isl_lp.c

Go to the documentation of this file.

/*
 * Copyright 2008-2009 Katholieke Universiteit Leuven
 *
 * Use of this software is governed by the MIT license
 *
 * Written by Sven Verdoolaege, K.U.Leuven, Departement
 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
 */
 
#include <isl_ctx_private.h>
#include <isl_map_private.h>
#include <isl/lp.h>
#include <isl_seq.h>
#include "isl_tab.h"
#include <isl_options_private.h>
#include <isl_local_space_private.h>
#include <isl_aff_private.h>
#include <isl_mat_private.h>
#include <isl_val_private.h>
#include <isl_vec_private.h>
 
#include <bset_to_bmap.c>
#include <set_to_map.c>
 
static enum isl_lp_result isl_tab_solve_lp(__isl_keep isl_basic_map *bmap,
  int maximize, isl_int *f, isl_int denom, isl_int *opt,
  isl_int *opt_denom, __isl_give isl_vec **sol)
{
  struct isl_tab *tab;
  enum isl_lp_result res;
  isl_size dim = isl_basic_map_dim(bmap, isl_dim_all);
 
  if (dim < 0)
    return isl_lp_error;
  if (maximize)
    isl_seq_neg(f, f, 1 + dim);
 
  bmap = isl_basic_map_gauss(bmap, NULL);
  tab = isl_tab_from_basic_map(bmap, 0);
  res = isl_tab_min(tab, f, denom, opt, opt_denom, 0);
  if (res == isl_lp_ok && sol) {
    *sol = isl_tab_get_sample_value(tab);
    if (!*sol)
      res = isl_lp_error;
  }
  isl_tab_free(tab);
 
  if (maximize)
    isl_seq_neg(f, f, 1 + dim);
  if (maximize && opt)
    isl_int_neg(*opt, *opt);
 
  return res;
}
 
/* Given a basic map "bmap" and an affine combination of the variables "f"
 * with denominator "denom", set *opt / *opt_denom to the minimal
 * (or maximal if "maximize" is true) value attained by f/d over "bmap",
 * assuming the basic map is not empty and the expression cannot attain
 * arbitrarily small (or large) values.
 * If opt_denom is NULL, then *opt is rounded up (or down)
 * to the nearest integer.
 * The return value reflects the nature of the result (empty, unbounded,
 * minimal or maximal value returned in *opt).
 */
enum isl_lp_result isl_basic_map_solve_lp(__isl_keep isl_basic_map *bmap,
  int max, isl_int *f, isl_int d, isl_int *opt, isl_int *opt_denom,
  __isl_give isl_vec **sol)
{
  if (sol)
    *sol = NULL;
 
  if (!bmap)
    return isl_lp_error;
 
  return isl_tab_solve_lp(bmap, max, f, d, opt, opt_denom, sol);
}
 
enum isl_lp_result isl_basic_set_solve_lp(__isl_keep isl_basic_set *bset,
  int max, isl_int *f, isl_int d, isl_int *opt, isl_int *opt_denom,
  __isl_give isl_vec **sol)
{
  return isl_basic_map_solve_lp(bset_to_bmap(bset), max,
          f, d, opt, opt_denom, sol);
}
 
enum isl_lp_result isl_map_solve_lp(__isl_keep isl_map *map, int max,
              isl_int *f, isl_int d, isl_int *opt,
              isl_int *opt_denom,
              __isl_give isl_vec **sol)
{
  int i;
  isl_int o;
  isl_int t;
  isl_int opt_i;
  isl_int opt_denom_i;
  enum isl_lp_result res;
  int max_div;
  isl_vec *v = NULL;
 
  if (!map)
    return isl_lp_error;
  if (map->n == 0)
    return isl_lp_empty;
 
  max_div = 0;
  for (i = 0; i < map->n; ++i)
    if (map->p[i]->n_div > max_div)
      max_div = map->p[i]->n_div;
  if (max_div > 0) {
    isl_size total = isl_map_dim(map, isl_dim_all);
    if (total < 0)
      return isl_lp_error;
    v = isl_vec_alloc(map->ctx, 1 + total + max_div);
    if (!v)
      return isl_lp_error;
    isl_seq_cpy(v->el, f, 1 + total);
    isl_seq_clr(v->el + 1 + total, max_div);
    f = v->el;
  }
 
  if (!opt && map->n > 1 && sol) {
    isl_int_init(o);
    opt = &o;
  }
  if (map->n > 0)
    isl_int_init(opt_i);
  if (map->n > 0 && opt_denom) {
    isl_int_init(opt_denom_i);
    isl_int_init(t);
  }
 
  res = isl_basic_map_solve_lp(map->p[0], max, f, d,
          opt, opt_denom, sol);
  if (res == isl_lp_error || res == isl_lp_unbounded)
    goto done;
 
  if (sol)
    *sol = NULL;
 
  for (i = 1; i < map->n; ++i) {
    isl_vec *sol_i = NULL;
    enum isl_lp_result res_i;
    int better;
 
    res_i = isl_basic_map_solve_lp(map->p[i], max, f, d,
              &opt_i,
              opt_denom ? &opt_denom_i : NULL,
              sol ? &sol_i : NULL);
    if (res_i == isl_lp_error || res_i == isl_lp_unbounded) {
      res = res_i;
      goto done;
    }
    if (res_i == isl_lp_empty)
      continue;
    if (res == isl_lp_empty) {
      better = 1;
    } else if (!opt_denom) {
      if (max)
        better = isl_int_gt(opt_i, *opt);
      else
        better = isl_int_lt(opt_i, *opt);
    } else {
      isl_int_mul(t, opt_i, *opt_denom);
      isl_int_submul(t, *opt, opt_denom_i);
      if (max)
        better = isl_int_is_pos(t);
      else
        better = isl_int_is_neg(t);
    }
    if (better) {
      res = res_i;
      if (opt)
        isl_int_set(*opt, opt_i);
      if (opt_denom)
        isl_int_set(*opt_denom, opt_denom_i);
      if (sol) {
        isl_vec_free(*sol);
        *sol = sol_i;
      }
    } else
      isl_vec_free(sol_i);
  }
 
done:
  isl_vec_free(v);
  if (map->n > 0 && opt_denom) {
    isl_int_clear(opt_denom_i);
    isl_int_clear(t);
  }
  if (map->n > 0)
    isl_int_clear(opt_i);
  if (opt == &o)
    isl_int_clear(o);
  return res;
}
 
enum isl_lp_result isl_set_solve_lp(__isl_keep isl_set *set, int max,
              isl_int *f, isl_int d, isl_int *opt,
              isl_int *opt_denom,
              __isl_give isl_vec **sol)
{
  return isl_map_solve_lp(set_to_map(set), max,
          f, d, opt, opt_denom, sol);
}
 
/* Return the optimal (rational) value of "obj" over "bset", assuming
 * that "obj" and "bset" have aligned parameters and divs.
 * If "max" is set, then the maximal value is computed.
 * Otherwise, the minimal value is computed.
 *
 * Return infinity or negative infinity if the optimal value is unbounded and
 * NaN if "bset" is empty.
 *
 * Call isl_basic_set_solve_lp and translate the results.
 */
static __isl_give isl_val *basic_set_opt_lp(
  __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
{
  isl_ctx *ctx;
  isl_val *res;
  enum isl_lp_result lp_res;
 
  if (!bset || !obj)
    return NULL;
 
  ctx = isl_aff_get_ctx(obj);
  res = isl_val_alloc(ctx);
  if (!res)
    return NULL;
  lp_res = isl_basic_set_solve_lp(bset, max, obj->v->el + 1,
          obj->v->el[0], &res->n, &res->d, NULL);
  if (lp_res == isl_lp_ok)
    return isl_val_normalize(res);
  isl_val_free(res);
  if (lp_res == isl_lp_error)
    return NULL;
  if (lp_res == isl_lp_empty)
    return isl_val_nan(ctx);
  if (max)
    return isl_val_infty(ctx);
  else
    return isl_val_neginfty(ctx);
}
 
/* Return the optimal (rational) value of "obj" over "bset", assuming
 * that "obj" and "bset" have aligned parameters.
 * If "max" is set, then the maximal value is computed.
 * Otherwise, the minimal value is computed.
 *
 * Return infinity or negative infinity if the optimal value is unbounded and
 * NaN if "bset" is empty.
 *
 * Align the divs of "bset" and "obj" and call basic_set_opt_lp.
 */
static __isl_give isl_val *isl_basic_set_opt_lp_val_aligned(
  __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
{
  int *exp1 = NULL;
  int *exp2 = NULL;
  isl_ctx *ctx;
  isl_mat *bset_div = NULL;
  isl_mat *div = NULL;
  isl_val *res;
  isl_size bset_n_div, obj_n_div;
 
  if (!bset || !obj)
    return NULL;
 
  ctx = isl_aff_get_ctx(obj);
  if (!isl_space_is_equal(bset->dim, obj->ls->dim))
    isl_die(ctx, isl_error_invalid,
      "spaces don't match", return NULL);
 
  bset_n_div = isl_basic_set_dim(bset, isl_dim_div);
  obj_n_div = isl_aff_dim(obj, isl_dim_div);
  if (bset_n_div < 0 || obj_n_div < 0)
    return NULL;
  if (bset_n_div == 0 && obj_n_div == 0)
    return basic_set_opt_lp(bset, max, obj);
 
  bset = isl_basic_set_copy(bset);
  obj = isl_aff_copy(obj);
 
  bset_div = isl_basic_set_get_divs(bset);
  exp1 = isl_alloc_array(ctx, int, bset_n_div);
  exp2 = isl_alloc_array(ctx, int, obj_n_div);
  if (!bset_div || (bset_n_div && !exp1) || (obj_n_div && !exp2))
    goto error;
 
  div = isl_merge_divs(bset_div, obj->ls->div, exp1, exp2);
 
  bset = isl_basic_set_expand_divs(bset, isl_mat_copy(div), exp1);
  obj = isl_aff_expand_divs(obj, isl_mat_copy(div), exp2);
 
  res = basic_set_opt_lp(bset, max, obj);
 
  isl_mat_free(bset_div);
  isl_mat_free(div);
  free(exp1);
  free(exp2);
  isl_basic_set_free(bset);
  isl_aff_free(obj);
 
  return res;
error:
  isl_mat_free(div);
  isl_mat_free(bset_div);
  free(exp1);
  free(exp2);
  isl_basic_set_free(bset);
  isl_aff_free(obj);
  return NULL;
}
 
/* Return the optimal (rational) value of "obj" over "bset".
 * If "max" is set, then the maximal value is computed.
 * Otherwise, the minimal value is computed.
 *
 * Return infinity or negative infinity if the optimal value is unbounded and
 * NaN if "bset" is empty.
 */
static __isl_give isl_val *isl_basic_set_opt_lp_val(
  __isl_keep isl_basic_set *bset, int max, __isl_keep isl_aff *obj)
{
  isl_bool equal;
  isl_val *res;
 
  if (!bset || !obj)
    return NULL;
 
  equal = isl_basic_set_space_has_equal_params(bset, obj->ls->dim);
  if (equal < 0)
    return NULL;
  if (equal)
    return isl_basic_set_opt_lp_val_aligned(bset, max, obj);
 
  bset = isl_basic_set_copy(bset);
  obj = isl_aff_copy(obj);
  bset = isl_basic_set_align_params(bset, isl_aff_get_domain_space(obj));
  obj = isl_aff_align_params(obj, isl_basic_set_get_space(bset));
 
  res = isl_basic_set_opt_lp_val_aligned(bset, max, obj);
 
  isl_basic_set_free(bset);
  isl_aff_free(obj);
 
  return res;
}
 
/* Return the minimal (rational) value of "obj" over "bset".
 *
 * Return negative infinity if the minimal value is unbounded and
 * NaN if "bset" is empty.
 */
__isl_give isl_val *isl_basic_set_min_lp_val(__isl_keep isl_basic_set *bset,
  __isl_keep isl_aff *obj)
{
  return isl_basic_set_opt_lp_val(bset, 0, obj);
}
 
/* Return the maximal (rational) value of "obj" over "bset".
 *
 * Return infinity if the maximal value is unbounded and
 * NaN if "bset" is empty.
 */
__isl_give isl_val *isl_basic_set_max_lp_val(__isl_keep isl_basic_set *bset,
  __isl_keep isl_aff *obj)
{
  return isl_basic_set_opt_lp_val(bset, 1, obj);
}