text: /*
   * 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());
  }
  
  static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
  	enum isl_fold type, __isl_take isl_space *space, int n)
  {
  	isl_qpolynomial_fold *fold;
  
  	if (!space)
  		goto error;
  
  	isl_assert(space->ctx, n >= 0, goto error);
  	fold = isl_calloc(space->ctx, struct isl_qpolynomial_fold,
  			sizeof(struct isl_qpolynomial_fold) +
  			(n - 1) * sizeof(struct isl_qpolynomial *));
  	if (!fold)
  		goto error;
  
  	fold->ref = 1;
  	fold->size = n;
  	fold->n = 0;
  	fold->type = type;
  	fold->dim = space;
  
  	return fold;
  error:
  	isl_space_free(space);
  	return NULL;
  }
  
  isl_ctx *isl_qpolynomial_fold_get_ctx(__isl_keep isl_qpolynomial_fold *fold)
  {
  	return fold ? fold->dim->ctx : NULL;
  }
  
  __isl_give isl_space *isl_qpolynomial_fold_get_domain_space(
  	__isl_keep isl_qpolynomial_fold *fold)
  {
  	return fold ? isl_space_copy(fold->dim) : 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;
  }
  
  __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_domain_space(
  	__isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
  {
  	int i;
  
  	fold = isl_qpolynomial_fold_cow(fold);
  	if (!fold || !dim)
  		goto error;
  
  	for (i = 0; i < fold->n; ++i) {
  		fold->qp[i] = isl_qpolynomial_reset_domain_space(fold->qp[i],
  							isl_space_copy(dim));
  		if (!fold->qp[i])
  			goto error;
  	}
  
  	isl_space_free(fold->dim);
  	fold->dim = dim;
  
  	return fold;
  error:
  	isl_qpolynomial_fold_free(fold);
  	isl_space_free(dim);
  	return NULL;
  }
  
  /* 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);
  }
  
  int isl_qpolynomial_fold_involves_dims(__isl_keep isl_qpolynomial_fold *fold,
  	enum isl_dim_type type, unsigned first, unsigned n)
  {
  	int i;
  
  	if (!fold)
  		return -1;
  	if (fold->n == 0 || n == 0)
  		return 0;
  
  	for (i = 0; i < fold->n; ++i) {
  		int involves = isl_qpolynomial_involves_dims(fold->qp[i],
  							    type, first, n);
  		if (involves < 0 || involves)
  			return involves;
  	}
  	return 0;
  }
  
  __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)
  {
  	int i;
  
  	fold = isl_qpolynomial_fold_cow(fold);
  	if (!fold)
  		return NULL;
  	fold->dim = isl_space_set_dim_name(fold->dim, type, pos, s);
  	if (!fold->dim)
  		goto error;
  
  	for (i = 0; i < fold->n; ++i) {
  		fold->qp[i] = isl_qpolynomial_set_dim_name(fold->qp[i],
  							    type, pos, s);
  		if (!fold->qp[i])
  			goto error;
  	}
  
  	return fold;
  error:
  	isl_qpolynomial_fold_free(fold);
  	return NULL;
  }
  
  /* 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_drop_dims(
  	__isl_take isl_qpolynomial_fold *fold,
  	enum isl_dim_type type, unsigned first, unsigned n)
  {
  	int i;
  	enum isl_dim_type set_type;
  
  	if (!fold)
  		return NULL;
  	if (n == 0)
  		return fold;
  
  	set_type = domain_type(type);
  
  	fold = isl_qpolynomial_fold_cow(fold);
  	if (!fold)
  		return NULL;
  	fold->dim = isl_space_drop_dims(fold->dim, set_type, first, n);
  	if (!fold->dim)
  		goto error;
  
  	for (i = 0; i < fold->n; ++i) {
  		fold->qp[i] = isl_qpolynomial_drop_dims(fold->qp[i],
  							    type, first, n);
  		if (!fold->qp[i])
  			goto error;
  	}
  
  	return fold;
  error:
  	isl_qpolynomial_fold_free(fold);
  	return NULL;
  }
  
  __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)
  {
  	int i;
  
  	if (!fold)
  		return NULL;
  	if (n == 0 && !isl_space_is_named_or_nested(fold->dim, type))
  		return fold;
  
  	fold = isl_qpolynomial_fold_cow(fold);
  	if (!fold)
  		return NULL;
  	fold->dim = isl_space_insert_dims(fold->dim, type, first, n);
  	if (!fold->dim)
  		goto error;
  
  	for (i = 0; i < fold->n; ++i) {
  		fold->qp[i] = isl_qpolynomial_insert_dims(fold->qp[i],
  							    type, first, n);
  		if (!fold->qp[i])
  			goto error;
  	}
  
  	return fold;
  error:
  	isl_qpolynomial_fold_free(fold);
  	return NULL;
  }
  
  /* 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;
  }
  
  /* 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)
  {
  	int i, j;
  	int n1;
  	struct isl_qpolynomial_fold *res = NULL;
  	int better;
  
  	if (!fold1 || !fold2)
  		goto error;
  
  	isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
  	isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
  			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;
  	}
  
  	res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
  					fold1->n + fold2->n);
  	if (!res)
  		goto error;
  
  	for (i = 0; i < fold1->n; ++i) {
  		res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
  		if (!res->qp[res->n])
  			goto error;
  		res->n++;
  	}
  	n1 = res->n;
  
  	for (i = 0; i < fold2->n; ++i) {
  		for (j = n1 - 1; j >= 0; --j) {
  			isl_qpolynomial *d;
  			int sgn, equal;
  			equal = isl_qpolynomial_plain_is_equal(res->qp[j],
  								fold2->qp[i]);
  			if (equal < 0)
  				goto error;
  			if (equal)
  				break;
  			d = isl_qpolynomial_sub(
  				isl_qpolynomial_copy(res->qp[j]),
  				isl_qpolynomial_copy(fold2->qp[i]));
  			sgn = isl_qpolynomial_sign(set, d);
  			isl_qpolynomial_free(d);
  			if (sgn == 0)
  				continue;
  			if (sgn != better)
  				break;
  			isl_qpolynomial_free(res->qp[j]);
  			if (j != n1 - 1)
  				res->qp[j] = res->qp[n1 - 1];
  			n1--;
  			if (n1 != res->n - 1)
  				res->qp[n1] = res->qp[res->n - 1];
  			res->n--;
  		}
  		if (j >= 0)
  			continue;
  		res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
  		if (!res->qp[res->n])
  			goto error;
  		res->n++;
  	}
  
  	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_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_qpolynomial(
  	__isl_take isl_qpolynomial_fold *fold, __isl_take isl_qpolynomial *qp)
  {
  	int i;
  
  	if (!fold || !qp)
  		goto error;
  
  	if (isl_qpolynomial_is_zero(qp)) {
  		isl_qpolynomial_free(qp);
  		return fold;
  	}
  
  	fold = isl_qpolynomial_fold_cow(fold);
  	if (!fold)
  		goto error;
  
  	for (i = 0; i < fold->n; ++i) {
  		fold->qp[i] = isl_qpolynomial_add(fold->qp[i],
  						isl_qpolynomial_copy(qp));
  		if (!fold->qp[i])
  			goto error;
  	}
  
  	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_qpolynomial_fold *res = NULL;
  
  	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;
  	}
  
  	if (fold1->n == 1 && fold2->n != 1)
  		return isl_qpolynomial_fold_add_on_domain(dom, fold2, fold1);
  
  	if (fold2->n == 1) {
  		res = isl_qpolynomial_fold_add_qpolynomial(fold1,
  					isl_qpolynomial_copy(fold2->qp[0]));
  		isl_qpolynomial_fold_free(fold2);
  		return res;
  	}
  
  	res = isl_qpolynomial_fold_add_qpolynomial(
  				isl_qpolynomial_fold_copy(fold1),
  				isl_qpolynomial_copy(fold2->qp[0]));
  
  	for (i = 1; i < fold2->n; ++i) {
  		isl_qpolynomial_fold *res_i;
  		res_i = isl_qpolynomial_fold_add_qpolynomial(
  					isl_qpolynomial_fold_copy(fold1),
  					isl_qpolynomial_copy(fold2->qp[i]));
  		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_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute_equalities(
  	__isl_take isl_qpolynomial_fold *fold, __isl_take isl_basic_set *eq)
  {
  	int i;
  
  	if (!fold || !eq)
  		goto error;
  
  	fold = isl_qpolynomial_fold_cow(fold);
  	if (!fold)
  		return NULL;
  
  	for (i = 0; i < fold->n; ++i) {
  		fold->qp[i] = isl_qpolynomial_substitute_equalities(fold->qp[i],
  							isl_basic_set_copy(eq));
  		if (!fold->qp[i])
  			goto error;
  	}
  
  	isl_basic_set_free(eq);
  	return fold;
  error:
  	isl_basic_set_free(eq);
  	isl_qpolynomial_fold_free(fold);
  	return NULL;
  }
  
  __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
  	__isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
  {
  	int i;
  
  	if (!fold || !context)
  		goto error;
  
  	fold = isl_qpolynomial_fold_cow(fold);
  	if (!fold)
  		return NULL;
  
  	for (i = 0; i < fold->n; ++i) {
  		fold->qp[i] = isl_qpolynomial_gist(fold->qp[i],
  							isl_set_copy(context));
  		if (!fold->qp[i])
  			goto error;
  	}
  
  	isl_set_free(context);
  	return fold;
  error:
  	isl_set_free(context);
  	isl_qpolynomial_fold_free(fold);
  	return NULL;
  }
  
  __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_eval.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
  
  #define NO_SUB
  
  #include <isl_union_single.c>
  #include <isl_union_eval.c>
  
  __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_empty(enum isl_fold type,
  	__isl_take isl_space *dim)
  {
  	return qpolynomial_fold_alloc(type, dim, 0);
  }
  
  __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_alloc(
  	enum isl_fold type, __isl_take isl_qpolynomial *qp)
  {
  	isl_qpolynomial_fold *fold;
  
  	if (!qp)
  		return NULL;
  
  	fold = qpolynomial_fold_alloc(type, isl_space_copy(qp->dim), 1);
  	if (!fold)
  		goto error;
  
  	fold->qp[0] = qp;
  	fold->n++;
  
  	return fold;
  error:
  	isl_qpolynomial_fold_free(fold);
  	isl_qpolynomial_free(qp);
  	return NULL;
  }
  
  __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)
  {
  	int i;
  	isl_qpolynomial_fold *dup;
  
  	if (!fold)
  		return NULL;
  	dup = qpolynomial_fold_alloc(fold->type,
  					isl_space_copy(fold->dim), fold->n);
  	if (!dup)
  		return NULL;
  	
  	dup->n = fold->n;
  	for (i = 0; i < fold->n; ++i) {
  		dup->qp[i] = isl_qpolynomial_copy(fold->qp[i]);
  		if (!dup->qp[i])
  			goto error;
  	}
  
  	return dup;
  error:
  	isl_qpolynomial_fold_free(dup);
  	return NULL;
  }
  
  __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)
  {
  	int i;
  
  	if (!fold)
  		return NULL;
  	if (--fold->ref > 0)
  		return NULL;
  
  	for (i = 0; i < fold->n; ++i)
  		isl_qpolynomial_free(fold->qp[i]);
  	isl_space_free(fold->dim);
  	free(fold);
  
  	return NULL;
  }
  
  isl_bool isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold *fold)
  {
  	if (!fold)
  		return isl_bool_error;
  
  	return isl_bool_ok(fold->n == 0);
  }
  
  /* Does "fold" represent max(NaN) or min(NaN)?
   */
  isl_bool isl_qpolynomial_fold_is_nan(__isl_keep isl_qpolynomial_fold *fold)
  {
  	if (!fold)
  		return isl_bool_error;
  	if (fold->n != 1)
  		return isl_bool_false;
  	return isl_qpolynomial_is_nan(fold->qp[0]);
  }
  
  __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold(
  	__isl_take isl_qpolynomial_fold *fold1,
  	__isl_take isl_qpolynomial_fold *fold2)
  {
  	int i;
  	struct isl_qpolynomial_fold *res = NULL;
  
  	if (!fold1 || !fold2)
  		goto error;
  
  	isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
  	isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
  			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;
  	}
  
  	res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
  					fold1->n + fold2->n);
  	if (!res)
  		goto error;
  
  	for (i = 0; i < fold1->n; ++i) {
  		res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
  		if (!res->qp[res->n])
  			goto error;
  		res->n++;
  	}
  
  	for (i = 0; i < fold2->n; ++i) {
  		res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
  		if (!res->qp[res->n])
  			goto error;
  		res->n++;
  	}
  
  	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_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;
  
  	if (fold1 == fold2)
  		return 0;
  	if (!fold1)
  		return -1;
  	if (!fold2)
  		return 1;
  
  	if (fold1->n != fold2->n)
  		return fold1->n - fold2->n;
  
  	for (i = 0; i < fold1->n; ++i) {
  		int cmp;
  
  		cmp = isl_qpolynomial_plain_cmp(fold1->qp[i], fold2->qp[i]);
  		if (cmp != 0)
  			return cmp;
  	}
  
  	return 0;
  }
  
  int isl_qpolynomial_fold_plain_is_equal(__isl_keep isl_qpolynomial_fold *fold1,
  	__isl_keep isl_qpolynomial_fold *fold2)
  {
  	int i;
  
  	if (!fold1 || !fold2)
  		return -1;
  
  	if (fold1->n != fold2->n)
  		return 0;
  
  	/* We probably want to sort the qps first... */
  	for (i = 0; i < fold1->n; ++i) {
  		int eq = isl_qpolynomial_plain_is_equal(fold1->qp[i], fold2->qp[i]);
  		if (eq < 0 || !eq)
  			return eq;
  	}
  
  	return 1;
  }
  
  __isl_give isl_val *isl_qpolynomial_fold_eval(
  	__isl_take isl_qpolynomial_fold *fold, __isl_take isl_point *pnt)
  {
  	isl_ctx *ctx;
  	isl_val *v;
  
  	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);
  
  	if (fold->n == 0)
  		v = isl_val_zero(ctx);
  	else {
  		int i;
  		v = isl_qpolynomial_eval(isl_qpolynomial_copy(fold->qp[0]),
  						isl_point_copy(pnt));
  		for (i = 1; i < fold->n; ++i) {
  			isl_val *v_i;
  			v_i = isl_qpolynomial_eval(
  					    isl_qpolynomial_copy(fold->qp[i]),
  					    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)
  		n += pwf->p[i].fold->n;
  
  	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_val *opt;
  
  	if (!set || !fold)
  		goto error;
  
  	if (fold->n == 0) {
  		opt = isl_val_zero(isl_set_get_ctx(set));
  		isl_set_free(set);
  		isl_qpolynomial_fold_free(fold);
  		return opt;
  	}
  
  	opt = isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold->qp[0]),
  						isl_set_copy(set), max);
  	for (i = 1; i < fold->n; ++i) {
  		isl_val *opt_i;
  		opt_i = isl_qpolynomial_opt_on_domain(
  				isl_qpolynomial_copy(fold->qp[i]),
  				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;
  
  	if (!set || !fold1 || !fold2)
  		return isl_bool_error;
  
  	covers = fold1->type == isl_fold_max ? 1 : -1;
  
  	for (i = 0; i < fold2->n; ++i) {
  		for (j = 0; j < fold1->n; ++j) {
  			isl_qpolynomial *d;
  			int sgn;
  
  			d = isl_qpolynomial_sub(
  				isl_qpolynomial_copy(fold1->qp[j]),
  				isl_qpolynomial_copy(fold2->qp[i]));
  			sgn = isl_qpolynomial_sign(set, d);
  			isl_qpolynomial_free(d);
  			if (sgn == covers)
  				break;
  		}
  		if (j >= fold1->n)
  			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_give isl_qpolynomial_fold *isl_qpolynomial_fold_morph_domain(
  	__isl_take isl_qpolynomial_fold *fold, __isl_take isl_morph *morph)
  {
  	int i;
  	isl_ctx *ctx;
  
  	if (!fold || !morph)
  		goto error;
  
  	ctx = fold->dim->ctx;
  	isl_assert(ctx, isl_space_is_equal(fold->dim, morph->dom->dim), goto error);
  
  	fold = isl_qpolynomial_fold_cow(fold);
  	if (!fold)
  		goto error;
  
  	isl_space_free(fold->dim);
  	fold->dim = isl_space_copy(morph->ran->dim);
  	if (!fold->dim)
  		goto error;
  
  	for (i = 0; i < fold->n; ++i) {
  		fold->qp[i] = isl_qpolynomial_morph_domain(fold->qp[i],
  						isl_morph_copy(morph));
  		if (!fold->qp[i])
  			goto error;
  	}
  
  	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_give isl_qpolynomial_fold *isl_qpolynomial_fold_lift(
  	__isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
  {
  	int i;
  
  	if (!fold || !dim)
  		goto error;
  
  	if (isl_space_is_equal(fold->dim, dim)) {
  		isl_space_free(dim);
  		return fold;
  	}
  
  	fold = isl_qpolynomial_fold_cow(fold);
  	if (!fold)
  		goto error;
  
  	isl_space_free(fold->dim);
  	fold->dim = isl_space_copy(dim);
  	if (!fold->dim)
  		goto error;
  
  	for (i = 0; i < fold->n; ++i) {
  		fold->qp[i] = isl_qpolynomial_lift(fold->qp[i],
  						isl_space_copy(dim));
  		if (!fold->qp[i])
  			goto error;
  	}
  
  	isl_space_free(dim);
  
  	return fold;
  error:
  	isl_qpolynomial_fold_free(fold);
  	isl_space_free(dim);
  	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)
  {
  	int i;
  
  	if (!fold)
  		return isl_stat_error;
  
  	for (i = 0; i < fold->n; ++i)
  		if (fn(isl_qpolynomial_copy(fold->qp[i]), user) < 0)
  			return isl_stat_error;
  
  	return isl_stat_ok;
  }
  
  __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)
  {
  	int i;
  	enum isl_dim_type set_src_type, set_dst_type;
  
  	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);
  
  	fold->dim = isl_space_move_dims(fold->dim, set_dst_type, dst_pos,
  						set_src_type, src_pos, n);
  	if (!fold->dim)
  		goto error;
  
  	for (i = 0; i < fold->n; ++i) {
  		fold->qp[i] = isl_qpolynomial_move_dims(fold->qp[i],
  				dst_type, dst_pos, src_type, src_pos, n);
  		if (!fold->qp[i])
  			goto error;
  	}
  
  	return fold;
  error:
  	isl_qpolynomial_fold_free(fold);
  	return NULL;
  }
  
  /* 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)
  {
  	int i;
  
  	if (n == 0)
  		return fold;
  
  	fold = isl_qpolynomial_fold_cow(fold);
  	if (!fold)
  		return NULL;
  
  	for (i = 0; i < fold->n; ++i) {
  		fold->qp[i] = isl_qpolynomial_substitute(fold->qp[i],
  				type, first, n, subs);
  		if (!fold->qp[i])
  			goto error;
  	}
  
  	return fold;
  error:
  	isl_qpolynomial_fold_free(fold);
  	return NULL;
  }
  
  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 *dim;
  	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;
  	dim = 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(dim, 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);
  }
  
  /* 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)
  {
  	int i;
  	isl_space *space;
  
  	fold = isl_qpolynomial_fold_cow(fold);
  	if (!fold || !r)
  		goto error;
  
  	for (i = 0; i < fold->n; ++i) {
  		fold->qp[i] = isl_qpolynomial_realign_domain(fold->qp[i],
  						    isl_reordering_copy(r));
  		if (!fold->qp[i])
  			goto error;
  	}
  
  	space = isl_reordering_get_space(r);
  	fold = isl_qpolynomial_fold_reset_domain_space(fold, space);
  
  	isl_reordering_free(r);
  
  	return fold;
  error:
  	isl_qpolynomial_fold_free(fold);
  	isl_reordering_free(r);
  	return NULL;
  }
  
  __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_mul_isl_int(
  	__isl_take isl_qpolynomial_fold *fold, isl_int v)
  {
  	int i;
  
  	if (isl_int_is_one(v))
  		return fold;
  	if (fold && isl_int_is_zero(v)) {
  		isl_qpolynomial_fold *zero;
  		isl_space *dim = isl_space_copy(fold->dim);
  		zero = isl_qpolynomial_fold_empty(fold->type, dim);
  		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);
  	for (i = 0; i < fold->n; ++i) {
  		fold->qp[i] = isl_qpolynomial_mul_isl_int(fold->qp[i], v);
  		if (!fold->qp[i])
  			goto error;
  	}
  
  	return fold;
  error:
  	isl_qpolynomial_fold_free(fold);
  	return NULL;
  }
  
  __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);
  }
  
  /* 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)
  {
  	int i;
  
  	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);
  	for (i = 0; i < fold->n; ++i) {
  		fold->qp[i] = isl_qpolynomial_scale_val(fold->qp[i],
  							isl_val_copy(v));
  		if (!fold->qp[i])
  			goto error;
  	}
  
  	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;
  }
  