isl_fold.c

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/*
 * Copyright 2010      INRIA Saclay
 *
 * Use of this software is governed by the MIT license
 *
 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
 * 91893 Orsay, France 
 */
 
#include <isl_map_private.h>
#include <isl_union_map_private.h>
#include <isl_polynomial_private.h>
#include <isl_point_private.h>
#include <isl_space_private.h>
#include <isl_lp_private.h>
#include <isl_seq.h>
#include <isl_mat_private.h>
#include <isl_val_private.h>
#include <isl_vec_private.h>
#include <isl_config.h>
 
#undef EL_BASE
#define EL_BASE pw_qpolynomial_fold
 
#include <isl_list_templ.c>
 
enum isl_fold isl_fold_type_negate(enum isl_fold type)
{
  switch (type) {
  case isl_fold_error:
    return isl_fold_error;
  case isl_fold_min:
    return isl_fold_max;
  case isl_fold_max:
    return isl_fold_min;
  case isl_fold_list:
    return isl_fold_list;
  }
 
  isl_die(NULL, isl_error_internal, "unhandled isl_fold type", abort());
}
 
/* Construct a new reduction with the given type, domain space and
 * list of polynomials.
 */
static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
  enum isl_fold type, __isl_take isl_space *space,
  __isl_take isl_qpolynomial_list *list)
{
  isl_ctx *ctx;
  isl_qpolynomial_fold *fold;
 
  if (type < 0 || !space || !list)
    goto error;
 
  ctx = isl_space_get_ctx(space);
  fold = isl_calloc_type(ctx, struct isl_qpolynomial_fold);
  if (!fold)
    goto error;
 
  fold->ref = 1;
  fold->type = type;
  fold->dim = space;
  fold->list = list;
 
  return fold;
error:
  isl_space_free(space);
  isl_qpolynomial_list_free(list);
  return NULL;
}
 
isl_ctx *isl_qpolynomial_fold_get_ctx(__isl_keep isl_qpolynomial_fold *fold)
{
  return fold ? fold->dim->ctx : NULL;
}
 
/* Return the domain space of "fold".
 */
static __isl_keep isl_space *isl_qpolynomial_fold_peek_domain_space(
  __isl_keep isl_qpolynomial_fold *fold)
{
  return fold ? fold->dim : NULL;
}
 
__isl_give isl_space *isl_qpolynomial_fold_get_domain_space(
  __isl_keep isl_qpolynomial_fold *fold)
{
  return isl_space_copy(isl_qpolynomial_fold_peek_domain_space(fold));
}
 
/* Return the space of the domain of "fold".
 * This may be either a copy or the space itself
 * if there is only one reference to "fold".
 * This allows the space to be modified inplace
 * if both the expression and its space have only a single reference.
 * The caller is not allowed to modify "fold" between this call and
 * a subsequent call to isl_qpolynomial_fold_restore_domain_space.
 * The only exception is that isl_qpolynomial_fold_free can be called instead.
 */
static __isl_give isl_space *isl_qpolynomial_fold_take_domain_space(
  __isl_keep isl_qpolynomial_fold *fold)
{
  isl_space *space;
 
  if (!fold)
    return NULL;
  if (fold->ref != 1)
    return isl_qpolynomial_fold_get_domain_space(fold);
  space = fold->dim;
  fold->dim = NULL;
  return space;
}
 
/* Set the space of the domain of "fold" to "space",
 * where the space of "fold" may be missing
 * due to a preceding call to isl_qpolynomial_fold_take_domain_space.
 * However, in this case, "fold" only has a single reference and
 * then the call to isl_qpolynomial_fold_cow has no effect.
 */
static
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_restore_domain_space(
  __isl_keep isl_qpolynomial_fold *fold, __isl_take isl_space *space)
{
  if (!fold || !space)
    goto error;
 
  if (fold->dim == space) {
    isl_space_free(space);
    return fold;
  }
 
  fold = isl_qpolynomial_fold_cow(fold);
  if (!fold)
    goto error;
  isl_space_free(fold->dim);
  fold->dim = space;
 
  return fold;
error:
  isl_qpolynomial_fold_free(fold);
  isl_space_free(space);
  return NULL;
}
 
__isl_give isl_space *isl_qpolynomial_fold_get_space(
  __isl_keep isl_qpolynomial_fold *fold)
{
  isl_space *space;
  if (!fold)
    return NULL;
  space = isl_space_copy(fold->dim);
  space = isl_space_from_domain(space);
  space = isl_space_add_dims(space, isl_dim_out, 1);
  return space;
}
 
/* Return the list of polynomials in the reduction "fold".
 */
__isl_keep isl_qpolynomial_list *isl_qpolynomial_fold_peek_list(
  __isl_keep isl_qpolynomial_fold *fold)
{
  return fold ? fold->list : NULL;
}
 
/* Return a copy of the list of polynomials in the reduction "fold".
 */
static __isl_give isl_qpolynomial_list *isl_qpolynomial_fold_get_list(
  __isl_keep isl_qpolynomial_fold *fold)
{
  return isl_qpolynomial_list_copy(isl_qpolynomial_fold_peek_list(fold));
}
 
/* Return the list of polynomials of "fold".
 * This may be either a copy or the list itself
 * if there is only one reference to "fold".
 * This allows the list to be modified inplace
 * if both the expression and its list have only a single reference.
 * The caller is not allowed to modify "fold" between this call and
 * a subsequent call to isl_qpolynomial_fold_restore_list.
 * The only exception is that isl_qpolynomial_fold_free can be called instead.
 */
static __isl_give isl_qpolynomial_list *isl_qpolynomial_fold_take_list(
  __isl_keep isl_qpolynomial_fold *fold)
{
  isl_qpolynomial_list *list;
 
  if (!fold)
    return NULL;
  if (fold->ref != 1)
    return isl_qpolynomial_fold_get_list(fold);
  list = fold->list;
  fold->list = NULL;
  return list;
}
 
/* Set the space of the list of polynomials of "fold" to "space",
 * where the list of polynomials of "fold" may be missing
 * due to a preceding call to isl_qpolynomial_fold_take_list.
 * However, in this case, "fold" only has a single reference and
 * then the call to isl_qpolynomial_fold_cow has no effect.
 */
static __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_restore_list(
  __isl_keep isl_qpolynomial_fold *fold,
  __isl_take isl_qpolynomial_list *list)
{
  if (!fold || !list)
    goto error;
 
  if (fold->list == list) {
    isl_qpolynomial_list_free(list);
    return fold;
  }
 
  fold = isl_qpolynomial_fold_cow(fold);
  if (!fold)
    goto error;
  isl_qpolynomial_list_free(fold->list);
  fold->list = list;
 
  return fold;
error:
  isl_qpolynomial_fold_free(fold);
  isl_qpolynomial_list_free(list);
  return NULL;
}
 
/* isl_qpolynomial_list_map callback that calls
 * isl_qpolynomial_reset_domain_space on "qp".
 */
static __isl_give isl_qpolynomial *reset_domain_space(
  __isl_take isl_qpolynomial *qp, void *user)
{
  isl_space *space = user;
 
  return isl_qpolynomial_reset_domain_space(qp, isl_space_copy(space));
}
 
/* Replace the domain space of "fold" by "space".
 *
 * Replace the domain space itself and that of all polynomials
 * in the list.
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_domain_space(
  __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *space)
{
  isl_qpolynomial_list *list;
 
  list = isl_qpolynomial_fold_take_list(fold);
  list = isl_qpolynomial_list_map(list, &reset_domain_space, space);
  fold = isl_qpolynomial_fold_restore_list(fold, list);
 
  isl_space_free(isl_qpolynomial_fold_take_domain_space(fold));
  fold = isl_qpolynomial_fold_restore_domain_space(fold, space);
 
  return fold;
}
 
/* Reset the space of "fold".  This function is called from isl_pw_templ.c
 * and doesn't know if the space of an element object is represented
 * directly or through its domain.  It therefore passes along both.
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_space_and_domain(
  __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *space,
  __isl_take isl_space *domain)
{
  isl_space_free(space);
  return isl_qpolynomial_fold_reset_domain_space(fold, domain);
}
 
/* Internal data structure for isl_qpolynomial_fold_*_dims
 * representing their arguments.
 */
struct isl_fold_dims_data {
  enum isl_dim_type type;
  unsigned first;
  unsigned n;
};
 
/* isl_qpolynomial_list_every callback that checks whether "qp"
 * does not involve any dimensions in the given range.
 */
static isl_bool not_involved(__isl_keep isl_qpolynomial *qp, void *user)
{
  struct isl_fold_dims_data *data = user;
  isl_bool involves;
 
  involves = isl_qpolynomial_involves_dims(qp, data->type,
              data->first, data->n);
  return isl_bool_not(involves);
}
 
/* Does "fold" involve any dimensions in the given range.
 *
 * It involves any of those dimensions if it is not the case
 * that every polynomial in the reduction does not involve
 * any of the dimensions.
 */
static isl_bool isl_qpolynomial_fold_involves_dims(
  __isl_keep isl_qpolynomial_fold *fold,
  enum isl_dim_type type, unsigned first, unsigned n)
{
  struct isl_fold_dims_data data = { type, first, n };
  isl_qpolynomial_list *list;
  isl_bool not;
 
  if (!fold)
    return isl_bool_error;
  if (n == 0)
    return isl_bool_false;
 
  list = isl_qpolynomial_fold_peek_list(fold);
  not = isl_qpolynomial_list_every(list, &not_involved, &data);
  return isl_bool_not(not);
}
 
/* Internal data structure for isl_qpolynomial_fold_set_dim_name
 * representing its arguments.
 */
struct isl_fold_set_dim_name_data {
  enum isl_dim_type type;
  unsigned pos;
  const char *s;
};
 
/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_set_dim_name on "qp".
 */
static __isl_give isl_qpolynomial *set_dim_name(__isl_take isl_qpolynomial *qp,
  void *user)
{
  struct isl_fold_set_dim_name_data *data = user;
 
  qp = isl_qpolynomial_set_dim_name(qp, data->type, data->pos, data->s);
  return qp;
}
 
/* Given a dimension type for an isl_qpolynomial_fold,
 * return the corresponding type for the domain.
 */
static enum isl_dim_type domain_type(enum isl_dim_type type)
{
  if (type == isl_dim_in)
    return isl_dim_set;
  return type;
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_set_dim_name(
  __isl_take isl_qpolynomial_fold *fold,
  enum isl_dim_type type, unsigned pos, const char *s)
{
  struct isl_fold_set_dim_name_data data = { type, pos, s };
  enum isl_dim_type set_type;
  isl_space *space;
  isl_qpolynomial_list *list;
 
  list = isl_qpolynomial_fold_take_list(fold);
  list = isl_qpolynomial_list_map(list, &set_dim_name, &data);
  fold = isl_qpolynomial_fold_restore_list(fold, list);
 
  set_type = domain_type(type);
  space = isl_qpolynomial_fold_take_domain_space(fold);
  space = isl_space_set_dim_name(space, set_type, pos, s);
  fold = isl_qpolynomial_fold_restore_domain_space(fold, space);
 
  return fold;
}
 
/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_drop_dims on "qp".
 */
static __isl_give isl_qpolynomial *drop_dims(__isl_take isl_qpolynomial *qp,
  void *user)
{
  struct isl_fold_dims_data *data = user;
 
  qp = isl_qpolynomial_drop_dims(qp, data->type, data->first, data->n);
  return qp;
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_drop_dims(
  __isl_take isl_qpolynomial_fold *fold,
  enum isl_dim_type type, unsigned first, unsigned n)
{
  struct isl_fold_dims_data data = { type, first, n };
  enum isl_dim_type set_type;
  isl_space *space;
  isl_qpolynomial_list *list;
 
  if (!fold)
    return NULL;
  if (n == 0)
    return fold;
 
  set_type = domain_type(type);
 
  list = isl_qpolynomial_fold_take_list(fold);
  list = isl_qpolynomial_list_map(list, &drop_dims, &data);
  fold = isl_qpolynomial_fold_restore_list(fold, list);
 
  space = isl_qpolynomial_fold_take_domain_space(fold);
  space = isl_space_drop_dims(space, set_type, first, n);
  fold = isl_qpolynomial_fold_restore_domain_space(fold, space);
 
  return fold;
}
 
/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_insert_dims on "qp".
 */
static __isl_give isl_qpolynomial *insert_dims(__isl_take isl_qpolynomial *qp,
  void *user)
{
  struct isl_fold_dims_data *data = user;
 
  qp = isl_qpolynomial_insert_dims(qp, data->type, data->first, data->n);
  return qp;
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_insert_dims(
  __isl_take isl_qpolynomial_fold *fold,
  enum isl_dim_type type, unsigned first, unsigned n)
{
  struct isl_fold_dims_data data = { type, first, n };
  enum isl_dim_type set_type;
  isl_space *space;
  isl_qpolynomial_list *list;
 
  if (!fold)
    return NULL;
  if (n == 0 && !isl_space_is_named_or_nested(fold->dim, type))
    return fold;
 
  list = isl_qpolynomial_fold_take_list(fold);
  list = isl_qpolynomial_list_map(list, &insert_dims, &data);
  fold = isl_qpolynomial_fold_restore_list(fold, list);
 
  set_type = domain_type(type);
  space = isl_qpolynomial_fold_take_domain_space(fold);
  space = isl_space_insert_dims(space, set_type, first, n);
  fold = isl_qpolynomial_fold_restore_domain_space(fold, space);
 
  return fold;
}
 
/* Determine the sign of the constant quasipolynomial "qp".
 *
 * Return
 *  -1 if qp <= 0
 *   1 if qp >= 0
 *   0 if unknown
 *
 * For qp == 0, we can return either -1 or 1.  In practice, we return 1.
 * For qp == NaN, the sign is undefined, so we return 0.
 */
static int isl_qpolynomial_cst_sign(__isl_keep isl_qpolynomial *qp)
{
  isl_poly_cst *cst;
 
  if (isl_qpolynomial_is_nan(qp))
    return 0;
 
  cst = isl_poly_as_cst(qp->poly);
  if (!cst)
    return 0;
 
  return isl_int_sgn(cst->n) < 0 ? -1 : 1;
}
 
static int isl_qpolynomial_aff_sign(__isl_keep isl_set *set,
  __isl_keep isl_qpolynomial *qp)
{
  enum isl_lp_result res;
  isl_vec *aff;
  isl_int opt;
  int sgn = 0;
 
  aff = isl_qpolynomial_extract_affine(qp);
  if (!aff)
    return 0;
 
  isl_int_init(opt);
 
  res = isl_set_solve_lp(set, 0, aff->el + 1, aff->el[0],
        &opt, NULL, NULL);
  if (res == isl_lp_error)
    goto done;
  if (res == isl_lp_empty ||
      (res == isl_lp_ok && !isl_int_is_neg(opt))) {
    sgn = 1;
    goto done;
  }
 
  res = isl_set_solve_lp(set, 1, aff->el + 1, aff->el[0],
        &opt, NULL, NULL);
  if (res == isl_lp_ok && !isl_int_is_pos(opt))
    sgn = -1;
 
done:
  isl_int_clear(opt);
  isl_vec_free(aff);
  return sgn;
}
 
/* Determine, if possible, the sign of the quasipolynomial "qp" on
 * the domain "set".
 *
 * If qp is a constant, then the problem is trivial.
 * If qp is linear, then we check if the minimum of the corresponding
 * affine constraint is non-negative or if the maximum is non-positive.
 *
 * Otherwise, we check if the outermost variable "v" has a lower bound "l"
 * in "set".  If so, we write qp(v,v') as
 *
 *  q(v,v') * (v - l) + r(v')
 *
 * if q(v,v') and r(v') have the same known sign, then the original
 * quasipolynomial has the same sign as well.
 *
 * Return
 *  -1 if qp <= 0
 *   1 if qp >= 0
 *   0 if unknown
 */
static int isl_qpolynomial_sign(__isl_keep isl_set *set,
  __isl_keep isl_qpolynomial *qp)
{
  isl_size d;
  int i;
  isl_bool is;
  isl_poly_rec *rec;
  isl_vec *v;
  isl_int l;
  enum isl_lp_result res;
  int sgn = 0;
 
  is = isl_qpolynomial_is_cst(qp, NULL, NULL);
  if (is < 0)
    return 0;
  if (is)
    return isl_qpolynomial_cst_sign(qp);
 
  is = isl_qpolynomial_is_affine(qp);
  if (is < 0)
    return 0;
  if (is)
    return isl_qpolynomial_aff_sign(set, qp);
 
  if (qp->div->n_row > 0)
    return 0;
 
  rec = isl_poly_as_rec(qp->poly);
  if (!rec)
    return 0;
 
  d = isl_space_dim(qp->dim, isl_dim_all);
  if (d < 0)
    return 0;
  v = isl_vec_alloc(set->ctx, 2 + d);
  if (!v)
    return 0;
 
  isl_seq_clr(v->el + 1, 1 + d);
  isl_int_set_si(v->el[0], 1);
  isl_int_set_si(v->el[2 + qp->poly->var], 1);
 
  isl_int_init(l);
 
  res = isl_set_solve_lp(set, 0, v->el + 1, v->el[0], &l, NULL, NULL);
  if (res == isl_lp_ok) {
    isl_qpolynomial *min;
    isl_qpolynomial *base;
    isl_qpolynomial *r, *q;
    isl_qpolynomial *t;
 
    min = isl_qpolynomial_cst_on_domain(isl_space_copy(qp->dim), l);
    base = isl_qpolynomial_var_pow_on_domain(isl_space_copy(qp->dim),
            qp->poly->var, 1);
 
    r = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
            isl_poly_copy(rec->p[rec->n - 1]));
    q = isl_qpolynomial_copy(r);
 
    for (i = rec->n - 2; i >= 0; --i) {
      r = isl_qpolynomial_mul(r, isl_qpolynomial_copy(min));
      t = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
              isl_poly_copy(rec->p[i]));
      r = isl_qpolynomial_add(r, t);
      if (i == 0)
        break;
      q = isl_qpolynomial_mul(q, isl_qpolynomial_copy(base));
      q = isl_qpolynomial_add(q, isl_qpolynomial_copy(r));
    }
 
    if (isl_qpolynomial_is_zero(q))
      sgn = isl_qpolynomial_sign(set, r);
    else if (isl_qpolynomial_is_zero(r))
      sgn = isl_qpolynomial_sign(set, q);
    else {
      int sgn_q, sgn_r;
      sgn_r = isl_qpolynomial_sign(set, r);
      sgn_q = isl_qpolynomial_sign(set, q);
      if (sgn_r == sgn_q)
        sgn = sgn_r;
    }
 
    isl_qpolynomial_free(min);
    isl_qpolynomial_free(base);
    isl_qpolynomial_free(q);
    isl_qpolynomial_free(r);
  }
 
  isl_int_clear(l);
 
  isl_vec_free(v);
 
  return sgn;
}
 
/* Check that "fold1" and "fold2" have the same type.
 */
static isl_stat isl_qpolynomial_fold_check_equal_type(
  __isl_keep isl_qpolynomial_fold *fold1,
  __isl_keep isl_qpolynomial_fold *fold2)
{
  enum isl_fold type1, type2;
 
  type1 = isl_qpolynomial_fold_get_type(fold1);
  type2 = isl_qpolynomial_fold_get_type(fold2);
  if (type1 < 0 || type2 < 0)
    return isl_stat_error;
  if (type1 != type2)
    isl_die(isl_qpolynomial_fold_get_ctx(fold1), isl_error_invalid,
      "fold types don't match", return isl_stat_error);
  return isl_stat_ok;
}
 
/* Check that "fold1" and "fold2" have the same (domain) space.
 */
static isl_stat isl_qpolynomial_fold_check_equal_space(
  __isl_keep isl_qpolynomial_fold *fold1,
  __isl_keep isl_qpolynomial_fold *fold2)
{
  isl_bool equal;
  isl_space *space1, *space2;
 
  space1 = isl_qpolynomial_fold_peek_domain_space(fold1);
  space2 = isl_qpolynomial_fold_peek_domain_space(fold2);
  equal = isl_space_is_equal(space1, space2);
  if (equal < 0)
    return isl_stat_error;
  if (!equal)
    isl_die(isl_qpolynomial_fold_get_ctx(fold1), isl_error_invalid,
      "spaces don't match", return isl_stat_error);
  return isl_stat_ok;
}
 
/* Combine "list1" and "list2" into a single list, eliminating
 * those elements of one list that are already covered by the other
 * list on "set".
 *
 * "better" is the sign that the difference qp1 - qp2 needs to have for qp1
 * to be covered by qp2.
 */
static __isl_give isl_qpolynomial_list *merge_lists(__isl_keep isl_set *set,
  __isl_take isl_qpolynomial_list *list1,
  __isl_take isl_qpolynomial_list *list2, int better)
{
  int i, j;
  isl_size n1, n2;
 
  n1 = isl_qpolynomial_list_size(list1);
  n2 = isl_qpolynomial_list_size(list2);
  if (n1 < 0 || n2 < 0)
    goto error;
 
  for (i = n2 - 1; i >= 0; --i) {
    for (j = n1 - 1; j >= 0; --j) {
      isl_qpolynomial *qp1, *qp2, *d;
      int sgn;
      isl_bool equal;
 
      qp1 = isl_qpolynomial_list_peek(list1, j);
      qp2 = isl_qpolynomial_list_peek(list2, i);
      equal = isl_qpolynomial_plain_is_equal(qp1, qp2);
      if (equal < 0)
        goto error;
      if (equal)
        break;
      d = isl_qpolynomial_sub(
        isl_qpolynomial_copy(qp1),
        isl_qpolynomial_copy(qp2));
      sgn = isl_qpolynomial_sign(set, d);
      isl_qpolynomial_free(d);
      if (sgn == 0)
        continue;
      if (sgn != better)
        break;
      list1 = isl_qpolynomial_list_drop(list1, j, 1);
      n1--;
    }
    if (j < 0)
      continue;
    list2 = isl_qpolynomial_list_drop(list2, i, 1);
    n2--;
  }
 
  return isl_qpolynomial_list_concat(list1, list2);
error:
  isl_qpolynomial_list_free(list1);
  isl_qpolynomial_list_free(list2);
  return NULL;
}
 
/* Combine "fold1" and "fold2" into a single reduction, eliminating
 * those elements of one reduction that are already covered by the other
 * reduction on "set".
 *
 * If "fold1" or "fold2" is an empty reduction, then return
 * the other reduction.
 * If "fold1" or "fold2" is a NaN, then return this NaN.
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold_on_domain(
  __isl_keep isl_set *set,
  __isl_take isl_qpolynomial_fold *fold1,
  __isl_take isl_qpolynomial_fold *fold2)
{
  isl_qpolynomial_list *list1;
  isl_qpolynomial_list *list2;
  int better;
 
  if (isl_qpolynomial_fold_check_equal_type(fold1, fold2) < 0)
    goto error;
  if (isl_qpolynomial_fold_check_equal_space(fold1, fold2) < 0)
    goto error;
 
  better = fold1->type == isl_fold_max ? -1 : 1;
 
  if (isl_qpolynomial_fold_is_empty(fold1) ||
      isl_qpolynomial_fold_is_nan(fold2)) {
    isl_qpolynomial_fold_free(fold1);
    return fold2;
  }
 
  if (isl_qpolynomial_fold_is_empty(fold2) ||
      isl_qpolynomial_fold_is_nan(fold1)) {
    isl_qpolynomial_fold_free(fold2);
    return fold1;
  }
 
  list1 = isl_qpolynomial_fold_take_list(fold1);
  list2 = isl_qpolynomial_fold_take_list(fold2);
 
  list1 = merge_lists(set, list1, list2, better);
 
  fold1 = isl_qpolynomial_fold_restore_list(fold1, list1);
  isl_qpolynomial_fold_free(fold2);
 
  return fold1;
error:
  isl_qpolynomial_fold_free(fold1);
  isl_qpolynomial_fold_free(fold2);
  return NULL;
}
 
/* isl_qpolynomial_list_map callback for adding "qp2" to "qp".
 */
static __isl_give isl_qpolynomial *add_qpolynomial(
  __isl_take isl_qpolynomial *qp, void *user)
{
  isl_qpolynomial *qp2 = user;
 
  return isl_qpolynomial_add(qp, isl_qpolynomial_copy(qp2));
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_qpolynomial(
  __isl_take isl_qpolynomial_fold *fold, __isl_take isl_qpolynomial *qp)
{
  isl_qpolynomial_list *list;
 
  if (!fold || !qp)
    goto error;
 
  if (isl_qpolynomial_is_zero(qp)) {
    isl_qpolynomial_free(qp);
    return fold;
  }
 
  list = isl_qpolynomial_fold_take_list(fold);
  list = isl_qpolynomial_list_map(list, &add_qpolynomial, qp);
  fold = isl_qpolynomial_fold_restore_list(fold, list);
 
  isl_qpolynomial_free(qp);
  return fold;
error:
  isl_qpolynomial_fold_free(fold);
  isl_qpolynomial_free(qp);
  return NULL;
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_on_domain(
  __isl_keep isl_set *dom,
  __isl_take isl_qpolynomial_fold *fold1,
  __isl_take isl_qpolynomial_fold *fold2)
{
  int i;
  isl_size n1, n2;
  isl_qpolynomial_fold *res = NULL;
  isl_qpolynomial *qp;
  isl_qpolynomial_list *list1, *list2;
 
  if (!fold1 || !fold2)
    goto error;
 
  if (isl_qpolynomial_fold_is_empty(fold1)) {
    isl_qpolynomial_fold_free(fold1);
    return fold2;
  }
 
  if (isl_qpolynomial_fold_is_empty(fold2)) {
    isl_qpolynomial_fold_free(fold2);
    return fold1;
  }
 
  list1 = isl_qpolynomial_fold_peek_list(fold1);
  list2 = isl_qpolynomial_fold_peek_list(fold2);
  n1 = isl_qpolynomial_list_size(list1);
  n2 = isl_qpolynomial_list_size(list2);
  if (n1 < 0 || n2 < 0)
    goto error;
 
  if (n1 == 1 && n2 != 1)
    return isl_qpolynomial_fold_add_on_domain(dom, fold2, fold1);
 
  qp = isl_qpolynomial_list_get_at(list2, 0);
  if (n2 == 1) {
    res = isl_qpolynomial_fold_add_qpolynomial(fold1, qp);
    isl_qpolynomial_fold_free(fold2);
    return res;
  }
 
  res = isl_qpolynomial_fold_add_qpolynomial(
        isl_qpolynomial_fold_copy(fold1), qp);
 
  for (i = 1; i < n2; ++i) {
    isl_qpolynomial_fold *res_i;
 
    qp = isl_qpolynomial_list_get_at(list2, i);
    res_i = isl_qpolynomial_fold_add_qpolynomial(
          isl_qpolynomial_fold_copy(fold1), qp);
    res = isl_qpolynomial_fold_fold_on_domain(dom, res, res_i);
  }
 
  isl_qpolynomial_fold_free(fold1);
  isl_qpolynomial_fold_free(fold2);
  return res;
error:
  isl_qpolynomial_fold_free(res);
  isl_qpolynomial_fold_free(fold1);
  isl_qpolynomial_fold_free(fold2);
  return NULL;
}
 
/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_substitute_equalities on "qp" and "eq".
 */
static __isl_give isl_qpolynomial *substitute_equalities(
  __isl_take isl_qpolynomial *qp, void *user)
{
  isl_basic_set *eq = user;
 
  eq = isl_basic_set_copy(eq);
  return isl_qpolynomial_substitute_equalities(qp, eq);
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute_equalities(
  __isl_take isl_qpolynomial_fold *fold, __isl_take isl_basic_set *eq)
{
  isl_qpolynomial_list *list;
 
  list = isl_qpolynomial_fold_take_list(fold);
  list = isl_qpolynomial_list_map(list, &substitute_equalities, eq);
  fold = isl_qpolynomial_fold_restore_list(fold, list);
 
  isl_basic_set_free(eq);
  return fold;
}
 
/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_substitute_equalities on "qp" and "context".
 */
static __isl_give isl_qpolynomial *gist(__isl_take isl_qpolynomial *qp,
  void *user)
{
  isl_set *context = user;
 
  return isl_qpolynomial_gist(qp, isl_set_copy(context));
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
  __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
{
  isl_qpolynomial_list *list;
 
  list = isl_qpolynomial_fold_take_list(fold);
  list = isl_qpolynomial_list_map(list, &gist, context);
  fold = isl_qpolynomial_fold_restore_list(fold, list);
 
  isl_set_free(context);
  return fold;
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
  __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
{
  isl_space *space = isl_qpolynomial_fold_get_domain_space(fold);
  isl_set *dom_context = isl_set_universe(space);
  dom_context = isl_set_intersect_params(dom_context, context);
  return isl_qpolynomial_fold_gist(fold, dom_context);
}
 
/* Return a zero (i.e., empty) isl_qpolynomial_fold in the given space.
 *
 * This is a helper function for isl_pw_*_as_* that ensures a uniform
 * interface over all piecewise types.
 */
static __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_zero_in_space(
  __isl_take isl_space *space, enum isl_fold type)
{
  return isl_qpolynomial_fold_empty(type, isl_space_domain(space));
}
 
#define isl_qpolynomial_fold_involves_nan isl_qpolynomial_fold_is_nan
 
#define HAS_TYPE
 
#undef PW
#define PW isl_pw_qpolynomial_fold
#undef BASE
#define BASE qpolynomial_fold
#undef EL_IS_ZERO
#define EL_IS_ZERO is_empty
#undef ZERO
#define ZERO zero
#undef IS_ZERO
#define IS_ZERO is_zero
#undef FIELD
#define FIELD fold
#undef DEFAULT_IS_ZERO
#define DEFAULT_IS_ZERO 1
 
#include <isl_pw_templ.c>
#include <isl_pw_add_disjoint_templ.c>
#include <isl_pw_eval.c>
#include <isl_pw_fix_templ.c>
#include <isl_pw_from_range_templ.c>
#include <isl_pw_insert_dims_templ.c>
#include <isl_pw_lift_templ.c>
#include <isl_pw_morph_templ.c>
#include <isl_pw_move_dims_templ.c>
#include <isl_pw_opt_templ.c>
 
#undef BASE
#define BASE pw_qpolynomial_fold
 
#include <isl_union_single.c>
#include <isl_union_eval.c>
 
/* Construct a new reduction of the given type and space
 * with an empty list of polynomials.
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_empty(enum isl_fold type,
  __isl_take isl_space *space)
{
  isl_ctx *ctx;
  isl_qpolynomial_list *list;
 
  if (!space)
    return NULL;
  ctx = isl_space_get_ctx(space);
  list = isl_qpolynomial_list_alloc(ctx, 0);
  return qpolynomial_fold_alloc(type, space, list);
}
 
/* Construct a new reduction of the given type and
 * a single given polynomial.
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_alloc(
  enum isl_fold type, __isl_take isl_qpolynomial *qp)
{
  isl_space *space;
  isl_qpolynomial_list *list;
 
  space = isl_qpolynomial_get_domain_space(qp);
  list = isl_qpolynomial_list_from_qpolynomial(qp);
  return qpolynomial_fold_alloc(type, space, list);
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
  __isl_keep isl_qpolynomial_fold *fold)
{
  if (!fold)
    return NULL;
 
  fold->ref++;
  return fold;
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_dup(
  __isl_keep isl_qpolynomial_fold *fold)
{
  enum isl_fold type;
  isl_space *space;
  isl_qpolynomial_list *list;
 
  type = isl_qpolynomial_fold_get_type(fold);
  space = isl_qpolynomial_fold_get_domain_space(fold);
  list = isl_qpolynomial_fold_get_list(fold);
  return qpolynomial_fold_alloc(type, space, list);
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_cow(
  __isl_take isl_qpolynomial_fold *fold)
{
  if (!fold)
    return NULL;
 
  if (fold->ref == 1)
    return fold;
  fold->ref--;
  return isl_qpolynomial_fold_dup(fold);
}
 
__isl_null isl_qpolynomial_fold *isl_qpolynomial_fold_free(
  __isl_take isl_qpolynomial_fold *fold)
{
  if (!fold)
    return NULL;
  if (--fold->ref > 0)
    return NULL;
 
  isl_qpolynomial_list_free(fold->list);
  isl_space_free(fold->dim);
  free(fold);
 
  return NULL;
}
 
isl_bool isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold *fold)
{
  isl_size n;
  isl_qpolynomial_list *list;
 
  list = isl_qpolynomial_fold_peek_list(fold);
  n = isl_qpolynomial_list_size(list);
  if (n < 0)
    return isl_bool_error;
 
  return isl_bool_ok(n == 0);
}
 
/* Does "fold" represent max(NaN) or min(NaN)?
 */
isl_bool isl_qpolynomial_fold_is_nan(__isl_keep isl_qpolynomial_fold *fold)
{
  isl_size n;
  isl_qpolynomial *qp;
  isl_qpolynomial_list *list;
 
  list = isl_qpolynomial_fold_peek_list(fold);
  n = isl_qpolynomial_list_size(list);
  if (n < 0)
    return isl_bool_error;
  if (n != 1)
    return isl_bool_false;
  qp = isl_qpolynomial_list_peek(list, 0);
  return isl_qpolynomial_is_nan(qp);
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold(
  __isl_take isl_qpolynomial_fold *fold1,
  __isl_take isl_qpolynomial_fold *fold2)
{
  isl_qpolynomial_list *list1, *list2;
 
  if (isl_qpolynomial_fold_check_equal_type(fold1, fold2) < 0)
    goto error;
  if (isl_qpolynomial_fold_check_equal_space(fold1, fold2) < 0)
    goto error;
 
  if (isl_qpolynomial_fold_is_empty(fold1)) {
    isl_qpolynomial_fold_free(fold1);
    return fold2;
  }
 
  if (isl_qpolynomial_fold_is_empty(fold2)) {
    isl_qpolynomial_fold_free(fold2);
    return fold1;
  }
 
  list1 = isl_qpolynomial_fold_take_list(fold1);
  list2 = isl_qpolynomial_fold_take_list(fold2);
  list1 = isl_qpolynomial_list_concat(list1, list2);
  fold1 = isl_qpolynomial_fold_restore_list(fold1, list1);
  isl_qpolynomial_fold_free(fold2);
 
  return fold1;
error:
  isl_qpolynomial_fold_free(fold1);
  isl_qpolynomial_fold_free(fold2);
  return NULL;
}
 
__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
  __isl_take isl_pw_qpolynomial_fold *pw1,
  __isl_take isl_pw_qpolynomial_fold *pw2)
{
  int i, j, n;
  struct isl_pw_qpolynomial_fold *res;
  isl_set *set;
 
  if (!pw1 || !pw2)
    goto error;
 
  isl_assert(pw1->dim->ctx, isl_space_is_equal(pw1->dim, pw2->dim), goto error);
 
  if (isl_pw_qpolynomial_fold_is_zero(pw1)) {
    isl_pw_qpolynomial_fold_free(pw1);
    return pw2;
  }
 
  if (isl_pw_qpolynomial_fold_is_zero(pw2)) {
    isl_pw_qpolynomial_fold_free(pw2);
    return pw1;
  }
 
  if (pw1->type != pw2->type)
    isl_die(pw1->dim->ctx, isl_error_invalid,
      "fold types don't match", goto error);
 
  n = (pw1->n + 1) * (pw2->n + 1);
  res = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pw1->dim),
            pw1->type, n);
 
  for (i = 0; i < pw1->n; ++i) {
    set = isl_set_copy(pw1->p[i].set);
    for (j = 0; j < pw2->n; ++j) {
      struct isl_set *common;
      isl_qpolynomial_fold *sum;
      set = isl_set_subtract(set,
          isl_set_copy(pw2->p[j].set));
      common = isl_set_intersect(isl_set_copy(pw1->p[i].set),
            isl_set_copy(pw2->p[j].set));
      if (isl_set_plain_is_empty(common)) {
        isl_set_free(common);
        continue;
      }
 
      sum = isl_qpolynomial_fold_fold_on_domain(common,
             isl_qpolynomial_fold_copy(pw1->p[i].fold),
             isl_qpolynomial_fold_copy(pw2->p[j].fold));
 
      res = isl_pw_qpolynomial_fold_add_piece(res, common, sum);
    }
    res = isl_pw_qpolynomial_fold_add_piece(res, set,
      isl_qpolynomial_fold_copy(pw1->p[i].fold));
  }
 
  for (j = 0; j < pw2->n; ++j) {
    set = isl_set_copy(pw2->p[j].set);
    for (i = 0; i < pw1->n; ++i)
      set = isl_set_subtract(set, isl_set_copy(pw1->p[i].set));
    res = isl_pw_qpolynomial_fold_add_piece(res, set,
            isl_qpolynomial_fold_copy(pw2->p[j].fold));
  }
 
  isl_pw_qpolynomial_fold_free(pw1);
  isl_pw_qpolynomial_fold_free(pw2);
 
  return res;
error:
  isl_pw_qpolynomial_fold_free(pw1);
  isl_pw_qpolynomial_fold_free(pw2);
  return NULL;
}
 
__isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
  __isl_take isl_union_pw_qpolynomial_fold *u,
  __isl_take isl_pw_qpolynomial_fold *part)
{
  struct isl_hash_table_entry *entry;
 
  u = isl_union_pw_qpolynomial_fold_cow(u);
 
  if (!part || !u)
    goto error;
  if (isl_space_check_equal_params(part->dim, u->space) < 0)
    goto error;
 
  entry = isl_union_pw_qpolynomial_fold_find_part_entry(u, part->dim, 1);
  if (!entry)
    goto error;
 
  if (!entry->data)
    entry->data = part;
  else {
    entry->data = isl_pw_qpolynomial_fold_fold(entry->data,
              isl_pw_qpolynomial_fold_copy(part));
    if (!entry->data)
      goto error;
    isl_pw_qpolynomial_fold_free(part);
  }
 
  return u;
error:
  isl_pw_qpolynomial_fold_free(part);
  isl_union_pw_qpolynomial_fold_free(u);
  return NULL;
}
 
static isl_stat fold_part(__isl_take isl_pw_qpolynomial_fold *part, void *user)
{
  isl_union_pw_qpolynomial_fold **u;
  u = (isl_union_pw_qpolynomial_fold **)user;
 
  *u = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(*u, part);
 
  return isl_stat_ok;
}
 
__isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
  __isl_take isl_union_pw_qpolynomial_fold *u1,
  __isl_take isl_union_pw_qpolynomial_fold *u2)
{
  u1 = isl_union_pw_qpolynomial_fold_cow(u1);
 
  if (!u1 || !u2)
    goto error;
 
  if (isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(u2,
              &fold_part, &u1) < 0)
    goto error;
 
  isl_union_pw_qpolynomial_fold_free(u2);
 
  return u1;
error:
  isl_union_pw_qpolynomial_fold_free(u1);
  isl_union_pw_qpolynomial_fold_free(u2);
  return NULL;
}
 
__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_from_pw_qpolynomial(
  enum isl_fold type, __isl_take isl_pw_qpolynomial *pwqp)
{
  int i;
  isl_pw_qpolynomial_fold *pwf;
 
  if (!pwqp)
    return NULL;
  
  pwf = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pwqp->dim),
            type, pwqp->n);
 
  for (i = 0; i < pwqp->n; ++i)
    pwf = isl_pw_qpolynomial_fold_add_piece(pwf,
      isl_set_copy(pwqp->p[i].set),
      isl_qpolynomial_fold_alloc(type,
        isl_qpolynomial_copy(pwqp->p[i].qp)));
 
  isl_pw_qpolynomial_free(pwqp);
 
  return pwf;
}
 
__isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
  __isl_take isl_pw_qpolynomial_fold *pwf1,
  __isl_take isl_pw_qpolynomial_fold *pwf2)
{
  return isl_pw_qpolynomial_fold_union_add_(pwf1, pwf2);
}
 
/* Compare two quasi-polynomial reductions.
 *
 * Return -1 if "fold1" is "smaller" than "fold2", 1 if "fold1" is "greater"
 * than "fold2" and 0 if they are equal.
 */
int isl_qpolynomial_fold_plain_cmp(__isl_keep isl_qpolynomial_fold *fold1,
  __isl_keep isl_qpolynomial_fold *fold2)
{
  int i;
  isl_size n1, n2;
  isl_qpolynomial_list *list1, *list2;
 
  if (fold1 == fold2)
    return 0;
  list1 = isl_qpolynomial_fold_peek_list(fold1);
  list2 = isl_qpolynomial_fold_peek_list(fold2);
  n1 = isl_qpolynomial_list_size(list1);
  n2 = isl_qpolynomial_list_size(list2);
  if (n1 < 0)
    return -1;
  if (n2 < 0)
    return 1;
 
  if (n1 != n2)
    return n1 - n2;
 
  for (i = 0; i < n1; ++i) {
    int cmp;
    isl_qpolynomial *qp1, *qp2;
 
    qp1 = isl_qpolynomial_list_peek(list1, i);
    qp2 = isl_qpolynomial_list_peek(list2, i);
    cmp = isl_qpolynomial_plain_cmp(qp1, qp2);
    if (cmp != 0)
      return cmp;
  }
 
  return 0;
}
 
/* Are the lists "list1" and "list2", both consisting of "n" elements
 * obviously equal to each other?
 */
static isl_bool isl_qpolynomial_list_plain_is_equal(unsigned n,
  isl_qpolynomial_list *list1, isl_qpolynomial_list *list2)
{
  int i;
 
  for (i = 0; i < n; ++i) {
    isl_bool eq;
    isl_qpolynomial *qp1, *qp2;
 
    qp1 = isl_qpolynomial_list_peek(list1, i);
    qp2 = isl_qpolynomial_list_peek(list2, i);
    eq = isl_qpolynomial_plain_is_equal(qp1, qp2);
    if (eq < 0 || !eq)
      return eq;
  }
 
  return isl_bool_true;
}
 
/* Wrapper around isl_qpolynomial_plain_cmp for use
 * as a isl_qpolynomial_list_sort callback.
 */
static int qpolynomial_cmp(__isl_keep isl_qpolynomial *a,
  __isl_keep isl_qpolynomial *b, void *user)
{
  return isl_qpolynomial_plain_cmp(a, b);
}
 
isl_bool isl_qpolynomial_fold_plain_is_equal(
  __isl_keep isl_qpolynomial_fold *fold1,
  __isl_keep isl_qpolynomial_fold *fold2)
{
  isl_bool equal;
  isl_size n1, n2;
  isl_qpolynomial_list *list1, *list2;
 
  list1 = isl_qpolynomial_fold_peek_list(fold1);
  list2 = isl_qpolynomial_fold_peek_list(fold2);
  n1 = isl_qpolynomial_list_size(list1);
  n2 = isl_qpolynomial_list_size(list2);
  if (n1 < 0 || n2 < 0)
    return isl_bool_error;
 
  if (n1 != n2)
    return isl_bool_false;
 
  list1 = isl_qpolynomial_list_copy(list1);
  list1 = isl_qpolynomial_list_sort(list1, &qpolynomial_cmp, NULL);
  list2 = isl_qpolynomial_list_copy(list2);
  list2 = isl_qpolynomial_list_sort(list2, &qpolynomial_cmp, NULL);
  equal = isl_qpolynomial_list_plain_is_equal(n1, list1, list2);
  isl_qpolynomial_list_free(list1);
  isl_qpolynomial_list_free(list2);
  return equal;
}
 
__isl_give isl_val *isl_qpolynomial_fold_eval(
  __isl_take isl_qpolynomial_fold *fold, __isl_take isl_point *pnt)
{
  isl_size n;
  isl_ctx *ctx;
  isl_val *v;
  isl_qpolynomial *qp;
  isl_qpolynomial_list *list;
 
  if (!fold || !pnt)
    goto error;
  ctx = isl_point_get_ctx(pnt);
  isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, fold->dim), goto error);
  isl_assert(pnt->dim->ctx,
    fold->type == isl_fold_max || fold->type == isl_fold_min,
    goto error);
 
  list = isl_qpolynomial_fold_peek_list(fold);
  n = isl_qpolynomial_list_size(list);
  if (n < 0)
    goto error;
 
  if (n == 0)
    v = isl_val_zero(ctx);
  else {
    int i;
 
    qp = isl_qpolynomial_list_get_at(list, 0);
    v = isl_qpolynomial_eval(qp, isl_point_copy(pnt));
    for (i = 1; i < n; ++i) {
      isl_val *v_i;
 
      qp = isl_qpolynomial_list_get_at(list, i);
      v_i = isl_qpolynomial_eval(qp, isl_point_copy(pnt));
      if (fold->type == isl_fold_max)
        v = isl_val_max(v, v_i);
      else
        v = isl_val_min(v, v_i);
    }
  }
  isl_qpolynomial_fold_free(fold);
  isl_point_free(pnt);
 
  return v;
error:
  isl_qpolynomial_fold_free(fold);
  isl_point_free(pnt);
  return NULL;
}
 
size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold *pwf)
{
  int i;
  size_t n = 0;
 
  for (i = 0; i < pwf->n; ++i) {
    isl_size n_i;
    isl_qpolynomial_list *list;
 
    list = isl_qpolynomial_fold_peek_list(pwf->p[i].fold);
    n_i = isl_qpolynomial_list_size(list);
    if (n_i < 0)
      return isl_size_error;
 
    n += n_i;
  }
 
  return n;
}
 
__isl_give isl_val *isl_qpolynomial_fold_opt_on_domain(
  __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *set, int max)
{
  int i;
  isl_size n;
  isl_val *opt;
  isl_qpolynomial *qp;
  isl_qpolynomial_list *list;
 
  list = isl_qpolynomial_fold_peek_list(fold);
  n = isl_qpolynomial_list_size(list);
  if (!set || n < 0)
    goto error;
 
  if (n == 0) {
    opt = isl_val_zero(isl_set_get_ctx(set));
    isl_set_free(set);
    isl_qpolynomial_fold_free(fold);
    return opt;
  }
 
  qp = isl_qpolynomial_list_get_at(list, 0);
  opt = isl_qpolynomial_opt_on_domain(qp, isl_set_copy(set), max);
  for (i = 1; i < n; ++i) {
    isl_val *opt_i;
 
    qp = isl_qpolynomial_list_get_at(list, i);
    opt_i = isl_qpolynomial_opt_on_domain(qp,
        isl_set_copy(set), max);
    if (max)
      opt = isl_val_max(opt, opt_i);
    else
      opt = isl_val_min(opt, opt_i);
  }
 
  isl_set_free(set);
  isl_qpolynomial_fold_free(fold);
 
  return opt;
error:
  isl_set_free(set);
  isl_qpolynomial_fold_free(fold);
  return NULL;
}
 
/* Check whether for each quasi-polynomial in "fold2" there is
 * a quasi-polynomial in "fold1" that dominates it on "set".
 */
static isl_bool qpolynomial_fold_covers_on_domain(__isl_keep isl_set *set,
  __isl_keep isl_qpolynomial_fold *fold1,
  __isl_keep isl_qpolynomial_fold *fold2)
{
  int i, j;
  int covers;
  isl_size n1, n2;
  isl_qpolynomial_list *list1, *list2;
 
  list1 = isl_qpolynomial_fold_peek_list(fold1);
  list2 = isl_qpolynomial_fold_peek_list(fold2);
  n1 = isl_qpolynomial_list_size(list1);
  n2 = isl_qpolynomial_list_size(list2);
  if (!set || n1 < 0 || n2 < 0)
    return isl_bool_error;
 
  covers = fold1->type == isl_fold_max ? 1 : -1;
 
  for (i = 0; i < n2; ++i) {
    for (j = 0; j < n1; ++j) {
      isl_qpolynomial *qp1, *qp2, *d;
      int sgn;
 
      qp1 = isl_qpolynomial_list_get_at(list1, j);
      qp2 = isl_qpolynomial_list_get_at(list2, i);
      d = isl_qpolynomial_sub(qp1, qp2);
      sgn = isl_qpolynomial_sign(set, d);
      isl_qpolynomial_free(d);
      if (sgn == covers)
        break;
    }
    if (j >= n1)
      return isl_bool_false;
  }
 
  return isl_bool_true;
}
 
/* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
 * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
 * that of pwf2.
 */
isl_bool isl_pw_qpolynomial_fold_covers(
  __isl_keep isl_pw_qpolynomial_fold *pwf1,
  __isl_keep isl_pw_qpolynomial_fold *pwf2)
{
  int i, j;
  isl_set *dom1, *dom2;
  isl_bool is_subset;
 
  if (!pwf1 || !pwf2)
    return isl_bool_error;
 
  if (pwf2->n == 0)
    return isl_bool_true;
  if (pwf1->n == 0)
    return isl_bool_false;
 
  dom1 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1));
  dom2 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2));
  is_subset = isl_set_is_subset(dom2, dom1);
  isl_set_free(dom1);
  isl_set_free(dom2);
 
  if (is_subset < 0 || !is_subset)
    return is_subset;
 
  for (i = 0; i < pwf2->n; ++i) {
    for (j = 0; j < pwf1->n; ++j) {
      isl_bool is_empty;
      isl_set *common;
      isl_bool covers;
 
      common = isl_set_intersect(isl_set_copy(pwf1->p[j].set),
               isl_set_copy(pwf2->p[i].set));
      is_empty = isl_set_is_empty(common);
      if (is_empty < 0 || is_empty) {
        isl_set_free(common);
        if (is_empty < 0)
          return isl_bool_error;
        continue;
      }
      covers = qpolynomial_fold_covers_on_domain(common,
          pwf1->p[j].fold, pwf2->p[i].fold);
      isl_set_free(common);
      if (covers < 0 || !covers)
        return covers;
    }
  }
 
  return isl_bool_true;
}
 
/* isl_qpolynomial_list_map callback that calls
 * isl_qpolynomial_morph_domain on "qp".
 */
static __isl_give isl_qpolynomial *morph_domain(
  __isl_take isl_qpolynomial *qp, void *user)
{
  isl_morph *morph = user;
 
  return isl_qpolynomial_morph_domain(qp, isl_morph_copy(morph));
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_morph_domain(
  __isl_take isl_qpolynomial_fold *fold, __isl_take isl_morph *morph)
{
  isl_space *space;
  isl_qpolynomial_list *list;
 
  space = isl_qpolynomial_fold_peek_domain_space(fold);
  if (isl_morph_check_applies(morph, space) < 0)
    goto error;
 
  list = isl_qpolynomial_fold_take_list(fold);
  list = isl_qpolynomial_list_map(list, &morph_domain, morph);
  fold = isl_qpolynomial_fold_restore_list(fold, list);
 
  space = isl_morph_get_ran_space(morph);
  isl_space_free(isl_qpolynomial_fold_take_domain_space(fold));
  fold = isl_qpolynomial_fold_restore_domain_space(fold, space);
 
  isl_morph_free(morph);
 
  return fold;
error:
  isl_qpolynomial_fold_free(fold);
  isl_morph_free(morph);
  return NULL;
}
 
enum isl_fold isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold *fold)
{
  if (!fold)
    return isl_fold_error;
  return fold->type;
}
 
/* Return the type of this piecewise quasipolynomial reduction.
 */
enum isl_fold isl_pw_qpolynomial_fold_get_type(
  __isl_keep isl_pw_qpolynomial_fold *pwf)
{
  if (!pwf)
    return isl_fold_error;
  return pwf->type;
}
 
enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
  __isl_keep isl_union_pw_qpolynomial_fold *upwf)
{
  if (!upwf)
    return isl_fold_error;
  return upwf->type;
}
 
/* isl_qpolynomial_list_map callback that calls
 * isl_qpolynomial_lift on "qp".
 */
static __isl_give isl_qpolynomial *lift(__isl_take isl_qpolynomial *qp,
  void *user)
{
  isl_space *space = user;
 
  return isl_qpolynomial_lift(qp, isl_space_copy(space));
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_lift(
  __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *space)
{
  isl_qpolynomial_list *list;
 
  if (!fold || !space)
    goto error;
 
  if (isl_space_is_equal(fold->dim, space)) {
    isl_space_free(space);
    return fold;
  }
 
  list = isl_qpolynomial_fold_take_list(fold);
  list = isl_qpolynomial_list_map(list, &lift, space);
  fold = isl_qpolynomial_fold_restore_list(fold, list);
 
  isl_space_free(isl_qpolynomial_fold_take_domain_space(fold));
  fold = isl_qpolynomial_fold_restore_domain_space(fold, space);
 
  return fold;
error:
  isl_qpolynomial_fold_free(fold);
  isl_space_free(space);
  return NULL;
}
 
isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
  __isl_keep isl_qpolynomial_fold *fold,
  isl_stat (*fn)(__isl_take isl_qpolynomial *qp, void *user), void *user)
{
  isl_qpolynomial_list *list;
 
  list = isl_qpolynomial_fold_peek_list(fold);
  return isl_qpolynomial_list_foreach(list, fn, user);
}
 
/* Internal data structure for isl_qpolynomial_fold_move_dims
 * representing its arguments.
 */
struct isl_fold_move_dims_data {
  enum isl_dim_type dst_type;
  unsigned dst_pos;
  enum isl_dim_type src_type;
  unsigned src_pos;
  unsigned n;
};
 
/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_move_dims on "qp".
 */
static __isl_give isl_qpolynomial *move_dims(__isl_take isl_qpolynomial *qp,
  void *user)
{
  struct isl_fold_move_dims_data *data = user;
 
  qp = isl_qpolynomial_move_dims(qp, data->dst_type, data->dst_pos,
          data->src_type, data->src_pos, data->n);
  return qp;
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_move_dims(
  __isl_take isl_qpolynomial_fold *fold,
  enum isl_dim_type dst_type, unsigned dst_pos,
  enum isl_dim_type src_type, unsigned src_pos, unsigned n)
{
  struct isl_fold_move_dims_data data =
    { dst_type, dst_pos, src_type, src_pos, n };
  enum isl_dim_type set_src_type, set_dst_type;
  isl_space *space;
  isl_qpolynomial_list *list;
 
  if (n == 0)
    return fold;
 
  fold = isl_qpolynomial_fold_cow(fold);
  if (!fold)
    return NULL;
 
  set_src_type = domain_type(src_type);
  set_dst_type = domain_type(dst_type);
 
  list = isl_qpolynomial_fold_take_list(fold);
  list = isl_qpolynomial_list_map(list, &move_dims, &data);
  fold = isl_qpolynomial_fold_restore_list(fold, list);
 
  space = isl_qpolynomial_fold_take_domain_space(fold);
  space = isl_space_move_dims(space, set_dst_type, dst_pos,
            set_src_type, src_pos, n);
  fold = isl_qpolynomial_fold_restore_domain_space(fold, space);
 
  return fold;
}
 
/* Internal data structure for isl_qpolynomial_fold_substitute
 * representing its arguments.
 */
struct isl_fold_substitute {
  enum isl_dim_type type;
  unsigned first;
  unsigned n;
  isl_qpolynomial **subs;
};
 
/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_substitute on "qp".
 */
static __isl_give isl_qpolynomial *substitute(__isl_take isl_qpolynomial *qp,
  void *user)
{
  struct isl_fold_substitute *data = user;
 
  qp = isl_qpolynomial_substitute(qp,
        data->type, data->first, data->n, data->subs);
  return qp;
}
 
/* For each 0 <= i < "n", replace variable "first" + i of type "type"
 * in fold->qp[k] by subs[i].
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute(
  __isl_take isl_qpolynomial_fold *fold,
  enum isl_dim_type type, unsigned first, unsigned n,
  __isl_keep isl_qpolynomial **subs)
{
  struct isl_fold_substitute data = { type, first, n, subs };
  isl_qpolynomial_list *list;
 
  if (n == 0)
    return fold;
 
  list = isl_qpolynomial_fold_take_list(fold);
  list = isl_qpolynomial_list_map(list, &substitute, &data);
  fold = isl_qpolynomial_fold_restore_list(fold, list);
 
  return fold;
}
 
static isl_stat add_pwqp(__isl_take isl_pw_qpolynomial *pwqp, void *user)
{
  isl_pw_qpolynomial_fold *pwf;
  isl_union_pw_qpolynomial_fold **upwf;
  struct isl_hash_table_entry *entry;
 
  upwf = (isl_union_pw_qpolynomial_fold **)user;
 
  entry = isl_union_pw_qpolynomial_fold_find_part_entry(*upwf,
       pwqp->dim, 1);
  if (!entry)
    goto error;
 
  pwf = isl_pw_qpolynomial_fold_from_pw_qpolynomial((*upwf)->type, pwqp);
  if (!entry->data)
    entry->data = pwf;
  else {
    entry->data = isl_pw_qpolynomial_fold_add(entry->data, pwf);
    if (!entry->data)
      return isl_stat_error;
    if (isl_pw_qpolynomial_fold_is_zero(entry->data))
      *upwf = isl_union_pw_qpolynomial_fold_remove_part_entry(
                *upwf, entry);
  }
 
  return isl_stat_ok;
error:
  isl_pw_qpolynomial_free(pwqp);
  return isl_stat_error;
}
 
__isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_add_union_pw_qpolynomial(
  __isl_take isl_union_pw_qpolynomial_fold *upwf,
  __isl_take isl_union_pw_qpolynomial *upwqp)
{
  upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
        isl_union_pw_qpolynomial_get_space(upwqp));
  upwqp = isl_union_pw_qpolynomial_align_params(upwqp,
        isl_union_pw_qpolynomial_fold_get_space(upwf));
 
  upwf = isl_union_pw_qpolynomial_fold_cow(upwf);
  if (!upwf || !upwqp)
    goto error;
 
  if (isl_union_pw_qpolynomial_foreach_pw_qpolynomial(upwqp, &add_pwqp,
               &upwf) < 0)
    goto error;
 
  isl_union_pw_qpolynomial_free(upwqp);
 
  return upwf;
error:
  isl_union_pw_qpolynomial_fold_free(upwf);
  isl_union_pw_qpolynomial_free(upwqp);
  return NULL;
}
 
static isl_bool join_compatible(__isl_keep isl_space *space1,
  __isl_keep isl_space *space2)
{
  isl_bool m;
  m = isl_space_has_equal_params(space1, space2);
  if (m < 0 || !m)
    return m;
  return isl_space_tuple_is_equal(space1, isl_dim_out,
          space2, isl_dim_in);
}
 
/* Compute the intersection of the range of the map and the domain
 * of the piecewise quasipolynomial reduction and then compute a bound
 * on the associated quasipolynomial reduction over all elements
 * in this intersection.
 *
 * We first introduce some unconstrained dimensions in the
 * piecewise quasipolynomial, intersect the resulting domain
 * with the wrapped map and the compute the sum.
 */
__isl_give isl_pw_qpolynomial_fold *isl_map_apply_pw_qpolynomial_fold(
  __isl_take isl_map *map, __isl_take isl_pw_qpolynomial_fold *pwf,
  isl_bool *tight)
{
  isl_ctx *ctx;
  isl_set *dom;
  isl_space *map_space;
  isl_space *pwf_space;
  isl_size n_in;
  isl_bool ok;
 
  ctx = isl_map_get_ctx(map);
  if (!ctx)
    goto error;
 
  map_space = isl_map_get_space(map);
  pwf_space = isl_pw_qpolynomial_fold_get_space(pwf);
  ok = join_compatible(map_space, pwf_space);
  isl_space_free(map_space);
  isl_space_free(pwf_space);
  if (ok < 0)
    goto error;
  if (!ok)
    isl_die(ctx, isl_error_invalid, "incompatible dimensions",
      goto error);
 
  n_in = isl_map_dim(map, isl_dim_in);
  if (n_in < 0)
    goto error;
  pwf = isl_pw_qpolynomial_fold_insert_dims(pwf, isl_dim_in, 0, n_in);
 
  dom = isl_map_wrap(map);
  pwf = isl_pw_qpolynomial_fold_reset_domain_space(pwf,
            isl_set_get_space(dom));
 
  pwf = isl_pw_qpolynomial_fold_intersect_domain(pwf, dom);
  pwf = isl_pw_qpolynomial_fold_bound(pwf, tight);
  
  return pwf;
error:
  isl_map_free(map);
  isl_pw_qpolynomial_fold_free(pwf);
  return NULL;
}
 
__isl_give isl_pw_qpolynomial_fold *isl_set_apply_pw_qpolynomial_fold(
  __isl_take isl_set *set, __isl_take isl_pw_qpolynomial_fold *pwf,
  isl_bool *tight)
{
  return isl_map_apply_pw_qpolynomial_fold(set, pwf, tight);
}
 
struct isl_apply_fold_data {
  isl_union_pw_qpolynomial_fold *upwf;
  isl_union_pw_qpolynomial_fold *res;
  isl_map *map;
  isl_bool tight;
};
 
static isl_stat pw_qpolynomial_fold_apply(
  __isl_take isl_pw_qpolynomial_fold *pwf, void *user)
{
  isl_space *map_dim;
  isl_space *pwf_dim;
  struct isl_apply_fold_data *data = user;
  isl_bool ok;
 
  map_dim = isl_map_get_space(data->map);
  pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
  ok = join_compatible(map_dim, pwf_dim);
  isl_space_free(map_dim);
  isl_space_free(pwf_dim);
 
  if (ok < 0)
    return isl_stat_error;
  if (ok) {
    pwf = isl_map_apply_pw_qpolynomial_fold(isl_map_copy(data->map),
            pwf, data->tight ? &data->tight : NULL);
    data->res = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
              data->res, pwf);
  } else
    isl_pw_qpolynomial_fold_free(pwf);
 
  return isl_stat_ok;
}
 
static isl_stat map_apply(__isl_take isl_map *map, void *user)
{
  struct isl_apply_fold_data *data = user;
  isl_stat r;
 
  data->map = map;
  r = isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
        data->upwf, &pw_qpolynomial_fold_apply, data);
 
  isl_map_free(map);
  return r;
}
 
__isl_give isl_union_pw_qpolynomial_fold *isl_union_map_apply_union_pw_qpolynomial_fold(
  __isl_take isl_union_map *umap,
  __isl_take isl_union_pw_qpolynomial_fold *upwf, isl_bool *tight)
{
  isl_space *space;
  enum isl_fold type;
  struct isl_apply_fold_data data;
 
  upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
        isl_union_map_get_space(umap));
  umap = isl_union_map_align_params(umap,
        isl_union_pw_qpolynomial_fold_get_space(upwf));
 
  data.upwf = upwf;
  data.tight = tight ? isl_bool_true : isl_bool_false;
  space = isl_union_pw_qpolynomial_fold_get_space(upwf);
  type = isl_union_pw_qpolynomial_fold_get_type(upwf);
  data.res = isl_union_pw_qpolynomial_fold_zero(space, type);
  if (isl_union_map_foreach_map(umap, &map_apply, &data) < 0)
    goto error;
 
  isl_union_map_free(umap);
  isl_union_pw_qpolynomial_fold_free(upwf);
 
  if (tight)
    *tight = data.tight;
 
  return data.res;
error:
  isl_union_map_free(umap);
  isl_union_pw_qpolynomial_fold_free(upwf);
  isl_union_pw_qpolynomial_fold_free(data.res);
  return NULL;
}
 
__isl_give isl_union_pw_qpolynomial_fold *isl_union_set_apply_union_pw_qpolynomial_fold(
  __isl_take isl_union_set *uset,
  __isl_take isl_union_pw_qpolynomial_fold *upwf, isl_bool *tight)
{
  return isl_union_map_apply_union_pw_qpolynomial_fold(uset, upwf, tight);
}
 
/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_realign_domain on "qp".
 */
static __isl_give isl_qpolynomial *realign_domain(
  __isl_take isl_qpolynomial *qp, void *user)
{
  isl_reordering *r = user;
 
  qp = isl_qpolynomial_realign_domain(qp, isl_reordering_copy(r));
  return qp;
}
 
/* Reorder the dimension of "fold" according to the given reordering.
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_realign_domain(
  __isl_take isl_qpolynomial_fold *fold, __isl_take isl_reordering *r)
{
  isl_space *space;
  isl_qpolynomial_list *list;
 
  list = isl_qpolynomial_fold_take_list(fold);
  list = isl_qpolynomial_list_map(list, &realign_domain, r);
  fold = isl_qpolynomial_fold_restore_list(fold, list);
 
  space = isl_reordering_get_space(r);
  fold = isl_qpolynomial_fold_reset_domain_space(fold, space);
 
  isl_reordering_free(r);
 
  return fold;
}
 
/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_mul_isl_int on "qp".
 */
static __isl_give isl_qpolynomial *mul_int(__isl_take isl_qpolynomial *qp,
  void *user)
{
  isl_int *v = user;
 
  qp = isl_qpolynomial_mul_isl_int(qp, *v);
  return qp;
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_mul_isl_int(
  __isl_take isl_qpolynomial_fold *fold, isl_int v)
{
  isl_qpolynomial_list *list;
 
  if (isl_int_is_one(v))
    return fold;
  if (fold && isl_int_is_zero(v)) {
    isl_qpolynomial_fold *zero;
    isl_space *space = isl_space_copy(fold->dim);
    zero = isl_qpolynomial_fold_empty(fold->type, space);
    isl_qpolynomial_fold_free(fold);
    return zero;
  }
 
  fold = isl_qpolynomial_fold_cow(fold);
  if (!fold)
    return NULL;
 
  if (isl_int_is_neg(v))
    fold->type = isl_fold_type_negate(fold->type);
 
  list = isl_qpolynomial_fold_take_list(fold);
  list = isl_qpolynomial_list_map(list, &mul_int, &v);
  fold = isl_qpolynomial_fold_restore_list(fold, list);
 
  return fold;
}
 
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
  __isl_take isl_qpolynomial_fold *fold, isl_int v)
{
  return isl_qpolynomial_fold_mul_isl_int(fold, v);
}
 
/* isl_qpolynomial_list_map callback for calling
 * isl_qpolynomial_scale_val on "qp".
 */
static __isl_give isl_qpolynomial *scale_val(__isl_take isl_qpolynomial *qp,
  void *user)
{
  isl_val *v = user;
 
  qp = isl_qpolynomial_scale_val(qp, isl_val_copy(v));
  return qp;
}
 
/* Multiply "fold" by "v".
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
  __isl_take isl_qpolynomial_fold *fold, __isl_take isl_val *v)
{
  isl_qpolynomial_list *list;
 
  if (!fold || !v)
    goto error;
 
  if (isl_val_is_one(v)) {
    isl_val_free(v);
    return fold;
  }
  if (isl_val_is_zero(v)) {
    isl_qpolynomial_fold *zero;
    isl_space *space = isl_qpolynomial_fold_get_domain_space(fold);
    zero = isl_qpolynomial_fold_empty(fold->type, space);
    isl_qpolynomial_fold_free(fold);
    isl_val_free(v);
    return zero;
  }
  if (!isl_val_is_rat(v))
    isl_die(isl_qpolynomial_fold_get_ctx(fold), isl_error_invalid,
      "expecting rational factor", goto error);
 
  fold = isl_qpolynomial_fold_cow(fold);
  if (!fold)
    goto error;
 
  if (isl_val_is_neg(v))
    fold->type = isl_fold_type_negate(fold->type);
 
  list = isl_qpolynomial_fold_take_list(fold);
  list = isl_qpolynomial_list_map(list, &scale_val, v);
  fold = isl_qpolynomial_fold_restore_list(fold, list);
 
  isl_val_free(v);
  return fold;
error:
  isl_val_free(v);
  isl_qpolynomial_fold_free(fold);
  return NULL;
}
 
/* Divide "fold" by "v".
 */
__isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_down_val(
  __isl_take isl_qpolynomial_fold *fold, __isl_take isl_val *v)
{
  if (!fold || !v)
    goto error;
 
  if (isl_val_is_one(v)) {
    isl_val_free(v);
    return fold;
  }
  if (!isl_val_is_rat(v))
    isl_die(isl_qpolynomial_fold_get_ctx(fold), isl_error_invalid,
      "expecting rational factor", goto error);
  if (isl_val_is_zero(v))
    isl_die(isl_val_get_ctx(v), isl_error_invalid,
      "cannot scale down by zero", goto error);
 
  return isl_qpolynomial_fold_scale_val(fold, isl_val_inv(v));
error:
  isl_val_free(v);
  isl_qpolynomial_fold_free(fold);
  return NULL;
}