_basic_set(context, dims);
        data.bmap = isl_basic_map_extend_space(data.bmap,
                keep_dim, nexist, keep, max_depth+2*nexist);
        if (!data.bmap)
                goto error2;

        if (data.bmap->extra) {
                int i;
                data.pos = isl_alloc_array(ctx, int, data.bmap->extra);
                if (!data.pos)
                        goto error;
                for (i = 0; i < data.bmap->n_div; ++i)
                        data.pos[i] = i;
        }

        map = scan_quast_r(&data, q, map);
        map = isl_map_finalize(map);
        if (!map)
                goto error2;
        if (rest) {
                *rest = isl_set_finalize(*rest);
                if (!*rest)
                        goto error2;
        }
        isl_basic_map_free(data.bmap);
        if (data.pos)
                free(data.pos);
        return map;
error:
        isl_basic_set_free(context);
        isl_space_free(keep_dim);
error2:
        if (data.pos)
                free(data.pos);
        isl_basic_map_free(data.bmap);
        isl_map_free(map);
        if (rest) {
                isl_set_free(*rest);
                *rest = NULL;
        }
        return NULL;
}

static void copy_values_to(Entier *dst, isl_int *src, unsigned n)
{
        int i;

        for (i = 0; i < n; ++i)
                entier_assign(dst[i], src[i]);
}

static void copy_constraint_to(Entier *dst, isl_int *src,
                unsigned pip_param, unsigned pip_var,
                unsigned extra_front, unsigned extra_back)
{
        copy_values_to(dst+1+extra_front+pip_var+pip_param+extra_back, src, 1);
        copy_values_to(dst+1+extra_front+pip_var, src+1, pip_param);
        copy_values_to(dst+1+extra_front, src+1+pip_param, pip_var);
}

PipMatrix *isl_basic_map_to_pip(struct isl_basic_map *bmap, unsigned pip_param,
                         unsigned extra_front, unsigned extra_back)
{
        int i;
        unsigned nrow;
        unsigned ncol;
        PipMatrix *M;
        unsigned off;
        unsigned pip_var = isl_basic_map_total_dim(bmap) - pip_param;

        nrow = extra_front + bmap->n_eq + bmap->n_ineq;
        ncol = 1 + extra_front + pip_var + pip_param + extra_back + 1;
        M = pip_matrix_alloc(nrow, ncol);
        if (!M)
                return NULL;

        off = extra_front;
        for (i = 0; i < bmap->n_eq; ++i) {
                entier_set_si(M->p[off+i][0], 0);
                copy_constraint_to(M->p[off+i], bmap->eq[i],
                                   pip_param, pip_var, extra_front, extra_back);
        }
        off += bmap->n_eq;
        for (i = 0; i < bmap->n_ineq; ++i) {
                entier_set_si(M->p[off+i][0], 1);
                copy_constraint_to(M->p[off+i], bmap->ineq[i],
                                   pip_param, pip_var, extra_front, extra_back);
        }
        return M;
}

PipMatrix *isl_basic_set_to_pip(struct isl_basic_set *bset, unsigned pip_param,
                         unsigned extra_front, unsigned extra_back)
{
        return isl_basic_map_to_pip((struct isl_basic_map *)bset,
                                        pip_param, extra_front, extra_back);
}

struct isl_map *isl_pip_basic_map_lexopt(
                struct isl_basic_map *bmap, struct isl_basic_set *dom,
                struct isl_set **empty, int max)
{
        PipOptions      *options;
        PipQuast        *sol;
        struct isl_map  *map;
        struct isl_ctx  *ctx;
        PipMatrix *domain = NULL, *context = NULL;
        unsigned         nparam, n_in, n_out;

        bmap = isl_basic_map_detect_equalities(bmap);
        if (!bmap || !dom)
                goto error;

        ctx = bmap->ctx;
        isl_assert(ctx, isl_basic_map_compatible_domain(bmap, dom), goto error);
        nparam = isl_basic_map_n_param(bmap);
        n_in = isl_basic_map_n_in(bmap);
        n_out = isl_basic_map_n_out(bmap);

        domain = isl_basic_map_to_pip(bmap, nparam + n_in, 0, dom->n_div);
        if (!domain)
                goto error;
        context = isl_basic_map_to_pip((struct isl_basic_map *)dom, 0, 0, 0);
        if (!context)
                goto error;

        options = pip_options_init();
        options->Simplify = 1;
        options->Maximize = max;
        options->Urs_unknowns = -1;
        options->Urs_parms = -1;
        sol = pip_solve(domain, context, -1, options);

        if (sol) {
                struct isl_basic_set *copy;
                copy = isl_basic_set_copy(dom);
                map = isl_map_from_quast(ctx, sol,
                                isl_space_copy(bmap->dim), copy, empty);
        } else {
                map = isl_map_empty_like_basic_map(bmap);
                if (empty)
                        *empty = NULL;
        }
        if (!map)
                goto error;
        if (map->n == 0 && empty) {
                isl_set_free(*empty);
                *empty = isl_set_from_basic_set(dom);
        } else
                isl_basic_set_free(dom);
        isl_basic_map_free(bmap);

        pip_quast_free(sol);
        pip_options_free(options);
        pip_matrix_free(domain);
        pip_matrix_free(context);

        return map;
error:
        if (domain)
                pip_matrix_free(domain);
        if (context)
                pip_matrix_free(context);
        isl_basic_map_free(bmap);
        isl_basic_set_free(dom);
        return NULL;
}