isl_pw_templ.c

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/*
 * 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>
 
#include "opt_type.h"
 
__isl_give PW *FN(PW,alloc_size)(__isl_take isl_space *space
  OPT_TYPE_PARAM, int n)
{
  isl_ctx *ctx;
  struct PW *pw;
 
  if (!space)
    return NULL;
  ctx = isl_space_get_ctx(space);
  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;
  OPT_SET_TYPE(pw->, type);
  pw->size = n;
  pw->n = 0;
  pw->dim = space;
  return pw;
error:
  isl_space_free(space);
  return NULL;
}
 
__isl_give PW *FN(PW,ZERO)(__isl_take isl_space *space OPT_TYPE_PARAM)
{
  return FN(PW,alloc_size)(space OPT_TYPE_ARG(NO_LOC), 0);
}
 
/* Add a piece with domain "set" and base expression "el"
 * to the piecewise expression "pw".
 *
 * Do this independently of the values of "set" and "el",
 * such that this function can be used by isl_pw_*_dup.
 */
static __isl_give PW *FN(PW,add_dup_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;
 
  ctx = isl_set_get_ctx(set);
  if (!OPT_EQUAL_TYPES(pw->, el->))
    isl_die(ctx, isl_error_invalid, "fold types don't match",
      goto error);
  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;
}
 
/* Add a piece with domain "set" and base expression "el"
 * to the piecewise expression "pw", provided the domain
 * is not obviously empty and the base expression
 * is not equal to the default value.
 */
__isl_give PW *FN(PW,add_piece)(__isl_take PW *pw,
  __isl_take isl_set *set, __isl_take EL *el)
{
  isl_bool skip;
 
  skip = isl_set_plain_is_empty(set);
  if (skip >= 0 && !skip)
    skip = FN(EL,EL_IS_ZERO)(el);
  if (skip >= 0 && !skip)
    return FN(PW,add_dup_piece)(pw, set, el);
 
  isl_set_free(set);
  FN(EL,free)(el);
  if (skip < 0)
    return FN(PW,free)(pw);
  return pw;
}
 
/* 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;
}
 
__isl_give PW *FN(PW,alloc)(OPT_TYPE_PARAM_FIRST
  __isl_take isl_set *set, __isl_take EL *el)
{
  PW *pw;
 
  if (FN(PW,check_compatible_domain)(el, set) < 0)
    goto error;
 
  pw = FN(PW,alloc_size)(FN(EL,get_space)(el) OPT_TYPE_ARG(NO_LOC), 1);
 
  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;
 
  dup = FN(PW,alloc_size)(isl_space_copy(pw->dim)
        OPT_TYPE_ARG(pw->), pw->n);
  if (!dup)
    return NULL;
 
  for (i = 0; i < pw->n; ++i)
    dup = FN(PW,add_dup_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;
}
 
/* 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));
}
 
/* Return the space of "pw".
 * This may be either a copy or the space itself
 * if there is only one reference to "pw".
 * This allows the space to be modified inplace
 * if both the piecewise expression and its space have only a single reference.
 * The caller is not allowed to modify "pw" between this call and
 * a subsequent call to isl_pw_*_restore_*.
 * The only exception is that isl_pw_*_free can be called instead.
 */
static __isl_give isl_space *FN(PW,take_space)(__isl_keep PW *pw)
{
  isl_space *space;
 
  if (!pw)
    return NULL;
  if (pw->ref != 1)
    return FN(PW,get_space)(pw);
  space = pw->dim;
  pw->dim = NULL;
  return space;
}
 
/* Set the space of "pw" to "space", where the space of "pw" may be missing
 * due to a preceding call to isl_pw_*_take_space.
 * However, in this case, "pw" only has a single reference and
 * then the call to isl_pw_*_cow has no effect.
 */
static __isl_give PW *FN(PW,restore_space)(__isl_take PW *pw,
  __isl_take isl_space *space)
{
  if (!pw || !space)
    goto error;
 
  if (pw->dim == space) {
    isl_space_free(space);
    return pw;
  }
 
  pw = FN(PW,cow)(pw);
  if (!pw)
    goto error;
  isl_space_free(pw->dim);
  pw->dim = space;
 
  return pw;
error:
  FN(PW,free)(pw);
  isl_space_free(space);
  return NULL;
}
 
/* Check that "pos" is a valid position for a cell in "pw".
 */
static isl_stat FN(PW,check_pos)(__isl_keep PW *pw, int pos)
{
  if (!pw)
    return isl_stat_error;
  if (pos < 0 || pos >= pw->n)
    isl_die(FN(PW,get_ctx)(pw), isl_error_internal,
      "position out of bounds", return isl_stat_error);
  return isl_stat_ok;
}
 
/* Return the cell at position "pos" in "pw".
 */
static __isl_keep isl_set *FN(PW,peek_domain_at)(__isl_keep PW *pw, int pos)
{
  if (FN(PW,check_pos)(pw, pos) < 0)
    return NULL;
  return pw->p[pos].set;
}
 
/* Return a copy of the cell at position "pos" in "pw".
 */
static __isl_give isl_set *FN(PW,get_domain_at)(__isl_keep PW *pw, int pos)
{
  return isl_set_copy(FN(PW,peek_domain_at)(pw, pos));
}
 
/* Return the cell at position "pos" in "pw".
 * This may be either a copy or the cell itself
 * if there is only one reference to "pw".
 * This allows the cell to be modified inplace
 * if both the piecewise expression and this cell
 * have only a single reference.
 * The caller is not allowed to modify "pw" between this call and
 * the subsequent call to isl_pw_*_restore_domain_at.
 * The only exception is that isl_pw_*_free can be called instead.
 */
static __isl_give isl_set *FN(PW,take_domain_at)(__isl_keep PW *pw, int pos)
{
  isl_set *domain;
 
  if (!pw)
    return NULL;
  if (pw->ref != 1)
    return FN(PW,get_domain_at)(pw, pos);
  if (FN(PW,check_pos)(pw, pos) < 0)
    return NULL;
  domain = pw->p[pos].set;
  pw->p[pos].set = NULL;
  return domain;
}
 
/* Set the cell at position "pos" in "pw" to "el",
 * where this cell may be missing
 * due to a preceding call to isl_pw_*_take_domain_at.
 * However, in this case, "pw" only has a single reference and
 * then the call to isl_pw_*_cow has no effect.
 */
static __isl_give PW *FN(PW,restore_domain_at)(__isl_take PW *pw, int pos,
  __isl_take isl_set *domain)
{
  if (FN(PW,check_pos)(pw, pos) < 0 || !domain)
    goto error;
 
  if (pw->p[pos].set == domain) {
    isl_set_free(domain);
    return pw;
  }
 
  pw = FN(PW,cow)(pw);
  if (!pw)
    goto error;
  isl_set_free(pw->p[pos].set);
  pw->p[pos].set = domain;
 
  return pw;
error:
  FN(PW,free)(pw);
  isl_set_free(domain);
  return NULL;
}
 
/* Return the base expression associated to
 * the cell at position "pos" in "pw".
 */
__isl_keep EL *FN(PW,peek_base_at)(__isl_keep PW *pw, int pos)
{
  if (FN(PW,check_pos)(pw, pos) < 0)
    return NULL;
  return pw->p[pos].FIELD;
}
 
/* Return a copy of the base expression associated to
 * the cell at position "pos" in "pw".
 */
static __isl_give EL *FN(PW,get_base_at)(__isl_keep PW *pw, int pos)
{
  return FN(EL,copy)(FN(PW,peek_base_at)(pw, pos));
}
 
/* Return the base expression associated to
 * the cell at position "pos" in "pw".
 * This may be either a copy or the base expression itself
 * if there is only one reference to "pw".
 * This allows the base expression to be modified inplace
 * if both the piecewise expression and this base expression
 * have only a single reference.
 * The caller is not allowed to modify "pw" between this call and
 * a subsequent call to isl_pw_*_restore_*.
 * The only exception is that isl_pw_*_free can be called instead.
 */
static __isl_give EL *FN(PW,take_base_at)(__isl_keep PW *pw, int pos)
{
  EL *el;
 
  if (!pw)
    return NULL;
  if (pw->ref != 1)
    return FN(PW,get_base_at)(pw, pos);
  if (FN(PW,check_pos)(pw, pos) < 0)
    return NULL;
  el = pw->p[pos].FIELD;
  pw->p[pos].FIELD = NULL;
  return el;
}
 
/* Set the base expression associated to
 * the cell at position "pos" in "pw" to "el",
 * where this base expression may be missing
 * due to a preceding call to isl_pw_*_take_base_at.
 * However, in this case, "pw" only has a single reference and
 * then the call to isl_pw_*_cow has no effect.
 * If "inplace" is set, then replacing the base expression by "el"
 * is known not to change the meaning of "pw".  It can therefore be replaced
 * in all references to "pw".
 */
static __isl_give PW *FN(PW,restore_base_at_)(__isl_take PW *pw, int pos,
  __isl_take EL *el, int inplace)
{
  if (FN(PW,check_pos)(pw, pos) < 0 || !el)
    goto error;
 
  if (pw->p[pos].FIELD == el) {
    FN(EL,free)(el);
    return pw;
  }
 
  if (!inplace)
    pw = FN(PW,cow)(pw);
  if (!pw)
    goto error;
  FN(EL,free)(pw->p[pos].FIELD);
  pw->p[pos].FIELD = el;
 
  return pw;
error:
  FN(PW,free)(pw);
  FN(EL,free)(el);
  return NULL;
}
 
/* Set the base expression associated to
 * the cell at position "pos" in "pw" to "el",
 * where this base expression may be missing
 * due to a preceding call to isl_pw_*_take_base_at.
 */
static __isl_give PW *FN(PW,restore_base_at)(__isl_take PW *pw, int pos,
  __isl_take EL *el)
{
  return FN(PW,restore_base_at_)(pw, pos, el, 0);
}
 
/* Set the base expression associated to
 * the cell at position "pos" in "pw" to "el",
 * where this base expression may be missing
 * due to a preceding call to isl_pw_*_take_base_at.
 * Furthermore, replacing the base expression by "el"
 * is known not to change the meaning of "pw".
 */
static __isl_give PW *FN(PW,restore_base_at_inplace)(__isl_take PW *pw, int pos,
  __isl_take EL *el)
{
  return FN(PW,restore_base_at_)(pw, pos, el, 1);
}
 
/* Create a piecewise expression with the given base expression on a universe
 * domain.
 */
static __isl_give PW *FN(FN(FN(PW,from),BASE),type_base)(__isl_take EL *el
  OPT_TYPE_PARAM)
{
  isl_set *dom = isl_set_universe(FN(EL,get_domain_space)(el));
  return FN(PW,alloc)(OPT_TYPE_ARG_FIRST(NO_LOC) dom, el);
}
 
/* Create a piecewise expression with the given base expression on a universe
 * domain.
 *
 * If the default value of this piecewise type is zero and
 * if "el" is effectively zero, then create an empty piecewise expression
 * instead.
 */
static __isl_give PW *FN(FN(FN(PW,from),BASE),type)(__isl_take EL *el
  OPT_TYPE_PARAM)
{
  isl_bool is_zero;
  isl_space *space;
 
  if (!DEFAULT_IS_ZERO)
    return FN(FN(FN(PW,from),BASE),type_base)(el
              OPT_TYPE_ARG(NO_LOC));
  is_zero = FN(EL,EL_IS_ZERO)(el);
  if (is_zero < 0)
    goto error;
  if (!is_zero)
    return FN(FN(FN(PW,from),BASE),type_base)(el
              OPT_TYPE_ARG(NO_LOC));
  space = FN(EL,get_space)(el);
  FN(EL,free)(el);
  return FN(PW,ZERO)(space OPT_TYPE_ARG(NO_LOC));
error:
  FN(EL,free)(el);
  return NULL;
}
 
#ifdef HAS_TYPE
/* Create a piecewise expression with the given base expression on a universe
 * domain.
 *
 * Pass along the type as an extra argument for improved uniformity
 * with piecewise types that do not have a fold type.
 */
__isl_give PW *FN(FN(PW,from),BASE)(__isl_take EL *el)
{
  enum isl_fold type = FN(EL,get_type)(el);
  return FN(FN(FN(PW,from),BASE),type)(el, type);
}
#else
__isl_give PW *FN(FN(PW,from),BASE)(__isl_take EL *el)
{
  return FN(FN(FN(PW,from),BASE),type)(el);
}
#endif
 
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 isl_bool_ok(pw->n == 0);
}
 
static __isl_give PW *FN(PW,realign_domain)(__isl_take PW *pw,
  __isl_take isl_reordering *exp)
{
  int i;
  isl_size n;
 
  n = FN(PW,n_piece)(pw);
  if (n < 0 || !exp)
    goto error;
 
  for (i = 0; i < n; ++i) {
    isl_set *domain;
    EL *el;
 
    domain = FN(PW,take_domain_at)(pw, i);
    domain = isl_set_realign(domain, isl_reordering_copy(exp));
    pw = FN(PW,restore_domain_at)(pw, i, domain);
 
    el = FN(PW,take_base_at)(pw, i);
    el = FN(EL,realign_domain)(el, isl_reordering_copy(exp));
    pw = FN(PW,restore_base_at)(pw, i, el);
  }
 
  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;
}
 
#undef TYPE
#define TYPE PW
 
#include "isl_check_named_params_templ.c"
 
/* 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_space *space;
    isl_reordering *exp;
 
    space = FN(PW,get_domain_space)(pw);
    exp = isl_parameter_alignment_reordering(space, model);
    isl_space_free(space);
    pw = FN(PW,realign_domain)(pw, exp);
  }
 
  isl_space_free(model);
  return pw;
error:
  isl_space_free(model);
  FN(PW,free)(pw);
  return NULL;
}
 
#undef TYPE
#define TYPE  PW
 
static
#include "isl_align_params_bin_templ.c"
 
#undef SUFFIX
#define SUFFIX  set
#undef ARG1
#define ARG1  PW
#undef ARG2
#define ARG2  isl_set
 
static
#include "isl_align_params_templ.c"
 
#undef TYPE
#define TYPE  PW
 
#include "isl_type_has_equal_space_bin_templ.c"
#include "isl_type_check_equal_space_templ.c"
 
/* 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)
{
  int i, j, n;
  struct PW *res;
  isl_ctx *ctx;
  isl_set *set;
 
  if (FN(PW,align_params_bin)(&pw1, &pw2) < 0)
    goto error;
 
  ctx = isl_space_get_ctx(pw1->dim);
  if (!OPT_EQUAL_TYPES(pw1->, pw2->))
    isl_die(ctx, isl_error_invalid,
      "fold types don't match", goto error);
  if (FN(PW,check_equal_space)(pw1, pw2) < 0)
    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);
  res = FN(PW,alloc_size)(isl_space_copy(pw1->dim)
        OPT_TYPE_ARG(pw1->), 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;
      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;
}
 
#if !DEFAULT_IS_ZERO
 
/* Compute the sum of "pw1" and "pw2 on the union of their domains,
 * with the actual sum on the shared domain and
 * the defined expression on the symmetric difference of the domains.
 *
 * This function is only defined for object types that do not have
 * a default zero value.  For other object types, this function
 * is simply called "add".
 */
__isl_give PW *FN(PW,union_add)(__isl_take PW *pw1, __isl_take PW *pw2)
{
  return FN(PW,union_add_)(pw1, pw2);
}
 
#endif
 
/* 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;
  res = FN(PW,alloc_size)(isl_space_copy(space) OPT_TYPE_ARG(pw1->), n);
 
  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 (FN(PW,check_equal_space)(pw1, pw2) < 0)
    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;
}
 
/* 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 __isl_give PW *FN(PW,exploit_equalities_and_remove_if_empty)(
  __isl_take PW *pw, int i)
{
  EL *el;
  isl_set *domain;
  isl_basic_set *aff;
  int empty;
 
  domain = FN(PW,peek_domain_at)(pw, i);
  empty = isl_set_plain_is_empty(domain);
  if (empty < 0)
    return FN(PW,free)(pw);
  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 pw;
  }
 
  aff = isl_set_affine_hull(FN(PW,get_domain_at)(pw, i));
  el = FN(PW,take_base_at)(pw, i);
  el = FN(EL,substitute_equalities)(el, aff);
  pw = FN(PW,restore_base_at_inplace)(pw, i, el);
 
  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, isl_set_intersect_factor_domain,
 * isl_set_intersect_factor_range or isl_set_subtract.
 */
static __isl_give PW *FN(PW,restrict_domain)(__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;
  isl_size n;
 
  FN(PW,align_params_set)(&pw, &set);
  n = FN(PW,n_piece)(pw);
  if (n < 0 || !set)
    goto error;
 
  for (i = n - 1; i >= 0; --i) {
    isl_set *domain;
 
    domain = FN(PW,take_domain_at)(pw, i);
    domain = fn(domain, isl_set_copy(set));
    pw = FN(PW,restore_domain_at)(pw, i, domain);
    pw = FN(PW,exploit_equalities_and_remove_if_empty)(pw, i);
  }
  
  isl_set_free(set);
  return pw;
error:
  isl_set_free(set);
  FN(PW,free)(pw);
  return NULL;
}
 
__isl_give PW *FN(PW,intersect_domain)(__isl_take PW *pw,
  __isl_take isl_set *context)
{
  return FN(PW,restrict_domain)(pw, context, &isl_set_intersect);
}
 
/* 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,restrict_domain)(pw, context, &isl_set_intersect_params);
}
 
/* Given a piecewise expression "pw" with domain in a space [A -> B] and
 * a set in the space A, intersect the domain with the set.
 */
__isl_give PW *FN(PW,intersect_domain_wrapped_domain)(__isl_take PW *pw,
  __isl_take isl_set *set)
{
  return FN(PW,restrict_domain)(pw, set,
              &isl_set_intersect_factor_domain);
}
 
/* Given a piecewise expression "pw" with domain in a space [A -> B] and
 * a set in the space B, intersect the domain with the set.
 */
__isl_give PW *FN(PW,intersect_domain_wrapped_range)(__isl_take PW *pw,
  __isl_take isl_set *set)
{
  return FN(PW,restrict_domain)(pw, set, &isl_set_intersect_factor_range);
}
 
/* 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,restrict_domain)(pw, domain, &isl_set_subtract);
}
 
/* 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.
 */
static __isl_give PW *FN(PW,sort_unique)(__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) {
    isl_bool equal;
    EL *el, *el_prev;
    isl_set *set_prev;
 
    el = FN(PW,peek_base_at)(pw, i);
    el_prev = FN(PW,peek_base_at)(pw, i - 1);
    equal = FN(EL,plain_is_equal)(el, el_prev);
    if (equal < 0)
      return FN(PW,free)(pw);
    if (!equal)
      continue;
    set = FN(PW,get_domain_at)(pw, i);
    set_prev = FN(PW,get_domain_at)(pw, i - 1);
    set = isl_set_union(set_prev, 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;
}
 
/* 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".
 * 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)
{
  int i;
  isl_space *space;
  EL *el;
 
  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);
  el = FN(PW,take_base_at)(pw, 0);
  el = FN(EL,gist)(el, context);
  pw = FN(PW,restore_base_at)(pw, 0, el);
  context = isl_set_universe(space);
  pw = FN(PW,restore_domain_at)(pw, 0, context);
 
  return pw;
}
 
/* Compute the gist of "pw" with respect to the domain constraints
 * of "context".
 * Call "fn_dom" to compute the gist of the domains and
 * "intersect_context" to intersect the domain with the context.
 *
 * If the piecewise expression is empty or the context is the universe,
 * then nothing can be simplified.
 * If "pw" has a single domain and it is equal to "context",
 * then simply replace the domain by the universe.
 * Combine duplicate function value expressions first
 * to increase the chance of "pw" having a single domain.
 */
static __isl_give PW *FN(PW,gist_fn)(__isl_take PW *pw,
  __isl_take isl_set *context,
  __isl_give isl_set *(*fn_dom)(__isl_take isl_set *set,
            __isl_take isl_set *context),
  __isl_give isl_set *intersect_context(__isl_take isl_set *set,
    __isl_take isl_set *context))
{
  int i;
  int is_universe;
 
  pw = FN(PW,sort_unique)(pw);
  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;
  }
 
  FN(PW,align_params_set)(&pw, &context);
 
  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);
  }
 
  context = isl_set_compute_divs(context);
 
  for (i = pw->n - 1; i >= 0; --i) {
    isl_set *set_i;
    EL *el;
    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)
        return FN(PW,gist_last)(pw, context);
    }
    set_i = FN(PW,get_domain_at)(pw, i);
    set_i = intersect_context(set_i, isl_set_copy(context));
    empty = isl_set_plain_is_empty(set_i);
    el = FN(PW,take_base_at)(pw, i);
    el = FN(EL,gist)(el, set_i);
    pw = FN(PW,restore_base_at)(pw, i, el);
    set_i = FN(PW,take_domain_at)(pw, i);
    set_i = fn_dom(set_i, isl_set_copy(context));
    pw = FN(PW,restore_domain_at)(pw, i, set_i);
    if (empty < 0 || !pw)
      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_set_free(context);
 
  return pw;
error:
  FN(PW,free)(pw);
  isl_set_free(context);
  return NULL;
}
 
__isl_give PW *FN(PW,gist)(__isl_take PW *pw, __isl_take isl_set *context)
{
  return FN(PW,gist_fn)(pw, context, &isl_set_gist,
          &isl_set_intersect);
}
 
__isl_give PW *FN(PW,gist_params)(__isl_take PW *pw,
  __isl_take isl_set *context)
{
  return FN(PW,gist_fn)(pw, context, &isl_set_gist_params,
          &isl_set_intersect_params);
}
 
/* 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;
  isl_size n;
 
  pw = FN(PW,sort_unique)(pw);
  n = FN(PW,n_piece)(pw);
  if (n < 0)
    return FN(PW,free)(pw);
 
  for (i = 0; i < 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)
{
  isl_space *space;
 
  space = FN(PW,get_space)(pw);
  space = isl_space_set_dim_name(space, type, pos, s);
  return FN(PW,reset_space)(pw, space);
}
 
__isl_give PW *FN(PW,drop_dims)(__isl_take PW *pw,
  enum isl_dim_type type, unsigned first, unsigned n)
{
  int i;
  isl_size n_piece;
  enum isl_dim_type set_type;
  isl_space *space;
 
  n_piece = FN(PW,n_piece)(pw);
  if (n_piece < 0)
    return FN(PW,free)(pw);
  if (n == 0 && !isl_space_get_tuple_name(pw->dim, type))
    return pw;
 
  set_type = type == isl_dim_in ? isl_dim_set : type;
 
  space = FN(PW,take_space)(pw);
  space = isl_space_drop_dims(space, type, first, n);
  pw = FN(PW,restore_space)(pw, space);
  for (i = 0; i < n_piece; ++i) {
    isl_set *domain;
    EL *el;
 
    el = FN(PW,take_base_at)(pw, i);
    el = FN(EL,drop_dims)(el, type, first, n);
    pw = FN(PW,restore_base_at)(pw, i, el);
    if (type == isl_dim_out)
      continue;
    domain = FN(PW,take_domain_at)(pw, i);
    domain = isl_set_drop(domain, set_type, first, n);
    pw = FN(PW,restore_domain_at)(pw, i, domain);
  }
 
  return pw;
}
 
/* 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;
  isl_size n_piece;
  enum isl_dim_type set_type;
  isl_space *space;
 
  n_piece = FN(PW,n_piece)(pw);
  if (n_piece < 0)
    return FN(PW,free)(pw);
  if (n == 0 && !isl_space_get_tuple_name(pw->dim, type))
    return pw;
 
  set_type = type == isl_dim_in ? isl_dim_set : type;
 
  space = FN(PW,take_space)(pw);
  space = isl_space_drop_dims(space, type, first, n);
  pw = FN(PW,restore_space)(pw, space);
  for (i = 0; i < n_piece; ++i) {
    isl_set *domain;
    EL *el;
 
    domain = FN(PW,take_domain_at)(pw, i);
    domain = isl_set_project_out(domain, set_type, first, n);
    pw = FN(PW,restore_domain_at)(pw, i, domain);
    el = FN(PW,take_base_at)(pw, i);
    el = FN(EL,drop_dims)(el, type, first, n);
    pw = FN(PW,restore_base_at)(pw, i, el);
  }
 
  return pw;
}
 
/* 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;
  isl_size n;
 
  n = FN(PW,dim)(pw, isl_dim_in);
  if (n < 0)
    return FN(PW,free)(pw);
  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;
}
 
#undef TYPE
#define TYPE  PW
#include "isl_drop_unused_params_templ.c"
 
isl_size FN(PW,dim)(__isl_keep PW *pw, enum isl_dim_type type)
{
  return isl_space_dim(FN(PW,peek_space)(pw), type);
}
 
__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);
}
 
/* Return the position of the dimension of the given type and identifier
 * in "pw".
 * Return -1 if no such dimension can be found.
 */
static int FN(PW,find_dim_by_id)(__isl_keep PW *pw,
  enum isl_dim_type type, __isl_keep isl_id *id)
{
  isl_space *space;
 
  space = FN(PW,peek_space)(pw);
  return isl_space_find_dim_by_id(space, type, id);
}
 
/* Does the piecewise expression "pw" depend in any way
 * on the parameter with identifier "id"?
 */
isl_bool FN(PW,involves_param_id)(__isl_keep PW *pw, __isl_keep isl_id *id)
{
  int pos;
 
  if (!pw || !id)
    return isl_bool_error;
  if (pw->n == 0)
    return isl_bool_false;
 
  pos = FN(PW,find_dim_by_id)(pw, isl_dim_param, id);
  if (pos < 0)
    return isl_bool_false;
  return FN(PW,involves_dims)(pw, isl_dim_param, pos, 1);
}
 
/* 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;
  isl_size n;
 
  n = FN(PW,n_piece)(pw);
  if (n < 0 || !space || !domain)
    goto error;
 
  for (i = 0; i < n; ++i) {
    isl_set *set;
    EL *el;
 
    set = FN(PW,take_domain_at)(pw, i);
    set = isl_set_reset_space(set, isl_space_copy(domain));
    pw = FN(PW,restore_domain_at)(pw, i, set);
    el = FN(PW,take_base_at)(pw, i);
    el = FN(EL,reset_space_and_domain)(el,
            isl_space_copy(space), isl_space_copy(domain));
    pw = FN(PW,restore_base_at)(pw, i, el);
  }
 
  isl_space_free(domain);
 
  pw = FN(PW,restore_space)(pw, 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 *space)
{
  isl_space *domain;
 
  domain = isl_space_domain(isl_space_copy(space));
  return FN(PW,reset_space_and_domain)(pw, space, 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)
{
  isl_space *space;
 
  space = FN(PW,get_space)(pw);
  space = isl_space_set_dim_id(space, type, pos, id);
  return FN(PW,reset_space)(pw, space);
}
 
/* 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_size FN(PW,n_piece)(__isl_keep PW *pw)
{
  return pw ? pw->n : isl_size_error;
}
 
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;
}
 
/* Does "test" succeed on every cell of "pw"?
 */
isl_bool FN(PW,every_piece)(__isl_keep PW *pw,
  isl_bool (*test)(__isl_keep isl_set *set,
    __isl_keep EL *el, void *user), void *user)
{
  int i;
 
  if (!pw)
    return isl_bool_error;
 
  for (i = 0; i < pw->n; ++i) {
    isl_bool r;
 
    r = test(pw->p[i].set, pw->p[i].FIELD, user);
    if (r < 0 || !r)
      return r;
  }
 
  return isl_bool_true;
}
 
/* Is "pw" defined over a single universe domain?
 *
 * If the default value of this piecewise type is zero,
 * then a "pw" with a zero number of cells is also accepted
 * as it represents the default zero value.
 */
isl_bool FN(FN(PW,isa),BASE)(__isl_keep PW *pw)
{
  isl_size n;
 
  n = FN(PW,n_piece)(pw);
  if (n < 0)
    return isl_bool_error;
  if (DEFAULT_IS_ZERO && n == 0)
    return isl_bool_true;
  if (n != 1)
    return isl_bool_false;
  return isl_set_plain_is_universe(FN(PW,peek_domain_at)(pw, 0));
}
 
/* Return a zero base expression in the same space (and of the same type)
 * as "pw".
 */
static __isl_give EL *FN(EL,zero_like_type)(__isl_take PW *pw OPT_TYPE_PARAM)
{
  isl_space *space;
 
  space = FN(PW,get_space)(pw);
  FN(PW,free)(pw);
  return FN(EL,zero_in_space)(space OPT_TYPE_ARG(NO_LOC));
}
 
#ifndef HAS_TYPE
/* Return a zero base expression in the same space as "pw".
 */
static __isl_give EL *FN(EL,zero_like)(__isl_take PW *pw)
{
  return FN(EL,zero_like_type)(pw);
}
#else
/* Return a zero base expression in the same space and of the same type
 * as "pw".
 *
 * Pass along the type as an explicit argument for uniform handling
 * in isl_*_zero_like_type.
 */
static __isl_give EL *FN(EL,zero_like)(__isl_take PW *pw)
{
  enum isl_fold type;
 
  type = FN(PW,get_type)(pw);
  if (type < 0)
    goto error;
  return FN(EL,zero_like_type)(pw, type);
error:
  FN(PW,free)(pw);
  return NULL;
}
#endif
 
/* Given that "pw" is defined over a single universe domain,
 * return the base expression associated to this domain.
 *
 * If the number of cells is zero, then "pw" is of a piecewise type
 * with a default zero value and effectively represents zero.
 * In this case, create a zero base expression in the same space
 * (and with the same type).
 * Otherwise, simply extract the associated base expression.
 */
__isl_give EL *FN(FN(PW,as),BASE)(__isl_take PW *pw)
{
  isl_bool is_total;
  isl_size n;
  EL *el;
 
  is_total = FN(FN(PW,isa),BASE)(pw);
  if (is_total < 0)
    goto error;
  if (!is_total)
    isl_die(FN(PW,get_ctx)(pw), isl_error_invalid,
      "expecting single total function", goto error);
  n = FN(PW,n_piece)(pw);
  if (n < 0)
    goto error;
  if (n == 0)
    return FN(EL,zero_like)(pw);
  el = FN(PW,take_base_at)(pw, 0);
  FN(PW,free)(pw);
  return el;
error:
  FN(PW,free)(pw);
  return NULL;
}
 
#ifdef HAS_TYPE
/* Negate the type of "pw".
 */
static __isl_give PW *FN(PW,negate_type)(__isl_take PW *pw)
{
  pw = FN(PW,cow)(pw);
  if (!pw)
    return NULL;
  pw->type = isl_fold_type_negate(pw->type);
  return pw;
}
#else
/* Negate the type of "pw".
 * Since "pw" does not have a type, do nothing.
 */
static __isl_give PW *FN(PW,negate_type)(__isl_take PW *pw)
{
  return pw;
}
#endif
 
/* 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;
  isl_size n;
 
  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);
    zero = FN(PW,ZERO)(space OPT_TYPE_ARG(pw->));
    FN(PW,free)(pw);
    isl_val_free(v);
    return zero;
  }
  if (isl_val_is_neg(v))
    pw = FN(PW,negate_type)(pw);
  n = FN(PW,n_piece)(pw);
  if (n < 0)
    goto error;
 
  for (i = 0; i < n; ++i) {
    EL *el;
 
    el = FN(PW,take_base_at)(pw, i);
    el = FN(EL,scale_val)(el, isl_val_copy(v));
    pw = FN(PW,restore_base_at)(pw, i, el);
  }
 
  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;
  isl_size n;
 
  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 (isl_val_is_neg(v))
    pw = FN(PW,negate_type)(pw);
  n = FN(PW,n_piece)(pw);
  if (n < 0)
    goto error;
 
  for (i = 0; i < n; ++i) {
    EL *el;
 
    el = FN(PW,take_base_at)(pw, i);
    el = FN(EL,scale_down_val)(el, isl_val_copy(v));
    pw = FN(PW,restore_base_at)(pw, i, el);
  }
 
  isl_val_free(v);
  return pw;
error:
  isl_val_free(v);
  FN(PW,free)(pw);
  return NULL;
}
 
/* 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".
 */
static __isl_give PW *FN(PW,normalize)(__isl_take PW *pw)
{
  int i;
  isl_set *set;
 
  pw = FN(PW,sort_unique)(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;
  equal = FN(PW,has_equal_space)(pw1, pw2);
  if (equal < 0 || !equal)
    return equal;
 
  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 = isl_bool_ok(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;
}