text: /*
   * Copyright 2010-2011 INRIA Saclay
   * Copyright 2011      Sven Verdoolaege
   * Copyright 2012-2014 Ecole Normale Superieure
   *
   * 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
   * and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
   */
  
  #include <isl/id.h>
  #include <isl/aff.h>
  #include <isl_sort.h>
  #include <isl_val_private.h>
  
  #include <isl_pw_macro.h>
  
  #ifdef HAS_TYPE
  __isl_give PW *FN(PW,alloc_size)(__isl_take isl_space *dim,
  	enum isl_fold type, int n)
  #else
  __isl_give PW *FN(PW,alloc_size)(__isl_take isl_space *dim, int n)
  #endif
  {
  	isl_ctx *ctx;
  	struct PW *pw;
  
  	if (!dim)
  		return NULL;
  	ctx = isl_space_get_ctx(dim);
  	isl_assert(ctx, n >= 0, goto error);
  	pw = isl_alloc(ctx, struct PW,
  			sizeof(struct PW) + (n - 1) * sizeof(S(PW,piece)));
  	if (!pw)
  		goto error;
  
  	pw->ref = 1;
  #ifdef HAS_TYPE
  	pw->type = type;
  #endif
  	pw->size = n;
  	pw->n = 0;
  	pw->dim = dim;
  	return pw;
  error:
  	isl_space_free(dim);
  	return NULL;
  }
  
  #ifdef HAS_TYPE
  __isl_give PW *FN(PW,ZERO)(__isl_take isl_space *dim, enum isl_fold type)
  {
  	return FN(PW,alloc_size)(dim, type, 0);
  }
  #else
  __isl_give PW *FN(PW,ZERO)(__isl_take isl_space *dim)
  {
  	return FN(PW,alloc_size)(dim, 0);
  }
  #endif
  
  __isl_give PW *FN(PW,add_piece)(__isl_take PW *pw,
  	__isl_take isl_set *set, __isl_take EL *el)
  {
  	isl_ctx *ctx;
  	isl_space *el_dim = NULL;
  
  	if (!pw || !set || !el)
  		goto error;
  
  	if (isl_set_plain_is_empty(set) || FN(EL,EL_IS_ZERO)(el)) {
  		isl_set_free(set);
  		FN(EL,free)(el);
  		return pw;
  	}
  
  	ctx = isl_set_get_ctx(set);
  #ifdef HAS_TYPE
  	if (pw->type != el->type)
  		isl_die(ctx, isl_error_invalid, "fold types don't match",
  			goto error);
  #endif
  	el_dim = FN(EL,get_space(el));
  	isl_assert(ctx, isl_space_is_equal(pw->dim, el_dim), goto error);
  	isl_assert(ctx, pw->n < pw->size, goto error);
  
  	pw->p[pw->n].set = set;
  	pw->p[pw->n].FIELD = el;
  	pw->n++;
  	
  	isl_space_free(el_dim);
  	return pw;
  error:
  	isl_space_free(el_dim);
  	FN(PW,free)(pw);
  	isl_set_free(set);
  	FN(EL,free)(el);
  	return NULL;
  }
  
  /* Does the space of "set" correspond to that of the domain of "el".
   */
  static isl_bool FN(PW,compatible_domain)(__isl_keep EL *el,
  	__isl_keep isl_set *set)
  {
  	isl_bool ok;
  	isl_space *el_space, *set_space;
  
  	if (!set || !el)
  		return isl_bool_error;
  	set_space = isl_set_get_space(set);
  	el_space = FN(EL,get_space)(el);
  	ok = isl_space_is_domain_internal(set_space, el_space);
  	isl_space_free(el_space);
  	isl_space_free(set_space);
  	return ok;
  }
  
  /* Check that the space of "set" corresponds to that of the domain of "el".
   */
  static isl_stat FN(PW,check_compatible_domain)(__isl_keep EL *el,
  	__isl_keep isl_set *set)
  {
  	isl_bool ok;
  
  	ok = FN(PW,compatible_domain)(el, set);
  	if (ok < 0)
  		return isl_stat_error;
  	if (!ok)
  		isl_die(isl_set_get_ctx(set), isl_error_invalid,
  			"incompatible spaces", return isl_stat_error);
  
  	return isl_stat_ok;
  }
  
  #ifdef HAS_TYPE
  __isl_give PW *FN(PW,alloc)(enum isl_fold type,
  	__isl_take isl_set *set, __isl_take EL *el)
  #else
  __isl_give PW *FN(PW,alloc)(__isl_take isl_set *set, __isl_take EL *el)
  #endif
  {
  	PW *pw;
  
  	if (FN(PW,check_compatible_domain)(el, set) < 0)
  		goto error;
  
  #ifdef HAS_TYPE
  	pw = FN(PW,alloc_size)(FN(EL,get_space)(el), type, 1);
  #else
  	pw = FN(PW,alloc_size)(FN(EL,get_space)(el), 1);
  #endif
  
  	return FN(PW,add_piece)(pw, set, el);
  error:
  	isl_set_free(set);
  	FN(EL,free)(el);
  	return NULL;
  }
  
  __isl_give PW *FN(PW,dup)(__isl_keep PW *pw)
  {
  	int i;
  	PW *dup;
  
  	if (!pw)
  		return NULL;
  
  #ifdef HAS_TYPE
  	dup = FN(PW,alloc_size)(isl_space_copy(pw->dim), pw->type, pw->n);
  #else
  	dup = FN(PW,alloc_size)(isl_space_copy(pw->dim), pw->n);
  #endif
  	if (!dup)
  		return NULL;
  
  	for (i = 0; i < pw->n; ++i)
  		dup = FN(PW,add_piece)(dup, isl_set_copy(pw->p[i].set),
  					    FN(EL,copy)(pw->p[i].FIELD));
  
  	return dup;
  }
  
  __isl_give PW *FN(PW,cow)(__isl_take PW *pw)
  {
  	if (!pw)
  		return NULL;
  
  	if (pw->ref == 1)
  		return pw;
  	pw->ref--;
  	return FN(PW,dup)(pw);
  }
  
  __isl_give PW *FN(PW,copy)(__isl_keep PW *pw)
  {
  	if (!pw)
  		return NULL;
  
  	pw->ref++;
  	return pw;
  }
  
  __isl_null PW *FN(PW,free)(__isl_take PW *pw)
  {
  	int i;
  
  	if (!pw)
  		return NULL;
  	if (--pw->ref > 0)
  		return NULL;
  
  	for (i = 0; i < pw->n; ++i) {
  		isl_set_free(pw->p[i].set);
  		FN(EL,free)(pw->p[i].FIELD);
  	}
  	isl_space_free(pw->dim);
  	free(pw);
  
  	return NULL;
  }
  
  const char *FN(PW,get_dim_name)(__isl_keep PW *pw, enum isl_dim_type type,
  	unsigned pos)
  {
  	return pw ? isl_space_get_dim_name(pw->dim, type, pos) : NULL;
  }
  
  isl_bool FN(PW,has_dim_id)(__isl_keep PW *pw, enum isl_dim_type type,
  	unsigned pos)
  {
  	return pw ? isl_space_has_dim_id(pw->dim, type, pos) : isl_bool_error;
  }
  
  __isl_give isl_id *FN(PW,get_dim_id)(__isl_keep PW *pw, enum isl_dim_type type,
  	unsigned pos)
  {
  	return pw ? isl_space_get_dim_id(pw->dim, type, pos) : NULL;
  }
  
  isl_bool FN(PW,has_tuple_name)(__isl_keep PW *pw, enum isl_dim_type type)
  {
  	return pw ? isl_space_has_tuple_name(pw->dim, type) : isl_bool_error;
  }
  
  const char *FN(PW,get_tuple_name)(__isl_keep PW *pw, enum isl_dim_type type)
  {
  	return pw ? isl_space_get_tuple_name(pw->dim, type) : NULL;
  }
  
  isl_bool FN(PW,has_tuple_id)(__isl_keep PW *pw, enum isl_dim_type type)
  {
  	return pw ? isl_space_has_tuple_id(pw->dim, type) : isl_bool_error;
  }
  
  __isl_give isl_id *FN(PW,get_tuple_id)(__isl_keep PW *pw, enum isl_dim_type type)
  {
  	return pw ? isl_space_get_tuple_id(pw->dim, type) : NULL;
  }
  
  isl_bool FN(PW,IS_ZERO)(__isl_keep PW *pw)
  {
  	if (!pw)
  		return isl_bool_error;
  
  	return pw->n == 0;
  }
  
  #ifndef NO_REALIGN
  __isl_give PW *FN(PW,realign_domain)(__isl_take PW *pw,
  	__isl_take isl_reordering *exp)
  {
  	int i;
  
  	pw = FN(PW,cow)(pw);
  	if (!pw || !exp)
  		goto error;
  
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].set = isl_set_realign(pw->p[i].set,
  						    isl_reordering_copy(exp));
  		if (!pw->p[i].set)
  			goto error;
  		pw->p[i].FIELD = FN(EL,realign_domain)(pw->p[i].FIELD,
  						    isl_reordering_copy(exp));
  		if (!pw->p[i].FIELD)
  			goto error;
  	}
  
  	pw = FN(PW,reset_domain_space)(pw, isl_reordering_get_space(exp));
  
  	isl_reordering_free(exp);
  	return pw;
  error:
  	isl_reordering_free(exp);
  	FN(PW,free)(pw);
  	return NULL;
  }
  
  /* Check that "pw" has only named parameters, reporting an error
   * if it does not.
   */
  isl_stat FN(PW,check_named_params)(__isl_keep PW *pw)
  {
  	return isl_space_check_named_params(FN(PW,peek_space)(pw));
  }
  
  /* Align the parameters of "pw" to those of "model".
   */
  __isl_give PW *FN(PW,align_params)(__isl_take PW *pw, __isl_take isl_space *model)
  {
  	isl_ctx *ctx;
  	isl_bool equal_params;
  
  	if (!pw || !model)
  		goto error;
  
  	ctx = isl_space_get_ctx(model);
  	if (!isl_space_has_named_params(model))
  		isl_die(ctx, isl_error_invalid,
  			"model has unnamed parameters", goto error);
  	if (FN(PW,check_named_params)(pw) < 0)
  		goto error;
  	equal_params = isl_space_has_equal_params(pw->dim, model);
  	if (equal_params < 0)
  		goto error;
  	if (!equal_params) {
  		isl_reordering *exp;
  
  		exp = isl_parameter_alignment_reordering(pw->dim, model);
  		exp = isl_reordering_extend_space(exp,
  					FN(PW,get_domain_space)(pw));
  		pw = FN(PW,realign_domain)(pw, exp);
  	}
  
  	isl_space_free(model);
  	return pw;
  error:
  	isl_space_free(model);
  	FN(PW,free)(pw);
  	return NULL;
  }
  
  static __isl_give PW *FN(PW,align_params_pw_pw_and)(__isl_take PW *pw1,
  	__isl_take PW *pw2,
  	__isl_give PW *(*fn)(__isl_take PW *pw1, __isl_take PW *pw2))
  {
  	isl_bool equal_params;
  
  	if (!pw1 || !pw2)
  		goto error;
  	equal_params = isl_space_has_equal_params(pw1->dim, pw2->dim);
  	if (equal_params < 0)
  		goto error;
  	if (equal_params)
  		return fn(pw1, pw2);
  	if (FN(PW,check_named_params)(pw1) < 0 ||
  	    FN(PW,check_named_params)(pw2) < 0)
  		goto error;
  	pw1 = FN(PW,align_params)(pw1, FN(PW,get_space)(pw2));
  	pw2 = FN(PW,align_params)(pw2, FN(PW,get_space)(pw1));
  	return fn(pw1, pw2);
  error:
  	FN(PW,free)(pw1);
  	FN(PW,free)(pw2);
  	return NULL;
  }
  
  static __isl_give PW *FN(PW,align_params_pw_set_and)(__isl_take PW *pw,
  	__isl_take isl_set *set,
  	__isl_give PW *(*fn)(__isl_take PW *pw, __isl_take isl_set *set))
  {
  	isl_ctx *ctx;
  	isl_bool aligned;
  
  	if (!pw || !set)
  		goto error;
  	aligned = isl_set_space_has_equal_params(set, pw->dim);
  	if (aligned < 0)
  		goto error;
  	if (aligned)
  		return fn(pw, set);
  	ctx = FN(PW,get_ctx)(pw);
  	if (FN(PW,check_named_params)(pw) < 0)
  		goto error;
  	if (!isl_space_has_named_params(set->dim))
  		isl_die(ctx, isl_error_invalid,
  			"unaligned unnamed parameters", goto error);
  	pw = FN(PW,align_params)(pw, isl_set_get_space(set));
  	set = isl_set_align_params(set, FN(PW,get_space)(pw));
  	return fn(pw, set);
  error:
  	FN(PW,free)(pw);
  	isl_set_free(set);
  	return NULL;
  }
  #endif
  
  static __isl_give PW *FN(PW,union_add_aligned)(__isl_take PW *pw1,
  	__isl_take PW *pw2)
  {
  	int i, j, n;
  	struct PW *res;
  	isl_ctx *ctx;
  	isl_set *set;
  
  	if (!pw1 || !pw2)
  		goto error;
  
  	ctx = isl_space_get_ctx(pw1->dim);
  #ifdef HAS_TYPE
  	if (pw1->type != pw2->type)
  		isl_die(ctx, isl_error_invalid,
  			"fold types don't match", goto error);
  #endif
  	isl_assert(ctx, isl_space_is_equal(pw1->dim, pw2->dim), goto error);
  
  	if (FN(PW,IS_ZERO)(pw1)) {
  		FN(PW,free)(pw1);
  		return pw2;
  	}
  
  	if (FN(PW,IS_ZERO)(pw2)) {
  		FN(PW,free)(pw2);
  		return pw1;
  	}
  
  	n = (pw1->n + 1) * (pw2->n + 1);
  #ifdef HAS_TYPE
  	res = FN(PW,alloc_size)(isl_space_copy(pw1->dim), pw1->type, n);
  #else
  	res = FN(PW,alloc_size)(isl_space_copy(pw1->dim), n);
  #endif
  
  	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;
  			EL *sum;
  			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;
  			}
  			set = isl_set_subtract(set,
  					isl_set_copy(pw2->p[j].set));
  
  			sum = FN(EL,add_on_domain)(common,
  						   FN(EL,copy)(pw1->p[i].FIELD),
  						   FN(EL,copy)(pw2->p[j].FIELD));
  
  			res = FN(PW,add_piece)(res, common, sum);
  		}
  		res = FN(PW,add_piece)(res, set, FN(EL,copy)(pw1->p[i].FIELD));
  	}
  
  	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 = FN(PW,add_piece)(res, set, FN(EL,copy)(pw2->p[j].FIELD));
  	}
  
  	FN(PW,free)(pw1);
  	FN(PW,free)(pw2);
  
  	return res;
  error:
  	FN(PW,free)(pw1);
  	FN(PW,free)(pw2);
  	return NULL;
  }
  
  /* Private version of "union_add".  For isl_pw_qpolynomial and
   * isl_pw_qpolynomial_fold, we prefer to simply call it "add".
   */
  static __isl_give PW *FN(PW,union_add_)(__isl_take PW *pw1, __isl_take PW *pw2)
  {
  	return FN(PW,align_params_pw_pw_and)(pw1, pw2,
  						&FN(PW,union_add_aligned));
  }
  
  /* Make sure "pw" has room for at least "n" more pieces.
   *
   * If there is only one reference to pw, we extend it in place.
   * Otherwise, we create a new PW and copy the pieces.
   */
  static __isl_give PW *FN(PW,grow)(__isl_take PW *pw, int n)
  {
  	int i;
  	isl_ctx *ctx;
  	PW *res;
  
  	if (!pw)
  		return NULL;
  	if (pw->n + n <= pw->size)
  		return pw;
  	ctx = FN(PW,get_ctx)(pw);
  	n += pw->n;
  	if (pw->ref == 1) {
  		res = isl_realloc(ctx, pw, struct PW,
  			    sizeof(struct PW) + (n - 1) * sizeof(S(PW,piece)));
  		if (!res)
  			return FN(PW,free)(pw);
  		res->size = n;
  		return res;
  	}
  #ifdef HAS_TYPE
  	res = FN(PW,alloc_size)(isl_space_copy(pw->dim), pw->type, n);
  #else
  	res = FN(PW,alloc_size)(isl_space_copy(pw->dim), n);
  #endif
  	if (!res)
  		return FN(PW,free)(pw);
  	for (i = 0; i < pw->n; ++i)
  		res = FN(PW,add_piece)(res, isl_set_copy(pw->p[i].set),
  					    FN(EL,copy)(pw->p[i].FIELD));
  	FN(PW,free)(pw);
  	return res;
  }
  
  static __isl_give PW *FN(PW,add_disjoint_aligned)(__isl_take PW *pw1,
  	__isl_take PW *pw2)
  {
  	int i;
  	isl_ctx *ctx;
  
  	if (!pw1 || !pw2)
  		goto error;
  
  	if (pw1->size < pw1->n + pw2->n && pw1->n < pw2->n)
  		return FN(PW,add_disjoint_aligned)(pw2, pw1);
  
  	ctx = isl_space_get_ctx(pw1->dim);
  #ifdef HAS_TYPE
  	if (pw1->type != pw2->type)
  		isl_die(ctx, isl_error_invalid,
  			"fold types don't match", goto error);
  #endif
  	isl_assert(ctx, isl_space_is_equal(pw1->dim, pw2->dim), goto error);
  
  	if (FN(PW,IS_ZERO)(pw1)) {
  		FN(PW,free)(pw1);
  		return pw2;
  	}
  
  	if (FN(PW,IS_ZERO)(pw2)) {
  		FN(PW,free)(pw2);
  		return pw1;
  	}
  
  	pw1 = FN(PW,grow)(pw1, pw2->n);
  	if (!pw1)
  		goto error;
  
  	for (i = 0; i < pw2->n; ++i)
  		pw1 = FN(PW,add_piece)(pw1,
  				isl_set_copy(pw2->p[i].set),
  				FN(EL,copy)(pw2->p[i].FIELD));
  
  	FN(PW,free)(pw2);
  
  	return pw1;
  error:
  	FN(PW,free)(pw1);
  	FN(PW,free)(pw2);
  	return NULL;
  }
  
  __isl_give PW *FN(PW,add_disjoint)(__isl_take PW *pw1, __isl_take PW *pw2)
  {
  	return FN(PW,align_params_pw_pw_and)(pw1, pw2,
  						&FN(PW,add_disjoint_aligned));
  }
  
  /* This function is currently only used from isl_aff.c
   */
  static __isl_give PW *FN(PW,on_shared_domain_in)(__isl_take PW *pw1,
  	__isl_take PW *pw2, __isl_take isl_space *space,
  	__isl_give EL *(*fn)(__isl_take EL *el1, __isl_take EL *el2))
  	__attribute__ ((unused));
  
  /* Apply "fn" to pairs of elements from pw1 and pw2 on shared domains.
   * The result of "fn" (and therefore also of this function) lives in "space".
   */
  static __isl_give PW *FN(PW,on_shared_domain_in)(__isl_take PW *pw1,
  	__isl_take PW *pw2, __isl_take isl_space *space,
  	__isl_give EL *(*fn)(__isl_take EL *el1, __isl_take EL *el2))
  {
  	int i, j, n;
  	PW *res = NULL;
  
  	if (!pw1 || !pw2)
  		goto error;
  
  	n = pw1->n * pw2->n;
  #ifdef HAS_TYPE
  	res = FN(PW,alloc_size)(isl_space_copy(space), pw1->type, n);
  #else
  	res = FN(PW,alloc_size)(isl_space_copy(space), n);
  #endif
  
  	for (i = 0; i < pw1->n; ++i) {
  		for (j = 0; j < pw2->n; ++j) {
  			isl_set *common;
  			EL *res_ij;
  			int empty;
  
  			common = isl_set_intersect(
  					isl_set_copy(pw1->p[i].set),
  					isl_set_copy(pw2->p[j].set));
  			empty = isl_set_plain_is_empty(common);
  			if (empty < 0 || empty) {
  				isl_set_free(common);
  				if (empty < 0)
  					goto error;
  				continue;
  			}
  
  			res_ij = fn(FN(EL,copy)(pw1->p[i].FIELD),
  				    FN(EL,copy)(pw2->p[j].FIELD));
  			res_ij = FN(EL,gist)(res_ij, isl_set_copy(common));
  
  			res = FN(PW,add_piece)(res, common, res_ij);
  		}
  	}
  
  	isl_space_free(space);
  	FN(PW,free)(pw1);
  	FN(PW,free)(pw2);
  	return res;
  error:
  	isl_space_free(space);
  	FN(PW,free)(pw1);
  	FN(PW,free)(pw2);
  	FN(PW,free)(res);
  	return NULL;
  }
  
  /* This function is currently only used from isl_aff.c
   */
  static __isl_give PW *FN(PW,on_shared_domain)(__isl_take PW *pw1,
  	__isl_take PW *pw2,
  	__isl_give EL *(*fn)(__isl_take EL *el1, __isl_take EL *el2))
  	__attribute__ ((unused));
  
  /* Apply "fn" to pairs of elements from pw1 and pw2 on shared domains.
   * The result of "fn" is assumed to live in the same space as "pw1" and "pw2".
   */
  static __isl_give PW *FN(PW,on_shared_domain)(__isl_take PW *pw1,
  	__isl_take PW *pw2,
  	__isl_give EL *(*fn)(__isl_take EL *el1, __isl_take EL *el2))
  {
  	isl_space *space;
  
  	if (!pw1 || !pw2)
  		goto error;
  
  	space = isl_space_copy(pw1->dim);
  	return FN(PW,on_shared_domain_in)(pw1, pw2, space, fn);
  error:
  	FN(PW,free)(pw1);
  	FN(PW,free)(pw2);
  	return NULL;
  }
  
  #ifndef NO_NEG
  __isl_give PW *FN(PW,neg)(__isl_take PW *pw)
  {
  	int i;
  
  	if (!pw)
  		return NULL;
  
  	if (FN(PW,IS_ZERO)(pw))
  		return pw;
  
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		return NULL;
  
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].FIELD = FN(EL,neg)(pw->p[i].FIELD);
  		if (!pw->p[i].FIELD)
  			return FN(PW,free)(pw);
  	}
  
  	return pw;
  }
  #endif
  
  #ifndef NO_SUB
  __isl_give PW *FN(PW,sub)(__isl_take PW *pw1, __isl_take PW *pw2)
  {
  	return FN(PW,add)(pw1, FN(PW,neg)(pw2));
  }
  #endif
  
  /* Return the parameter domain of "pw".
   */
  __isl_give isl_set *FN(PW,params)(__isl_take PW *pw)
  {
  	return isl_set_params(FN(PW,domain)(pw));
  }
  
  __isl_give isl_set *FN(PW,domain)(__isl_take PW *pw)
  {
  	int i;
  	isl_set *dom;
  
  	if (!pw)
  		return NULL;
  
  	dom = isl_set_empty(FN(PW,get_domain_space)(pw));
  	for (i = 0; i < pw->n; ++i)
  		dom = isl_set_union_disjoint(dom, isl_set_copy(pw->p[i].set));
  
  	FN(PW,free)(pw);
  
  	return dom;
  }
  
  /* Exploit the equalities in the domain of piece "i" of "pw"
   * to simplify the associated function.
   * If the domain of piece "i" is empty, then remove it entirely,
   * replacing it with the final piece.
   */
  static int FN(PW,exploit_equalities_and_remove_if_empty)(__isl_keep PW *pw,
  	int i)
  {
  	isl_basic_set *aff;
  	int empty = isl_set_plain_is_empty(pw->p[i].set);
  
  	if (empty < 0)
  		return -1;
  	if (empty) {
  		isl_set_free(pw->p[i].set);
  		FN(EL,free)(pw->p[i].FIELD);
  		if (i != pw->n - 1)
  			pw->p[i] = pw->p[pw->n - 1];
  		pw->n--;
  
  		return 0;
  	}
  
  	aff = isl_set_affine_hull(isl_set_copy(pw->p[i].set));
  	pw->p[i].FIELD = FN(EL,substitute_equalities)(pw->p[i].FIELD, aff);
  	if (!pw->p[i].FIELD)
  		return -1;
  
  	return 0;
  }
  
  /* Convert a piecewise expression defined over a parameter domain
   * into one that is defined over a zero-dimensional set.
   */
  __isl_give PW *FN(PW,from_range)(__isl_take PW *pw)
  {
  	isl_space *space;
  
  	if (!pw)
  		return NULL;
  	if (!isl_space_is_set(pw->dim))
  		isl_die(FN(PW,get_ctx)(pw), isl_error_invalid,
  			"not living in a set space", return FN(PW,free)(pw));
  
  	space = FN(PW,get_space)(pw);
  	space = isl_space_from_range(space);
  	pw = FN(PW,reset_space)(pw, space);
  
  	return pw;
  }
  
  /* Fix the value of the given parameter or domain dimension of "pw"
   * to be equal to "value".
   */
  __isl_give PW *FN(PW,fix_si)(__isl_take PW *pw, enum isl_dim_type type,
  	unsigned pos, int value)
  {
  	int i;
  
  	if (!pw)
  		return NULL;
  
  	if (type == isl_dim_out)
  		isl_die(FN(PW,get_ctx)(pw), isl_error_invalid,
  			"cannot fix output dimension", return FN(PW,free)(pw));
  
  	if (pw->n == 0)
  		return pw;
  
  	if (type == isl_dim_in)
  		type = isl_dim_set;
  
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		return FN(PW,free)(pw);
  
  	for (i = pw->n - 1; i >= 0; --i) {
  		pw->p[i].set = isl_set_fix_si(pw->p[i].set, type, pos, value);
  		if (FN(PW,exploit_equalities_and_remove_if_empty)(pw, i) < 0)
  			return FN(PW,free)(pw);
  	}
  
  	return pw;
  }
  
  /* Restrict the domain of "pw" by combining each cell
   * with "set" through a call to "fn", where "fn" may be
   * isl_set_intersect, isl_set_intersect_params or isl_set_subtract.
   */
  static __isl_give PW *FN(PW,restrict_domain_aligned)(__isl_take PW *pw,
  	__isl_take isl_set *set,
  	__isl_give isl_set *(*fn)(__isl_take isl_set *set1,
  				    __isl_take isl_set *set2))
  {
  	int i;
  
  	if (!pw || !set)
  		goto error;
  
  	if (pw->n == 0) {
  		isl_set_free(set);
  		return pw;
  	}
  
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		goto error;
  
  	for (i = pw->n - 1; i >= 0; --i) {
  		pw->p[i].set = fn(pw->p[i].set, isl_set_copy(set));
  		if (FN(PW,exploit_equalities_and_remove_if_empty)(pw, i) < 0)
  			goto error;
  	}
  	
  	isl_set_free(set);
  	return pw;
  error:
  	isl_set_free(set);
  	FN(PW,free)(pw);
  	return NULL;
  }
  
  static __isl_give PW *FN(PW,intersect_domain_aligned)(__isl_take PW *pw,
  	__isl_take isl_set *set)
  {
  	return FN(PW,restrict_domain_aligned)(pw, set, &isl_set_intersect);
  }
  
  __isl_give PW *FN(PW,intersect_domain)(__isl_take PW *pw,
  	__isl_take isl_set *context)
  {
  	return FN(PW,align_params_pw_set_and)(pw, context,
  					&FN(PW,intersect_domain_aligned));
  }
  
  static __isl_give PW *FN(PW,intersect_params_aligned)(__isl_take PW *pw,
  	__isl_take isl_set *set)
  {
  	return FN(PW,restrict_domain_aligned)(pw, set,
  					&isl_set_intersect_params);
  }
  
  /* Intersect the domain of "pw" with the parameter domain "context".
   */
  __isl_give PW *FN(PW,intersect_params)(__isl_take PW *pw,
  	__isl_take isl_set *context)
  {
  	return FN(PW,align_params_pw_set_and)(pw, context,
  					&FN(PW,intersect_params_aligned));
  }
  
  /* Subtract "domain' from the domain of "pw", assuming their
   * parameters have been aligned.
   */
  static __isl_give PW *FN(PW,subtract_domain_aligned)(__isl_take PW *pw,
  	__isl_take isl_set *domain)
  {
  	return FN(PW,restrict_domain_aligned)(pw, domain, &isl_set_subtract);
  }
  
  /* Subtract "domain' from the domain of "pw".
   */
  __isl_give PW *FN(PW,subtract_domain)(__isl_take PW *pw,
  	__isl_take isl_set *domain)
  {
  	return FN(PW,align_params_pw_set_and)(pw, domain,
  					&FN(PW,subtract_domain_aligned));
  }
  
  /* Compute the gist of "pw" with respect to the domain constraints
   * of "context" for the case where the domain of the last element
   * of "pw" is equal to "context".
   * Call "fn_el" to compute the gist of this element, replace
   * its domain by the universe and drop all other elements
   * as their domains are necessarily disjoint from "context".
   */
  static __isl_give PW *FN(PW,gist_last)(__isl_take PW *pw,
  	__isl_take isl_set *context,
  	__isl_give EL *(*fn_el)(__isl_take EL *el, __isl_take isl_set *set))
  {
  	int i;
  	isl_space *space;
  
  	for (i = 0; i < pw->n - 1; ++i) {
  		isl_set_free(pw->p[i].set);
  		FN(EL,free)(pw->p[i].FIELD);
  	}
  	pw->p[0].FIELD = pw->p[pw->n - 1].FIELD;
  	pw->p[0].set = pw->p[pw->n - 1].set;
  	pw->n = 1;
  
  	space = isl_set_get_space(context);
  	pw->p[0].FIELD = fn_el(pw->p[0].FIELD, context);
  	context = isl_set_universe(space);
  	isl_set_free(pw->p[0].set);
  	pw->p[0].set = context;
  
  	if (!pw->p[0].FIELD || !pw->p[0].set)
  		return FN(PW,free)(pw);
  
  	return pw;
  }
  
  /* Compute the gist of "pw" with respect to the domain constraints
   * of "context".  Call "fn_el" to compute the gist of the elements
   * and "fn_dom" to compute the gist of the domains.
   *
   * If the piecewise expression is empty or the context is the universe,
   * then nothing can be simplified.
   */
  static __isl_give PW *FN(PW,gist_aligned)(__isl_take PW *pw,
  	__isl_take isl_set *context,
  	__isl_give EL *(*fn_el)(__isl_take EL *el,
  				    __isl_take isl_set *set),
  	__isl_give isl_set *(*fn_dom)(__isl_take isl_set *set,
  				    __isl_take isl_basic_set *bset))
  {
  	int i;
  	int is_universe;
  	isl_bool aligned;
  	isl_basic_set *hull = NULL;
  
  	if (!pw || !context)
  		goto error;
  
  	if (pw->n == 0) {
  		isl_set_free(context);
  		return pw;
  	}
  
  	is_universe = isl_set_plain_is_universe(context);
  	if (is_universe < 0)
  		goto error;
  	if (is_universe) {
  		isl_set_free(context);
  		return pw;
  	}
  
  	aligned = isl_set_space_has_equal_params(context, pw->dim);
  	if (aligned < 0)
  		goto error;
  	if (!aligned) {
  		pw = FN(PW,align_params)(pw, isl_set_get_space(context));
  		context = isl_set_align_params(context, FN(PW,get_space)(pw));
  	}
  
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		goto error;
  
  	if (pw->n == 1) {
  		int equal;
  
  		equal = isl_set_plain_is_equal(pw->p[0].set, context);
  		if (equal < 0)
  			goto error;
  		if (equal)
  			return FN(PW,gist_last)(pw, context, fn_el);
  	}
  
  	context = isl_set_compute_divs(context);
  	hull = isl_set_simple_hull(isl_set_copy(context));
  
  	for (i = pw->n - 1; i >= 0; --i) {
  		isl_set *set_i;
  		int empty;
  
  		if (i == pw->n - 1) {
  			int equal;
  			equal = isl_set_plain_is_equal(pw->p[i].set, context);
  			if (equal < 0)
  				goto error;
  			if (equal) {
  				isl_basic_set_free(hull);
  				return FN(PW,gist_last)(pw, context, fn_el);
  			}
  		}
  		set_i = isl_set_intersect(isl_set_copy(pw->p[i].set),
  						 isl_set_copy(context));
  		empty = isl_set_plain_is_empty(set_i);
  		pw->p[i].FIELD = fn_el(pw->p[i].FIELD, set_i);
  		pw->p[i].set = fn_dom(pw->p[i].set, isl_basic_set_copy(hull));
  		if (empty < 0 || !pw->p[i].FIELD || !pw->p[i].set)
  			goto error;
  		if (empty) {
  			isl_set_free(pw->p[i].set);
  			FN(EL,free)(pw->p[i].FIELD);
  			if (i != pw->n - 1)
  				pw->p[i] = pw->p[pw->n - 1];
  			pw->n--;
  		}
  	}
  
  	isl_basic_set_free(hull);
  	isl_set_free(context);
  
  	return pw;
  error:
  	FN(PW,free)(pw);
  	isl_basic_set_free(hull);
  	isl_set_free(context);
  	return NULL;
  }
  
  static __isl_give PW *FN(PW,gist_domain_aligned)(__isl_take PW *pw,
  	__isl_take isl_set *set)
  {
  	return FN(PW,gist_aligned)(pw, set, &FN(EL,gist),
  					&isl_set_gist_basic_set);
  }
  
  __isl_give PW *FN(PW,gist)(__isl_take PW *pw, __isl_take isl_set *context)
  {
  	return FN(PW,align_params_pw_set_and)(pw, context,
  						&FN(PW,gist_domain_aligned));
  }
  
  static __isl_give PW *FN(PW,gist_params_aligned)(__isl_take PW *pw,
  	__isl_take isl_set *set)
  {
  	return FN(PW,gist_aligned)(pw, set, &FN(EL,gist_params),
  					&isl_set_gist_params_basic_set);
  }
  
  __isl_give PW *FN(PW,gist_params)(__isl_take PW *pw,
  	__isl_take isl_set *context)
  {
  	return FN(PW,align_params_pw_set_and)(pw, context,
  						&FN(PW,gist_params_aligned));
  }
  
  /* Return -1 if the piece "p1" should be sorted before "p2"
   * and 1 if it should be sorted after "p2".
   * Return 0 if they do not need to be sorted in a specific order.
   *
   * The two pieces are compared on the basis of their function value expressions.
   */
  static int FN(PW,sort_field_cmp)(const void *p1, const void *p2, void *arg)
  {
  	struct FN(PW,piece) const *pc1 = p1;
  	struct FN(PW,piece) const *pc2 = p2;
  
  	return FN(EL,plain_cmp)(pc1->FIELD, pc2->FIELD);
  }
  
  /* Sort the pieces of "pw" according to their function value
   * expressions and then combine pairs of adjacent pieces with
   * the same such expression.
   *
   * The sorting is performed in place because it does not
   * change the meaning of "pw", but care needs to be
   * taken not to change any possible other copies of "pw"
   * in case anything goes wrong.
   */
  __isl_give PW *FN(PW,sort)(__isl_take PW *pw)
  {
  	int i, j;
  	isl_set *set;
  
  	if (!pw)
  		return NULL;
  	if (pw->n <= 1)
  		return pw;
  	if (isl_sort(pw->p, pw->n, sizeof(pw->p[0]),
  		    &FN(PW,sort_field_cmp), NULL) < 0)
  		return FN(PW,free)(pw);
  	for (i = pw->n - 1; i >= 1; --i) {
  		if (!FN(EL,plain_is_equal)(pw->p[i - 1].FIELD, pw->p[i].FIELD))
  			continue;
  		set = isl_set_union(isl_set_copy(pw->p[i - 1].set),
  				    isl_set_copy(pw->p[i].set));
  		if (!set)
  			return FN(PW,free)(pw);
  		isl_set_free(pw->p[i].set);
  		FN(EL,free)(pw->p[i].FIELD);
  		isl_set_free(pw->p[i - 1].set);
  		pw->p[i - 1].set = set;
  		for (j = i + 1; j < pw->n; ++j)
  			pw->p[j - 1] = pw->p[j];
  		pw->n--;
  	}
  
  	return pw;
  }
  
  /* Coalesce the domains of "pw".
   *
   * Prior to the actual coalescing, first sort the pieces such that
   * pieces with the same function value expression are combined
   * into a single piece, the combined domain of which can then
   * be coalesced.
   */
  __isl_give PW *FN(PW,coalesce)(__isl_take PW *pw)
  {
  	int i;
  
  	pw = FN(PW,sort)(pw);
  	if (!pw)
  		return NULL;
  
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].set = isl_set_coalesce(pw->p[i].set);
  		if (!pw->p[i].set)
  			goto error;
  	}
  
  	return pw;
  error:
  	FN(PW,free)(pw);
  	return NULL;
  }
  
  isl_ctx *FN(PW,get_ctx)(__isl_keep PW *pw)
  {
  	return pw ? isl_space_get_ctx(pw->dim) : NULL;
  }
  
  isl_bool FN(PW,involves_dims)(__isl_keep PW *pw, enum isl_dim_type type,
  	unsigned first, unsigned n)
  {
  	int i;
  	enum isl_dim_type set_type;
  
  	if (!pw)
  		return isl_bool_error;
  	if (pw->n == 0 || n == 0)
  		return isl_bool_false;
  
  	set_type = type == isl_dim_in ? isl_dim_set : type;
  
  	for (i = 0; i < pw->n; ++i) {
  		isl_bool involves = FN(EL,involves_dims)(pw->p[i].FIELD,
  							type, first, n);
  		if (involves < 0 || involves)
  			return involves;
  		involves = isl_set_involves_dims(pw->p[i].set,
  							set_type, first, n);
  		if (involves < 0 || involves)
  			return involves;
  	}
  	return isl_bool_false;
  }
  
  __isl_give PW *FN(PW,set_dim_name)(__isl_take PW *pw,
  	enum isl_dim_type type, unsigned pos, const char *s)
  {
  	int i;
  	enum isl_dim_type set_type;
  
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		return NULL;
  
  	set_type = type == isl_dim_in ? isl_dim_set : type;
  
  	pw->dim = isl_space_set_dim_name(pw->dim, type, pos, s);
  	if (!pw->dim)
  		goto error;
  
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].set = isl_set_set_dim_name(pw->p[i].set,
  							set_type, pos, s);
  		if (!pw->p[i].set)
  			goto error;
  		pw->p[i].FIELD = FN(EL,set_dim_name)(pw->p[i].FIELD, type, pos, s);
  		if (!pw->p[i].FIELD)
  			goto error;
  	}
  
  	return pw;
  error:
  	FN(PW,free)(pw);
  	return NULL;
  }
  
  __isl_give PW *FN(PW,drop_dims)(__isl_take PW *pw,
  	enum isl_dim_type type, unsigned first, unsigned n)
  {
  	int i;
  	enum isl_dim_type set_type;
  
  	if (!pw)
  		return NULL;
  	if (n == 0 && !isl_space_get_tuple_name(pw->dim, type))
  		return pw;
  
  	set_type = type == isl_dim_in ? isl_dim_set : type;
  
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		return NULL;
  	pw->dim = isl_space_drop_dims(pw->dim, type, first, n);
  	if (!pw->dim)
  		goto error;
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].FIELD = FN(EL,drop_dims)(pw->p[i].FIELD, type, first, n);
  		if (!pw->p[i].FIELD)
  			goto error;
  		if (type == isl_dim_out)
  			continue;
  		pw->p[i].set = isl_set_drop(pw->p[i].set, set_type, first, n);
  		if (!pw->p[i].set)
  			goto error;
  	}
  
  	return pw;
  error:
  	FN(PW,free)(pw);
  	return NULL;
  }
  
  /* This function is very similar to drop_dims.
   * The only difference is that the cells may still involve
   * the specified dimensions.  They are removed using
   * isl_set_project_out instead of isl_set_drop.
   */
  __isl_give PW *FN(PW,project_out)(__isl_take PW *pw,
  	enum isl_dim_type type, unsigned first, unsigned n)
  {
  	int i;
  	enum isl_dim_type set_type;
  
  	if (!pw)
  		return NULL;
  	if (n == 0 && !isl_space_get_tuple_name(pw->dim, type))
  		return pw;
  
  	set_type = type == isl_dim_in ? isl_dim_set : type;
  
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		return NULL;
  	pw->dim = isl_space_drop_dims(pw->dim, type, first, n);
  	if (!pw->dim)
  		goto error;
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].set = isl_set_project_out(pw->p[i].set,
  							set_type, first, n);
  		if (!pw->p[i].set)
  			goto error;
  		pw->p[i].FIELD = FN(EL,drop_dims)(pw->p[i].FIELD, type, first, n);
  		if (!pw->p[i].FIELD)
  			goto error;
  	}
  
  	return pw;
  error:
  	FN(PW,free)(pw);
  	return NULL;
  }
  
  /* Project the domain of pw onto its parameter space.
   */
  __isl_give PW *FN(PW,project_domain_on_params)(__isl_take PW *pw)
  {
  	isl_space *space;
  	unsigned n;
  
  	n = FN(PW,dim)(pw, isl_dim_in);
  	pw = FN(PW,project_out)(pw, isl_dim_in, 0, n);
  	space = FN(PW,get_domain_space)(pw);
  	space = isl_space_params(space);
  	pw = FN(PW,reset_domain_space)(pw, space);
  	return pw;
  }
  
  /* Drop all parameters not referenced by "pw".
   */
  __isl_give PW *FN(PW,drop_unused_params)(__isl_take PW *pw)
  {
  	int i;
  
  	if (FN(PW,check_named_params)(pw) < 0)
  		return FN(PW,free)(pw);
  
  	for (i = FN(PW,dim)(pw, isl_dim_param) - 1; i >= 0; i--) {
  		isl_bool involves;
  
  		involves = FN(PW,involves_dims)(pw, isl_dim_param, i, 1);
  		if (involves < 0)
  			return FN(PW,free)(pw);
  		if (!involves)
  			pw = FN(PW,drop_dims)(pw, isl_dim_param, i, 1);
  	}
  
  	return pw;
  }
  
  #ifndef NO_INSERT_DIMS
  __isl_give PW *FN(PW,insert_dims)(__isl_take PW *pw, enum isl_dim_type type,
  	unsigned first, unsigned n)
  {
  	int i;
  	enum isl_dim_type set_type;
  
  	if (!pw)
  		return NULL;
  	if (n == 0 && !isl_space_is_named_or_nested(pw->dim, type))
  		return pw;
  
  	set_type = type == isl_dim_in ? isl_dim_set : type;
  
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		return NULL;
  
  	pw->dim = isl_space_insert_dims(pw->dim, type, first, n);
  	if (!pw->dim)
  		goto error;
  
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].set = isl_set_insert_dims(pw->p[i].set,
  							    set_type, first, n);
  		if (!pw->p[i].set)
  			goto error;
  		pw->p[i].FIELD = FN(EL,insert_dims)(pw->p[i].FIELD,
  								type, first, n);
  		if (!pw->p[i].FIELD)
  			goto error;
  	}
  
  	return pw;
  error:
  	FN(PW,free)(pw);
  	return NULL;
  }
  #endif
  
  __isl_give PW *FN(PW,fix_dim)(__isl_take PW *pw,
  	enum isl_dim_type type, unsigned pos, isl_int v)
  {
  	int i;
  
  	if (!pw)
  		return NULL;
  
  	if (type == isl_dim_in)
  		type = isl_dim_set;
  
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		return NULL;
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].set = isl_set_fix(pw->p[i].set, type, pos, v);
  		if (FN(PW,exploit_equalities_and_remove_if_empty)(pw, i) < 0)
  			return FN(PW,free)(pw);
  	}
  
  	return pw;
  }
  
  /* Fix the value of the variable at position "pos" of type "type" of "pw"
   * to be equal to "v".
   */
  __isl_give PW *FN(PW,fix_val)(__isl_take PW *pw,
  	enum isl_dim_type type, unsigned pos, __isl_take isl_val *v)
  {
  	if (!v)
  		return FN(PW,free)(pw);
  	if (!isl_val_is_int(v))
  		isl_die(FN(PW,get_ctx)(pw), isl_error_invalid,
  			"expecting integer value", goto error);
  
  	pw = FN(PW,fix_dim)(pw, type, pos, v->n);
  	isl_val_free(v);
  
  	return pw;
  error:
  	isl_val_free(v);
  	return FN(PW,free)(pw);
  }
  
  unsigned FN(PW,dim)(__isl_keep PW *pw, enum isl_dim_type type)
  {
  	return pw ? isl_space_dim(pw->dim, type) : 0;
  }
  
  __isl_give PW *FN(PW,split_dims)(__isl_take PW *pw,
  	enum isl_dim_type type, unsigned first, unsigned n)
  {
  	int i;
  
  	if (!pw)
  		return NULL;
  	if (n == 0)
  		return pw;
  
  	if (type == isl_dim_in)
  		type = isl_dim_set;
  
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		return NULL;
  	if (!pw->dim)
  		goto error;
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].set = isl_set_split_dims(pw->p[i].set, type, first, n);
  		if (!pw->p[i].set)
  			goto error;
  	}
  
  	return pw;
  error:
  	FN(PW,free)(pw);
  	return NULL;
  }
  
  #ifndef NO_OPT
  /* Compute the maximal value attained by the piecewise quasipolynomial
   * on its domain or zero if the domain is empty.
   * In the worst case, the domain is scanned completely,
   * so the domain is assumed to be bounded.
   */
  __isl_give isl_val *FN(PW,opt)(__isl_take PW *pw, int max)
  {
  	int i;
  	isl_val *opt;
  
  	if (!pw)
  		return NULL;
  
  	if (pw->n == 0) {
  		opt = isl_val_zero(FN(PW,get_ctx)(pw));
  		FN(PW,free)(pw);
  		return opt;
  	}
  
  	opt = FN(EL,opt_on_domain)(FN(EL,copy)(pw->p[0].FIELD),
  					isl_set_copy(pw->p[0].set), max);
  	for (i = 1; i < pw->n; ++i) {
  		isl_val *opt_i;
  		opt_i = FN(EL,opt_on_domain)(FN(EL,copy)(pw->p[i].FIELD),
  						isl_set_copy(pw->p[i].set), max);
  		if (max)
  			opt = isl_val_max(opt, opt_i);
  		else
  			opt = isl_val_min(opt, opt_i);
  	}
  
  	FN(PW,free)(pw);
  	return opt;
  }
  
  __isl_give isl_val *FN(PW,max)(__isl_take PW *pw)
  {
  	return FN(PW,opt)(pw, 1);
  }
  
  __isl_give isl_val *FN(PW,min)(__isl_take PW *pw)
  {
  	return FN(PW,opt)(pw, 0);
  }
  #endif
  
  /* Return the space of "pw".
   */
  __isl_keep isl_space *FN(PW,peek_space)(__isl_keep PW *pw)
  {
  	return pw ? pw->dim : NULL;
  }
  
  __isl_give isl_space *FN(PW,get_space)(__isl_keep PW *pw)
  {
  	return isl_space_copy(FN(PW,peek_space)(pw));
  }
  
  __isl_give isl_space *FN(PW,get_domain_space)(__isl_keep PW *pw)
  {
  	return pw ? isl_space_domain(isl_space_copy(pw->dim)) : NULL;
  }
  
  /* Return the position of the dimension of the given type and name
   * in "pw".
   * Return -1 if no such dimension can be found.
   */
  int FN(PW,find_dim_by_name)(__isl_keep PW *pw,
  	enum isl_dim_type type, const char *name)
  {
  	if (!pw)
  		return -1;
  	return isl_space_find_dim_by_name(pw->dim, type, name);
  }
  
  #ifndef NO_RESET_DIM
  /* Reset the space of "pw".  Since we don't know if the elements
   * represent the spaces themselves or their domains, we pass along
   * both when we call their reset_space_and_domain.
   */
  static __isl_give PW *FN(PW,reset_space_and_domain)(__isl_take PW *pw,
  	__isl_take isl_space *space, __isl_take isl_space *domain)
  {
  	int i;
  
  	pw = FN(PW,cow)(pw);
  	if (!pw || !space || !domain)
  		goto error;
  
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].set = isl_set_reset_space(pw->p[i].set,
  						 isl_space_copy(domain));
  		if (!pw->p[i].set)
  			goto error;
  		pw->p[i].FIELD = FN(EL,reset_space_and_domain)(pw->p[i].FIELD,
  			      isl_space_copy(space), isl_space_copy(domain));
  		if (!pw->p[i].FIELD)
  			goto error;
  	}
  
  	isl_space_free(domain);
  
  	isl_space_free(pw->dim);
  	pw->dim = space;
  
  	return pw;
  error:
  	isl_space_free(domain);
  	isl_space_free(space);
  	FN(PW,free)(pw);
  	return NULL;
  }
  
  __isl_give PW *FN(PW,reset_domain_space)(__isl_take PW *pw,
  	__isl_take isl_space *domain)
  {
  	isl_space *space;
  
  	space = isl_space_extend_domain_with_range(isl_space_copy(domain),
  						   FN(PW,get_space)(pw));
  	return FN(PW,reset_space_and_domain)(pw, space, domain);
  }
  
  __isl_give PW *FN(PW,reset_space)(__isl_take PW *pw, __isl_take isl_space *dim)
  {
  	isl_space *domain;
  
  	domain = isl_space_domain(isl_space_copy(dim));
  	return FN(PW,reset_space_and_domain)(pw, dim, domain);
  }
  
  __isl_give PW *FN(PW,set_tuple_id)(__isl_take PW *pw, enum isl_dim_type type,
  	__isl_take isl_id *id)
  {
  	isl_space *space;
  
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		goto error;
  
  	space = FN(PW,get_space)(pw);
  	space = isl_space_set_tuple_id(space, type, id);
  
  	return FN(PW,reset_space)(pw, space);
  error:
  	isl_id_free(id);
  	return FN(PW,free)(pw);
  }
  
  /* Drop the id on the specified tuple.
   */
  __isl_give PW *FN(PW,reset_tuple_id)(__isl_take PW *pw, enum isl_dim_type type)
  {
  	isl_space *space;
  
  	if (!pw)
  		return NULL;
  	if (!FN(PW,has_tuple_id)(pw, type))
  		return pw;
  
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		return NULL;
  
  	space = FN(PW,get_space)(pw);
  	space = isl_space_reset_tuple_id(space, type);
  
  	return FN(PW,reset_space)(pw, space);
  }
  
  __isl_give PW *FN(PW,set_dim_id)(__isl_take PW *pw,
  	enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
  {
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		goto error;
  	pw->dim = isl_space_set_dim_id(pw->dim, type, pos, id);
  	return FN(PW,reset_space)(pw, isl_space_copy(pw->dim));
  error:
  	isl_id_free(id);
  	return FN(PW,free)(pw);
  }
  #endif
  
  /* Reset the user pointer on all identifiers of parameters and tuples
   * of the space of "pw".
   */
  __isl_give PW *FN(PW,reset_user)(__isl_take PW *pw)
  {
  	isl_space *space;
  
  	space = FN(PW,get_space)(pw);
  	space = isl_space_reset_user(space);
  
  	return FN(PW,reset_space)(pw, space);
  }
  
  isl_bool FN(PW,has_equal_space)(__isl_keep PW *pw1, __isl_keep PW *pw2)
  {
  	if (!pw1 || !pw2)
  		return isl_bool_error;
  
  	return isl_space_is_equal(pw1->dim, pw2->dim);
  }
  
  #ifndef NO_MORPH
  __isl_give PW *FN(PW,morph_domain)(__isl_take PW *pw,
  	__isl_take isl_morph *morph)
  {
  	int i;
  	isl_ctx *ctx;
  
  	if (!pw || !morph)
  		goto error;
  
  	ctx = isl_space_get_ctx(pw->dim);
  	isl_assert(ctx, isl_space_is_domain_internal(morph->dom->dim, pw->dim),
  		goto error);
  
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		goto error;
  	pw->dim = isl_space_extend_domain_with_range(
  			isl_space_copy(morph->ran->dim), pw->dim);
  	if (!pw->dim)
  		goto error;
  
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].set = isl_morph_set(isl_morph_copy(morph), pw->p[i].set);
  		if (!pw->p[i].set)
  			goto error;
  		pw->p[i].FIELD = FN(EL,morph_domain)(pw->p[i].FIELD,
  						isl_morph_copy(morph));
  		if (!pw->p[i].FIELD)
  			goto error;
  	}
  
  	isl_morph_free(morph);
  
  	return pw;
  error:
  	FN(PW,free)(pw);
  	isl_morph_free(morph);
  	return NULL;
  }
  #endif
  
  int FN(PW,n_piece)(__isl_keep PW *pw)
  {
  	return pw ? pw->n : 0;
  }
  
  isl_stat FN(PW,foreach_piece)(__isl_keep PW *pw,
  	isl_stat (*fn)(__isl_take isl_set *set, __isl_take EL *el, void *user),
  	void *user)
  {
  	int i;
  
  	if (!pw)
  		return isl_stat_error;
  
  	for (i = 0; i < pw->n; ++i)
  		if (fn(isl_set_copy(pw->p[i].set),
  				FN(EL,copy)(pw->p[i].FIELD), user) < 0)
  			return isl_stat_error;
  
  	return isl_stat_ok;
  }
  
  #ifndef NO_LIFT
  static isl_bool any_divs(__isl_keep isl_set *set)
  {
  	int i;
  
  	if (!set)
  		return isl_bool_error;
  
  	for (i = 0; i < set->n; ++i)
  		if (set->p[i]->n_div > 0)
  			return isl_bool_true;
  
  	return isl_bool_false;
  }
  
  static isl_stat foreach_lifted_subset(__isl_take isl_set *set,
  	__isl_take EL *el,
  	isl_stat (*fn)(__isl_take isl_set *set, __isl_take EL *el,
  		void *user), void *user)
  {
  	int i;
  
  	if (!set || !el)
  		goto error;
  
  	for (i = 0; i < set->n; ++i) {
  		isl_set *lift;
  		EL *copy;
  
  		lift = isl_set_from_basic_set(isl_basic_set_copy(set->p[i]));
  		lift = isl_set_lift(lift);
  
  		copy = FN(EL,copy)(el);
  		copy = FN(EL,lift)(copy, isl_set_get_space(lift));
  
  		if (fn(lift, copy, user) < 0)
  			goto error;
  	}
  
  	isl_set_free(set);
  	FN(EL,free)(el);
  
  	return isl_stat_ok;
  error:
  	isl_set_free(set);
  	FN(EL,free)(el);
  	return isl_stat_error;
  }
  
  isl_stat FN(PW,foreach_lifted_piece)(__isl_keep PW *pw,
  	isl_stat (*fn)(__isl_take isl_set *set, __isl_take EL *el,
  		    void *user), void *user)
  {
  	int i;
  
  	if (!pw)
  		return isl_stat_error;
  
  	for (i = 0; i < pw->n; ++i) {
  		isl_bool any;
  		isl_set *set;
  		EL *el;
  
  		any = any_divs(pw->p[i].set);
  		if (any < 0)
  			return isl_stat_error;
  		set = isl_set_copy(pw->p[i].set);
  		el = FN(EL,copy)(pw->p[i].FIELD);
  		if (!any) {
  			if (fn(set, el, user) < 0)
  				return isl_stat_error;
  			continue;
  		}
  		if (foreach_lifted_subset(set, el, fn, user) < 0)
  			return isl_stat_error;
  	}
  
  	return isl_stat_ok;
  }
  #endif
  
  #ifndef NO_MOVE_DIMS
  __isl_give PW *FN(PW,move_dims)(__isl_take PW *pw,
  	enum isl_dim_type dst_type, unsigned dst_pos,
  	enum isl_dim_type src_type, unsigned src_pos, unsigned n)
  {
  	int i;
  
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		return NULL;
  
  	pw->dim = isl_space_move_dims(pw->dim, dst_type, dst_pos, src_type, src_pos, n);
  	if (!pw->dim)
  		goto error;
  
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].FIELD = FN(EL,move_dims)(pw->p[i].FIELD,
  					dst_type, dst_pos, src_type, src_pos, n);
  		if (!pw->p[i].FIELD)
  			goto error;
  	}
  
  	if (dst_type == isl_dim_in)
  		dst_type = isl_dim_set;
  	if (src_type == isl_dim_in)
  		src_type = isl_dim_set;
  
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].set = isl_set_move_dims(pw->p[i].set,
  						dst_type, dst_pos,
  						src_type, src_pos, n);
  		if (!pw->p[i].set)
  			goto error;
  	}
  
  	return pw;
  error:
  	FN(PW,free)(pw);
  	return NULL;
  }
  #endif
  
  __isl_give PW *FN(PW,mul_isl_int)(__isl_take PW *pw, isl_int v)
  {
  	int i;
  
  	if (isl_int_is_one(v))
  		return pw;
  	if (pw && DEFAULT_IS_ZERO && isl_int_is_zero(v)) {
  		PW *zero;
  		isl_space *dim = FN(PW,get_space)(pw);
  #ifdef HAS_TYPE
  		zero = FN(PW,ZERO)(dim, pw->type);
  #else
  		zero = FN(PW,ZERO)(dim);
  #endif
  		FN(PW,free)(pw);
  		return zero;
  	}
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		return NULL;
  	if (pw->n == 0)
  		return pw;
  
  #ifdef HAS_TYPE
  	if (isl_int_is_neg(v))
  		pw->type = isl_fold_type_negate(pw->type);
  #endif
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].FIELD = FN(EL,scale)(pw->p[i].FIELD, v);
  		if (!pw->p[i].FIELD)
  			goto error;
  	}
  
  	return pw;
  error:
  	FN(PW,free)(pw);
  	return NULL;
  }
  
  /* Multiply the pieces of "pw" by "v" and return the result.
   */
  __isl_give PW *FN(PW,scale_val)(__isl_take PW *pw, __isl_take isl_val *v)
  {
  	int i;
  
  	if (!pw || !v)
  		goto error;
  
  	if (isl_val_is_one(v)) {
  		isl_val_free(v);
  		return pw;
  	}
  	if (pw && DEFAULT_IS_ZERO && isl_val_is_zero(v)) {
  		PW *zero;
  		isl_space *space = FN(PW,get_space)(pw);
  #ifdef HAS_TYPE
  		zero = FN(PW,ZERO)(space, pw->type);
  #else
  		zero = FN(PW,ZERO)(space);
  #endif
  		FN(PW,free)(pw);
  		isl_val_free(v);
  		return zero;
  	}
  	if (pw->n == 0) {
  		isl_val_free(v);
  		return pw;
  	}
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		goto error;
  
  #ifdef HAS_TYPE
  	if (isl_val_is_neg(v))
  		pw->type = isl_fold_type_negate(pw->type);
  #endif
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].FIELD = FN(EL,scale_val)(pw->p[i].FIELD,
  						    isl_val_copy(v));
  		if (!pw->p[i].FIELD)
  			goto error;
  	}
  
  	isl_val_free(v);
  	return pw;
  error:
  	isl_val_free(v);
  	FN(PW,free)(pw);
  	return NULL;
  }
  
  /* Divide the pieces of "pw" by "v" and return the result.
   */
  __isl_give PW *FN(PW,scale_down_val)(__isl_take PW *pw, __isl_take isl_val *v)
  {
  	int i;
  
  	if (!pw || !v)
  		goto error;
  
  	if (isl_val_is_one(v)) {
  		isl_val_free(v);
  		return pw;
  	}
  
  	if (!isl_val_is_rat(v))
  		isl_die(isl_val_get_ctx(v), 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);
  
  	if (pw->n == 0) {
  		isl_val_free(v);
  		return pw;
  	}
  	pw = FN(PW,cow)(pw);
  	if (!pw)
  		goto error;
  
  #ifdef HAS_TYPE
  	if (isl_val_is_neg(v))
  		pw->type = isl_fold_type_negate(pw->type);
  #endif
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].FIELD = FN(EL,scale_down_val)(pw->p[i].FIELD,
  						    isl_val_copy(v));
  		if (!pw->p[i].FIELD)
  			goto error;
  	}
  
  	isl_val_free(v);
  	return pw;
  error:
  	isl_val_free(v);
  	FN(PW,free)(pw);
  	return NULL;
  }
  
  __isl_give PW *FN(PW,scale)(__isl_take PW *pw, isl_int v)
  {
  	return FN(PW,mul_isl_int)(pw, v);
  }
  
  /* Apply some normalization to "pw".
   * In particular, sort the pieces according to their function value
   * expressions, combining pairs of adjacent pieces with
   * the same such expression, and then normalize the domains of the pieces.
   *
   * We normalize in place, but if anything goes wrong we need
   * to return NULL, so we need to make sure we don't change the
   * meaning of any possible other copies of "pw".
   */
  __isl_give PW *FN(PW,normalize)(__isl_take PW *pw)
  {
  	int i;
  	isl_set *set;
  
  	pw = FN(PW,sort)(pw);
  	if (!pw)
  		return NULL;
  	for (i = 0; i < pw->n; ++i) {
  		set = isl_set_normalize(isl_set_copy(pw->p[i].set));
  		if (!set)
  			return FN(PW,free)(pw);
  		isl_set_free(pw->p[i].set);
  		pw->p[i].set = set;
  	}
  
  	return pw;
  }
  
  /* Is pw1 obviously equal to pw2?
   * That is, do they have obviously identical cells and obviously identical
   * elements on each cell?
   *
   * If "pw1" or "pw2" contain any NaNs, then they are considered
   * not to be the same.  A NaN is not equal to anything, not even
   * to another NaN.
   */
  isl_bool FN(PW,plain_is_equal)(__isl_keep PW *pw1, __isl_keep PW *pw2)
  {
  	int i;
  	isl_bool equal, has_nan;
  
  	if (!pw1 || !pw2)
  		return isl_bool_error;
  
  	has_nan = FN(PW,involves_nan)(pw1);
  	if (has_nan >= 0 && !has_nan)
  		has_nan = FN(PW,involves_nan)(pw2);
  	if (has_nan < 0 || has_nan)
  		return isl_bool_not(has_nan);
  
  	if (pw1 == pw2)
  		return isl_bool_true;
  	if (!isl_space_is_equal(pw1->dim, pw2->dim))
  		return isl_bool_false;
  
  	pw1 = FN(PW,copy)(pw1);
  	pw2 = FN(PW,copy)(pw2);
  	pw1 = FN(PW,normalize)(pw1);
  	pw2 = FN(PW,normalize)(pw2);
  	if (!pw1 || !pw2)
  		goto error;
  
  	equal = pw1->n == pw2->n;
  	for (i = 0; equal && i < pw1->n; ++i) {
  		equal = isl_set_plain_is_equal(pw1->p[i].set, pw2->p[i].set);
  		if (equal < 0)
  			goto error;
  		if (!equal)
  			break;
  		equal = FN(EL,plain_is_equal)(pw1->p[i].FIELD, pw2->p[i].FIELD);
  		if (equal < 0)
  			goto error;
  	}
  
  	FN(PW,free)(pw1);
  	FN(PW,free)(pw2);
  	return equal;
  error:
  	FN(PW,free)(pw1);
  	FN(PW,free)(pw2);
  	return isl_bool_error;
  }
  
  /* Does "pw" involve any NaNs?
   */
  isl_bool FN(PW,involves_nan)(__isl_keep PW *pw)
  {
  	int i;
  
  	if (!pw)
  		return isl_bool_error;
  	if (pw->n == 0)
  		return isl_bool_false;
  
  	for (i = 0; i < pw->n; ++i) {
  		isl_bool has_nan = FN(EL,involves_nan)(pw->p[i].FIELD);
  		if (has_nan < 0 || has_nan)
  			return has_nan;
  	}
  
  	return isl_bool_false;
  }
  
  #ifndef NO_PULLBACK
  static __isl_give PW *FN(PW,align_params_pw_multi_aff_and)(__isl_take PW *pw,
  	__isl_take isl_multi_aff *ma,
  	__isl_give PW *(*fn)(__isl_take PW *pw, __isl_take isl_multi_aff *ma))
  {
  	isl_ctx *ctx;
  	isl_bool equal_params;
  	isl_space *ma_space;
  
  	ma_space = isl_multi_aff_get_space(ma);
  	if (!pw || !ma || !ma_space)
  		goto error;
  	equal_params = isl_space_has_equal_params(pw->dim, ma_space);
  	if (equal_params < 0)
  		goto error;
  	if (equal_params) {
  		isl_space_free(ma_space);
  		return fn(pw, ma);
  	}
  	ctx = FN(PW,get_ctx)(pw);
  	if (FN(PW,check_named_params)(pw) < 0)
  		goto error;
  	if (!isl_space_has_named_params(ma_space))
  		isl_die(ctx, isl_error_invalid,
  			"unaligned unnamed parameters", goto error);
  	pw = FN(PW,align_params)(pw, ma_space);
  	ma = isl_multi_aff_align_params(ma, FN(PW,get_space)(pw));
  	return fn(pw, ma);
  error:
  	isl_space_free(ma_space);
  	FN(PW,free)(pw);
  	isl_multi_aff_free(ma);
  	return NULL;
  }
  
  static __isl_give PW *FN(PW,align_params_pw_pw_multi_aff_and)(__isl_take PW *pw,
  	__isl_take isl_pw_multi_aff *pma,
  	__isl_give PW *(*fn)(__isl_take PW *pw,
  		__isl_take isl_pw_multi_aff *ma))
  {
  	isl_bool equal_params;
  	isl_space *pma_space;
  
  	pma_space = isl_pw_multi_aff_get_space(pma);
  	if (!pw || !pma || !pma_space)
  		goto error;
  	equal_params = isl_space_has_equal_params(pw->dim, pma_space);
  	if (equal_params < 0)
  		goto error;
  	if (equal_params) {
  		isl_space_free(pma_space);
  		return fn(pw, pma);
  	}
  	if (FN(PW,check_named_params)(pw) < 0 ||
  	    isl_pw_multi_aff_check_named_params(pma) < 0)
  		goto error;
  	pw = FN(PW,align_params)(pw, pma_space);
  	pma = isl_pw_multi_aff_align_params(pma, FN(PW,get_space)(pw));
  	return fn(pw, pma);
  error:
  	isl_space_free(pma_space);
  	FN(PW,free)(pw);
  	isl_pw_multi_aff_free(pma);
  	return NULL;
  }
  
  /* Compute the pullback of "pw" by the function represented by "ma".
   * In other words, plug in "ma" in "pw".
   */
  static __isl_give PW *FN(PW,pullback_multi_aff_aligned)(__isl_take PW *pw,
  	__isl_take isl_multi_aff *ma)
  {
  	int i;
  	isl_space *space = NULL;
  
  	ma = isl_multi_aff_align_divs(ma);
  	pw = FN(PW,cow)(pw);
  	if (!pw || !ma)
  		goto error;
  
  	space = isl_space_join(isl_multi_aff_get_space(ma),
  				FN(PW,get_space)(pw));
  
  	for (i = 0; i < pw->n; ++i) {
  		pw->p[i].set = isl_set_preimage_multi_aff(pw->p[i].set,
  						    isl_multi_aff_copy(ma));
  		if (!pw->p[i].set)
  			goto error;
  		pw->p[i].FIELD = FN(EL,pullback_multi_aff)(pw->p[i].FIELD,
  						    isl_multi_aff_copy(ma));
  		if (!pw->p[i].FIELD)
  			goto error;
  	}
  
  	pw = FN(PW,reset_space)(pw, space);
  	isl_multi_aff_free(ma);
  	return pw;
  error:
  	isl_space_free(space);
  	isl_multi_aff_free(ma);
  	FN(PW,free)(pw);
  	return NULL;
  }
  
  __isl_give PW *FN(PW,pullback_multi_aff)(__isl_take PW *pw,
  	__isl_take isl_multi_aff *ma)
  {
  	return FN(PW,align_params_pw_multi_aff_and)(pw, ma,
  					&FN(PW,pullback_multi_aff_aligned));
  }
  
  /* Compute the pullback of "pw" by the function represented by "pma".
   * In other words, plug in "pma" in "pw".
   */
  static __isl_give PW *FN(PW,pullback_pw_multi_aff_aligned)(__isl_take PW *pw,
  	__isl_take isl_pw_multi_aff *pma)
  {
  	int i;
  	PW *res;
  
  	if (!pma)
  		goto error;
  
  	if (pma->n == 0) {
  		isl_space *space;
  		space = isl_space_join(isl_pw_multi_aff_get_space(pma),
  					FN(PW,get_space)(pw));
  		isl_pw_multi_aff_free(pma);
  		res = FN(PW,empty)(space);
  		FN(PW,free)(pw);
  		return res;
  	}
  
  	res = FN(PW,pullback_multi_aff)(FN(PW,copy)(pw),
  					isl_multi_aff_copy(pma->p[0].maff));
  	res = FN(PW,intersect_domain)(res, isl_set_copy(pma->p[0].set));
  
  	for (i = 1; i < pma->n; ++i) {
  		PW *res_i;
  
  		res_i = FN(PW,pullback_multi_aff)(FN(PW,copy)(pw),
  					isl_multi_aff_copy(pma->p[i].maff));
  		res_i = FN(PW,intersect_domain)(res_i,
  					isl_set_copy(pma->p[i].set));
  		res = FN(PW,add_disjoint)(res, res_i);
  	}
  
  	isl_pw_multi_aff_free(pma);
  	FN(PW,free)(pw);
  	return res;
  error:
  	isl_pw_multi_aff_free(pma);
  	FN(PW,free)(pw);
  	return NULL;
  }
  
  __isl_give PW *FN(PW,pullback_pw_multi_aff)(__isl_take PW *pw,
  	__isl_take isl_pw_multi_aff *pma)
  {
  	return FN(PW,align_params_pw_pw_multi_aff_and)(pw, pma,
  					&FN(PW,pullback_pw_multi_aff_aligned));
  }
  #endif
  