basis_reduction_tab.c

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/*
 * 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 <assert.h>
#include <isl_map_private.h>
#include <isl_seq.h>
#include "isl_tab.h"
#include <isl_int.h>
#include <isl_config.h>
 
struct tab_lp {
  struct isl_ctx  *ctx;
  struct isl_vec  *row;
  struct isl_tab  *tab;
  struct isl_tab_undo **stack;
  isl_int   *obj;
  isl_int    opt;
  isl_int    opt_denom;
  isl_int    tmp;
  isl_int    tmp2;
  int          neq;
  unsigned   dim;
  /* number of constraints in initial product tableau */
  int    con_offset;
  /* objective function has fixed or no integer value */
  int    is_fixed;
};
 
#ifdef USE_GMP_FOR_MP
#define GBR_type              mpq_t
#define GBR_init(v)             mpq_init(v)
#define GBR_clear(v)              mpq_clear(v)
#define GBR_set(a,b)          mpq_set(a,b)
#define GBR_set_ui(a,b)         mpq_set_ui(a,b,1)
#define GBR_mul(a,b,c)          mpq_mul(a,b,c)
#define GBR_lt(a,b)         (mpq_cmp(a,b) < 0)
#define GBR_is_zero(a)          (mpq_sgn(a) == 0)
#define GBR_numref(a)         mpq_numref(a)
#define GBR_denref(a)         mpq_denref(a)
#define GBR_floor(a,b)          mpz_fdiv_q(a,GBR_numref(b),GBR_denref(b))
#define GBR_ceil(a,b)         mpz_cdiv_q(a,GBR_numref(b),GBR_denref(b))
#define GBR_set_num_neg(a, b)       mpz_neg(GBR_numref(*a), b);
#define GBR_set_den(a, b)       mpz_set(GBR_denref(*a), b);
#endif /* USE_GMP_FOR_MP */
 
#ifdef USE_IMATH_FOR_MP
#include <imrat.h>
 
#define GBR_type              mp_rat
#define GBR_init(v)             v = mp_rat_alloc()
#define GBR_clear(v)              mp_rat_free(v)
#define GBR_set(a,b)          mp_rat_copy(b,a)
#define GBR_set_ui(a,b)         mp_rat_set_uvalue(a,b,1)
#define GBR_mul(a,b,c)          mp_rat_mul(b,c,a)
#define GBR_lt(a,b)         (mp_rat_compare(a,b) < 0)
#define GBR_is_zero(a)          (mp_rat_compare_zero(a) == 0)
#ifdef USE_SMALL_INT_OPT
#define GBR_numref(a) isl_sioimath_encode_big(mp_rat_numer_ref(a))
#define GBR_denref(a) isl_sioimath_encode_big(mp_rat_denom_ref(a))
#define GBR_floor(a, b) isl_sioimath_fdiv_q((a), GBR_numref(b), GBR_denref(b))
#define GBR_ceil(a, b)  isl_sioimath_cdiv_q((a), GBR_numref(b), GBR_denref(b))
#define GBR_set_num_neg(a, b)                              \
  do {                                               \
    isl_sioimath_scratchspace_t scratch;       \
    impz_neg(mp_rat_numer_ref(*a),             \
        isl_sioimath_bigarg_src(*b, &scratch));\
  } while (0)
#define GBR_set_den(a, b)                                  \
  do {                                               \
    isl_sioimath_scratchspace_t scratch;       \
    impz_set(mp_rat_denom_ref(*a),             \
        isl_sioimath_bigarg_src(*b, &scratch));\
  } while (0)
#else /* USE_SMALL_INT_OPT */
#define GBR_numref(a)   mp_rat_numer_ref(a)
#define GBR_denref(a)   mp_rat_denom_ref(a)
#define GBR_floor(a,b)    impz_fdiv_q(a,GBR_numref(b),GBR_denref(b))
#define GBR_ceil(a,b)   impz_cdiv_q(a,GBR_numref(b),GBR_denref(b))
#define GBR_set_num_neg(a, b) impz_neg(GBR_numref(*a), b)
#define GBR_set_den(a, b) impz_set(GBR_denref(*a), b)
#endif /* USE_SMALL_INT_OPT */
#endif /* USE_IMATH_FOR_MP */
 
static struct tab_lp *init_lp(struct isl_tab *tab);
static void set_lp_obj(struct tab_lp *lp, isl_int *row, int dim);
static int solve_lp(struct tab_lp *lp);
static void get_obj_val(struct tab_lp* lp, GBR_type *F);
static void delete_lp(struct tab_lp *lp);
static int add_lp_row(struct tab_lp *lp, isl_int *row, int dim);
static void get_alpha(struct tab_lp* lp, int row, GBR_type *alpha);
static int del_lp_row(struct tab_lp *lp) WARN_UNUSED;
static int cut_lp_to_hyperplane(struct tab_lp *lp, isl_int *row);
 
#define GBR_LP                struct tab_lp
#define GBR_lp_init(P)              init_lp(P)
#define GBR_lp_set_obj(lp, obj, dim)      set_lp_obj(lp, obj, dim)
#define GBR_lp_solve(lp)        solve_lp(lp)
#define GBR_lp_get_obj_val(lp, F)     get_obj_val(lp, F)
#define GBR_lp_delete(lp)       delete_lp(lp)
#define GBR_lp_next_row(lp)       lp->neq
#define GBR_lp_add_row(lp, row, dim)      add_lp_row(lp, row, dim)
#define GBR_lp_get_alpha(lp, row, alpha)    get_alpha(lp, row, alpha)
#define GBR_lp_del_row(lp)        del_lp_row(lp)
#define GBR_lp_is_fixed(lp)       (lp)->is_fixed
#define GBR_lp_cut(lp, obj)           cut_lp_to_hyperplane(lp, obj)
#include "basis_reduction_templ.c"
 
/* Set up a tableau for the Cartesian product of bset with itself.
 * This could be optimized by first setting up a tableau for bset
 * and then performing the Cartesian product on the tableau.
 */
static struct isl_tab *gbr_tab(struct isl_tab *tab, struct isl_vec *row)
{
  unsigned dim;
  struct isl_tab *prod;
 
  if (!tab || !row)
    return NULL;
 
  dim = tab->n_var;
  prod = isl_tab_product(tab, tab);
  if (isl_tab_extend_cons(prod, 3 * dim + 1) < 0) {
    isl_tab_free(prod);
    return NULL;
  }
  return prod;
}
 
static struct tab_lp *init_lp(struct isl_tab *tab)
{
  struct tab_lp *lp = NULL;
 
  if (!tab)
    return NULL;
 
  lp = isl_calloc_type(tab->mat->ctx, struct tab_lp);
  if (!lp)
    return NULL;
 
  isl_int_init(lp->opt);
  isl_int_init(lp->opt_denom);
  isl_int_init(lp->tmp);
  isl_int_init(lp->tmp2);
 
  lp->dim = tab->n_var;
 
  lp->ctx = tab->mat->ctx;
  isl_ctx_ref(lp->ctx);
 
  lp->stack = isl_alloc_array(lp->ctx, struct isl_tab_undo *, lp->dim);
 
  lp->row = isl_vec_alloc(lp->ctx, 1 + 2 * lp->dim);
  if (!lp->row)
    goto error;
  lp->tab = gbr_tab(tab, lp->row);
  if (!lp->tab)
    goto error;
  lp->con_offset = lp->tab->n_con;
  lp->obj = NULL;
  lp->neq = 0;
 
  return lp;
error:
  delete_lp(lp);
  return NULL;
}
 
static void set_lp_obj(struct tab_lp *lp, isl_int *row, int dim)
{
  lp->obj = row;
}
 
static int solve_lp(struct tab_lp *lp)
{
  enum isl_lp_result res;
  unsigned flags = 0;
 
  lp->is_fixed = 0;
 
  isl_int_set_si(lp->row->el[0], 0);
  isl_seq_cpy(lp->row->el + 1, lp->obj, lp->dim);
  isl_seq_neg(lp->row->el + 1 + lp->dim, lp->obj, lp->dim);
  if (lp->neq)
    flags = ISL_TAB_SAVE_DUAL;
  res = isl_tab_min(lp->tab, lp->row->el, lp->ctx->one,
        &lp->opt, &lp->opt_denom, flags);
  isl_int_mul_ui(lp->opt_denom, lp->opt_denom, 2);
  if (isl_int_abs_lt(lp->opt, lp->opt_denom)) {
    struct isl_vec *sample = isl_tab_get_sample_value(lp->tab);
    if (!sample)
      return -1;
    isl_seq_inner_product(lp->obj, sample->el + 1, lp->dim, &lp->tmp);
    isl_seq_inner_product(lp->obj, sample->el + 1 + lp->dim, lp->dim, &lp->tmp2);
    isl_int_cdiv_q(lp->tmp, lp->tmp, sample->el[0]);
    isl_int_fdiv_q(lp->tmp2, lp->tmp2, sample->el[0]);
    if (isl_int_ge(lp->tmp, lp->tmp2))
      lp->is_fixed = 1;
    isl_vec_free(sample);
  }
  isl_int_divexact_ui(lp->opt_denom, lp->opt_denom, 2);
  if (res < 0)
    return -1;
  if (res != isl_lp_ok)
    isl_die(lp->ctx, isl_error_internal,
      "unexpected missing (bounded) solution", return -1);
  return 0;
}
 
/* The current objective function has a fixed (or no) integer value.
 * Cut the tableau to the hyperplane that fixes this value in
 * both halves of the tableau.
 * Return 1 if the resulting tableau is empty.
 */
static int cut_lp_to_hyperplane(struct tab_lp *lp, isl_int *row)
{
  enum isl_lp_result res;
 
  isl_int_set_si(lp->row->el[0], 0);
  isl_seq_cpy(lp->row->el + 1, row, lp->dim);
  isl_seq_clr(lp->row->el + 1 + lp->dim, lp->dim);
  res = isl_tab_min(lp->tab, lp->row->el, lp->ctx->one,
        &lp->tmp, NULL, 0);
  if (res != isl_lp_ok)
    return -1;
 
  isl_int_neg(lp->row->el[0], lp->tmp);
  if (isl_tab_add_eq(lp->tab, lp->row->el) < 0)
    return -1;
 
  isl_seq_cpy(lp->row->el + 1 + lp->dim, row, lp->dim);
  isl_seq_clr(lp->row->el + 1, lp->dim);
  if (isl_tab_add_eq(lp->tab, lp->row->el) < 0)
    return -1;
 
  lp->con_offset += 2;
 
  return lp->tab->empty;
}
 
static void get_obj_val(struct tab_lp* lp, GBR_type *F)
{
  GBR_set_num_neg(F, lp->opt);
  GBR_set_den(F, lp->opt_denom);
}
 
static void delete_lp(struct tab_lp *lp)
{
  if (!lp)
    return;
 
  isl_int_clear(lp->opt);
  isl_int_clear(lp->opt_denom);
  isl_int_clear(lp->tmp);
  isl_int_clear(lp->tmp2);
  isl_vec_free(lp->row);
  free(lp->stack);
  isl_tab_free(lp->tab);
  isl_ctx_deref(lp->ctx);
  free(lp);
}
 
static int add_lp_row(struct tab_lp *lp, isl_int *row, int dim)
{
  lp->stack[lp->neq] = isl_tab_snap(lp->tab);
 
  isl_int_set_si(lp->row->el[0], 0);
  isl_seq_cpy(lp->row->el + 1, row, lp->dim);
  isl_seq_neg(lp->row->el + 1 + lp->dim, row, lp->dim);
 
  if (isl_tab_add_valid_eq(lp->tab, lp->row->el) < 0)
    return -1;
 
  return lp->neq++;
}
 
static void get_alpha(struct tab_lp* lp, int row, GBR_type *alpha)
{
  row += lp->con_offset;
  GBR_set_num_neg(alpha, lp->tab->dual->el[1 + row]);
  GBR_set_den(alpha, lp->tab->dual->el[0]);
}
 
static int del_lp_row(struct tab_lp *lp)
{
  lp->neq--;
  return isl_tab_rollback(lp->tab, lp->stack[lp->neq]);
}