/Users/buildslave/jenkins/workspace/clang-stage2-coverage-R/llvm/tools/polly/lib/External/isl/isl_aff.c

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/*
 * Copyright 2011      INRIA Saclay
 * Copyright 2011      Sven Verdoolaege
 * Copyright 2012-2014 Ecole Normale Superieure
 * Copyright 2014      INRIA Rocquencourt
 *
 * 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
 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
 * B.P. 105 - 78153 Le Chesnay, France
 */

#include <isl_ctx_private.h>
#include <isl_map_private.h>
#include <isl_union_map_private.h>
#include <isl_aff_private.h>
#include <isl_space_private.h>
#include <isl_local_space_private.h>
#include <isl_vec_private.h>
#include <isl_mat_private.h>
#include <isl/id.h>
#include <isl/constraint.h>
#include <isl_seq.h>
#include <isl/set.h>
#include <isl_val_private.h>
#include <isl_point_private.h>
#include <isl_config.h>

#undef BASE
#define BASE aff

#include <isl_list_templ.c>

#undef BASE
#define BASE pw_aff

#include <isl_list_templ.c>

#undef BASE
#define BASE pw_multi_aff

#include <isl_list_templ.c>

#undef BASE
#define BASE union_pw_aff

#include <isl_list_templ.c>

#undef BASE
#define BASE union_pw_multi_aff

#include <isl_list_templ.c>

__isl_give isl_aff *isl_aff_alloc_vec(__isl_take isl_local_space *ls,
  __isl_take isl_vec *v)
{
  isl_aff *aff;

  if (!ls || !v)
    goto error;

  aff = isl_calloc_type(v->ctx, struct isl_aff);
  if (!aff)
    goto error;

  aff->ref = 1;
  aff->ls = ls;
  aff->v = v;

  return aff;
error:
  isl_local_space_free(ls);
  isl_vec_free(v);
  return NULL;
}

__isl_give isl_aff *isl_aff_alloc(__isl_take isl_local_space *ls)
{
  isl_ctx *ctx;
  isl_vec *v;
  unsigned total;

  if (!ls)
    return NULL;

  ctx = isl_local_space_get_ctx(ls);
  if (!isl_local_space_divs_known(ls))
    isl_die0(ctx, isl_error_invalid, "local space has unknown divs",
      goto error);
  if (!isl_local_space_is_set(ls))
    isl_die0(ctx, isl_error_invalid,
      "domain of affine expression should be a set",
      goto error);

  total = isl_local_space_dim(ls, isl_dim_all);
  v = isl_vec_alloc(ctx, 1 + 1 + total);
  return isl_aff_alloc_vec(ls, v);
error:
  isl_local_space_free(ls);
  return NULL;
}

__isl_give isl_aff *isl_aff_zero_on_domain(__isl_take isl_local_space *ls)
{
  isl_aff *aff;

  aff = isl_aff_alloc(ls);
  if (!aff)
    return NULL;

  isl_int_set_si(aff->v->el[0], 1);
  isl_seq_clr(aff->v->el + 1, aff->v->size - 1);

  return aff;
}

/* Return a piecewise affine expression defined on the specified domain
 * that is equal to zero.
 */
__isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(__isl_take isl_local_space *ls)
{
  return isl_pw_aff_from_aff(isl_aff_zero_on_domain(ls));
}

/* Return an affine expression defined on the specified domain
 * that represents NaN.
 */
__isl_give isl_aff *isl_aff_nan_on_domain(__isl_take isl_local_space *ls)
{
  isl_aff *aff;

  aff = isl_aff_alloc(ls);
  if (!aff)
    return NULL;

  isl_seq_clr(aff->v->el, aff->v->size);

  return aff;
}

/* Return a piecewise affine expression defined on the specified domain
 * that represents NaN.
 */
__isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(__isl_take isl_local_space *ls)
{
  return isl_pw_aff_from_aff(isl_aff_nan_on_domain(ls));
}

/* Return an affine expression that is equal to "val" on
 * domain local space "ls".
 */
__isl_give isl_aff *isl_aff_val_on_domain(__isl_take isl_local_space *ls,
  __isl_take isl_val *val)
{
  isl_aff *aff;

  if (!ls || !val)
    goto error;
  if (!isl_val_is_rat(val))
    isl_die0(isl_val_get_ctx(val), isl_error_invalid,
      "expecting rational value", goto error);

  aff = isl_aff_alloc(isl_local_space_copy(ls));
  if (!aff)
    goto error;

  isl_seq_clr(aff->v->el + 2, aff->v->size - 2);
  isl_int_set(aff->v->el[1], val->n);
  isl_int_set(aff->v->el[0], val->d);

  isl_local_space_free(ls);
  isl_val_free(val);
  return aff;
error:
  isl_local_space_free(ls);
  isl_val_free(val);
  return NULL;
}

/* Return an affine expression that is equal to the specified dimension
 * in "ls".
 */
__isl_give isl_aff *isl_aff_var_on_domain(__isl_take isl_local_space *ls,
  enum isl_dim_type type, unsigned pos)
{
  isl_space *space;
  isl_aff *aff;

  if (!ls)
    return NULL;

  space = isl_local_space_get_space(ls);
  if (!space)
    goto error;
  if (isl_space_is_map(space))
    isl_die0(isl_space_get_ctx(space), isl_error_invalid,
      "expecting (parameter) set space", goto error);
  if (pos >= isl_local_space_dim(ls, type))
    isl_die0(isl_space_get_ctx(space), isl_error_invalid,
      "position out of bounds", goto error);

  isl_space_free(space);
  aff = isl_aff_alloc(ls);
  if (!aff)
    return NULL;

  pos += isl_local_space_offset(aff->ls, type);

  isl_int_set_si(aff->v->el[0], 1);
  isl_seq_clr(aff->v->el + 1, aff->v->size - 1);
  isl_int_set_si(aff->v->el[1 + pos], 1);

  return aff;
error:
  isl_local_space_free(ls);
  isl_space_free(space);
  return NULL;
}

/* Return a piecewise affine expression that is equal to
 * the specified dimension in "ls".
 */
__isl_give isl_pw_aff *isl_pw_aff_var_on_domain(__isl_take isl_local_space *ls,
  enum isl_dim_type type, unsigned pos)
{
  return isl_pw_aff_from_aff(isl_aff_var_on_domain(ls, type, pos));
}

/* Return an affine expression that is equal to the parameter
 * in the domain space "space" with identifier "id".
 */
__isl_give isl_aff *isl_aff_param_on_domain_space_id(
  __isl_take isl_space *space, __isl_take isl_id *id)
{
  int pos;
  isl_local_space *ls;

  if (!space || !id)
    goto error;
  pos = isl_space_find_dim_by_id(space, isl_dim_param, id);
  if (pos < 0)
    isl_die0(isl_space_get_ctx(space), isl_error_invalid,
      "parameter not found in space", goto error);
  isl_id_free(id);
  ls = isl_local_space_from_space(space);
  return isl_aff_var_on_domain(ls, isl_dim_param, pos);
error:
  isl_space_free(space);
  isl_id_free(id);
  return NULL;
}

__isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff)
{
  if (!aff)
    return NULL;

  aff->ref++;
  return aff;
}

__isl_give isl_aff *isl_aff_dup(__isl_keep isl_aff *aff)
{
  if (!aff)
    return NULL;

  return isl_aff_alloc_vec(isl_local_space_copy(aff->ls),
         isl_vec_copy(aff->v));
}

__isl_give isl_aff *isl_aff_cow(__isl_take isl_aff *aff)
{
  if (!aff)
    return NULL;

  if (aff->ref == 1)
    return aff;
  aff->ref--;
  return isl_aff_dup(aff);
}

__isl_null isl_aff *isl_aff_free(__isl_take isl_aff *aff)
{
  if (!aff)
    return NULL;

  if (--aff->ref > 0)
    return NULL;

  isl_local_space_free(aff->ls);
  isl_vec_free(aff->v);

  free(aff);

  return NULL;
}

isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff)
{
  return aff ? isl_local_space_get_ctx(aff->ls) : NULL;
}

/* Return a hash value that digests "aff".
 */
uint32_t isl_aff_get_hash(__isl_keep isl_aff *aff)
{
  uint32_t hash, ls_hash, v_hash;

  if (!aff)
    return 0;

  hash = isl_hash_init();
  ls_hash = isl_local_space_get_hash(aff->ls);
  isl_hash_hash(hash, ls_hash);
  v_hash = isl_vec_get_hash(aff->v);
  isl_hash_hash(hash, v_hash);

  return hash;
}

/* Externally, an isl_aff has a map space, but internally, the
 * ls field corresponds to the domain of that space.
 */
int isl_aff_dim(__isl_keep isl_aff *aff, enum isl_dim_type type)
{
  if (!aff)
    return 0;
  if (type == isl_dim_out)
    return 1;
  if (type == isl_dim_in)
    type = isl_dim_set;
  return isl_local_space_dim(aff->ls, type);
}

/* Return the position of the dimension of the given type and name
 * in "aff".
 * Return -1 if no such dimension can be found.
 */
int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff, enum isl_dim_type type,
  const char *name)
{
  if (!aff)
    return -1;
  if (type == isl_dim_out)
    return -1;
  if (type == isl_dim_in)
    type = isl_dim_set;
  return isl_local_space_find_dim_by_name(aff->ls, type, name);
}

/* Return the domain space of "aff".
 */
static __isl_keep isl_space *isl_aff_peek_domain_space(__isl_keep isl_aff *aff)
{
  return aff ? isl_local_space_peek_space(aff->ls)3.17M : NULL;
}

__isl_give isl_space *isl_aff_get_domain_space(__isl_keep isl_aff *aff)
{
  return isl_space_copy(isl_aff_peek_domain_space(aff));
}

__isl_give isl_space *isl_aff_get_space(__isl_keep isl_aff *aff)
{
  isl_space *space;
  if (!aff)
    return NULL;
  space = isl_local_space_get_space(aff->ls);
  space = isl_space_from_domain(space);
  space = isl_space_add_dims(space, isl_dim_out, 1);
  return space;
}

__isl_give isl_local_space *isl_aff_get_domain_local_space(
  __isl_keep isl_aff *aff)
{
  return aff ? isl_local_space_copy(aff->ls) : NULL;
}

__isl_give isl_local_space *isl_aff_get_local_space(__isl_keep isl_aff *aff)
{
  isl_local_space *ls;
  if (!aff)
    return NULL;
  ls = isl_local_space_copy(aff->ls);
  ls = isl_local_space_from_domain(ls);
  ls = isl_local_space_add_dims(ls, isl_dim_out, 1);
  return ls;
}

/* Return the local space of the domain of "aff".
 * This may be either a copy or the local space itself
 * if there is only one reference to "aff".
 * This allows the local space to be modified inplace
 * if both the expression and its local space have only a single reference.
 * The caller is not allowed to modify "aff" between this call and
 * a subsequent call to isl_aff_restore_domain_local_space.
 * The only exception is that isl_aff_free can be called instead.
 */
__isl_give isl_local_space *isl_aff_take_domain_local_space(
  __isl_keep isl_aff *aff)
{
  isl_local_space *ls;

  if (!aff)
    return NULL;
  if (aff->ref != 1)
    return isl_aff_get_domain_local_space(aff);
  ls = aff->ls;
  aff->ls = NULL;
  return ls;
}

/* Set the local space of the domain of "aff" to "ls",
 * where the local space of "aff" may be missing
 * due to a preceding call to isl_aff_take_domain_local_space.
 * However, in this case, "aff" only has a single reference and
 * then the call to isl_aff_cow has no effect.
 */
__isl_give isl_aff *isl_aff_restore_domain_local_space(
  __isl_keep isl_aff *aff, __isl_take isl_local_space *ls)
{
  if (!aff || !ls)
    goto error;

  if (aff->ls == ls) {
    isl_local_space_free(ls);
    return aff;
  }

  aff = isl_aff_cow(aff);
  if (!aff)
    goto error;
  isl_local_space_free(aff->ls);
  aff->ls = ls;

  return aff;
error:
  isl_aff_free(aff);
  isl_local_space_free(ls);
  return NULL;
}

/* Externally, an isl_aff has a map space, but internally, the
 * ls field corresponds to the domain of that space.
 */
const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
  enum isl_dim_type type, unsigned pos)
{
  if (!aff)
    return NULL;
  if (type == isl_dim_out)
    return NULL;
  if (type == isl_dim_in)
    type = isl_dim_set;
  return isl_local_space_get_dim_name(aff->ls, type, pos);
}

__isl_give isl_aff *isl_aff_reset_domain_space(__isl_take isl_aff *aff,
  __isl_take isl_space *dim)
{
  aff = isl_aff_cow(aff);
  if (!aff || !dim)
    goto error;

  aff->ls = isl_local_space_reset_space(aff->ls, dim);
  if (!aff->ls)
    return isl_aff_free(aff);

  return aff;
error:
  isl_aff_free(aff);
  isl_space_free(dim);
  return NULL;
}

/* Reset the space of "aff".  This function is called from isl_pw_templ.c
 * and doesn't know if the space of an element object is represented
 * directly or through its domain.  It therefore passes along both.
 */
__isl_give isl_aff *isl_aff_reset_space_and_domain(__isl_take isl_aff *aff,
  __isl_take isl_space *space, __isl_take isl_space *domain)
{
  isl_space_free(space);
  return isl_aff_reset_domain_space(aff, domain);
}

/* Reorder the coefficients of the affine expression based
 * on the given reordering.
 * The reordering r is assumed to have been extended with the local
 * variables.
 */
static __isl_give isl_vec *vec_reorder(__isl_take isl_vec *vec,
  __isl_take isl_reordering *r, int n_div)
{
  isl_space *space;
  isl_vec *res;
  int i;

  if (!vec || !r)
    goto error;

  space = isl_reordering_peek_space(r);
  res = isl_vec_alloc(vec->ctx,
          2 + isl_space_dim(space, isl_dim_all) + n_div);
  if (!res)
    goto error;
  isl_seq_cpy(res->el, vec->el, 2);
  isl_seq_clr(res->el + 2, res->size - 2);
  for (i = 0; i < r->len; ++i19.5k)
    isl_int_set(res->el[2 + r->pos[i]], vec->el[2 + i]);

  isl_reordering_free(r);
  isl_vec_free(vec);
  return res;
error:
  isl_vec_free(vec);
  isl_reordering_free(r);
  return NULL;
}

/* Reorder the dimensions of the domain of "aff" according
 * to the given reordering.
 */
__isl_give isl_aff *isl_aff_realign_domain(__isl_take isl_aff *aff,
  __isl_take isl_reordering *r)
{
  aff = isl_aff_cow(aff);
  if (!aff)
    goto error;

  r = isl_reordering_extend(r, aff->ls->div->n_row);
  aff->v = vec_reorder(aff->v, isl_reordering_copy(r),
        aff->ls->div->n_row);
  aff->ls = isl_local_space_realign(aff->ls, r);

  if (!aff->v || !aff->ls)
    return isl_aff_free(aff);

  return aff;
error:
  isl_aff_free(aff);
  isl_reordering_free(r);
  return NULL;
}

__isl_give isl_aff *isl_aff_align_params(__isl_take isl_aff *aff,
  __isl_take isl_space *model)
{
  isl_bool equal_params;

  if (!aff || !model)
    goto error;

  equal_params = isl_space_has_equal_params(aff->ls->dim, model);
  if (equal_params < 0)
    goto error;
  if (!equal_params) {
    isl_reordering *exp;

    exp = isl_parameter_alignment_reordering(aff->ls->dim, model);
    exp = isl_reordering_extend_space(exp,
          isl_aff_get_domain_space(aff));
    aff = isl_aff_realign_domain(aff, exp);
  }

  isl_space_free(model);
  return aff;
error:
  isl_space_free(model);
  isl_aff_free(aff);
  return NULL;
}

/* Is "aff" obviously equal to zero?
 *
 * If the denominator is zero, then "aff" is not equal to zero.
 */
isl_bool isl_aff_plain_is_zero(__isl_keep isl_aff *aff)
{
  if (!aff)
    return isl_bool_error;

  if (isl_int_is_zero(aff->v->el[0]))
    return isl_bool_false0;
  return isl_seq_first_non_zero(aff->v->el + 1, aff->v->size - 1) < 0;
}

/* Does "aff" represent NaN?
 */
isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff)
{
  if (!aff)
    return isl_bool_error;

  return isl_seq_first_non_zero(aff->v->el, 2) < 0;
}

/* Are "aff1" and "aff2" obviously equal?
 *
 * NaN is not equal to anything, not even to another NaN.
 */
isl_bool isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
  __isl_keep isl_aff *aff2)
{
  isl_bool equal;

  if (!aff1 || !aff2)
    return isl_bool_error;

  if (isl_aff_is_nan(aff1) || isl_aff_is_nan(aff2))
    return isl_bool_false;

  equal = isl_local_space_is_equal(aff1->ls, aff2->ls);
  if (equal < 0 || !equal)
    return equal;

  return isl_vec_is_equal(aff1->v, aff2->v);
}

/* Return the common denominator of "aff" in "v".
 *
 * We cannot return anything meaningful in case of a NaN.
 */
isl_stat isl_aff_get_denominator(__isl_keep isl_aff *aff, isl_int *v)
{
  if (!aff)
    return isl_stat_error;
  if (isl_aff_is_nan(aff))
    isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
      "cannot get denominator of NaN", return isl_stat_error);
  isl_int_set(*v, aff->v->el[0]);
  return isl_stat_ok;
}

/* Return the common denominator of "aff".
 */
__isl_give isl_val *isl_aff_get_denominator_val(__isl_keep isl_aff *aff)
{
  isl_ctx *ctx;

  if (!aff)
    return NULL;

  ctx = isl_aff_get_ctx(aff);
  if (isl_aff_is_nan(aff))
    return isl_val_nan(ctx);
  return isl_val_int_from_isl_int(ctx, aff->v->el[0]);
}

/* Return the constant term of "aff".
 */
__isl_give isl_val *isl_aff_get_constant_val(__isl_keep isl_aff *aff)
{
  isl_ctx *ctx;
  isl_val *v;

  if (!aff)
    return NULL;

  ctx = isl_aff_get_ctx(aff);
  if (isl_aff_is_nan(aff))
    return isl_val_nan(ctx);
  v = isl_val_rat_from_isl_int(ctx, aff->v->el[1], aff->v->el[0]);
  return isl_val_normalize(v);
}

/* Return the coefficient of the variable of type "type" at position "pos"
 * of "aff".
 */
__isl_give isl_val *isl_aff_get_coefficient_val(__isl_keep isl_aff *aff,
  enum isl_dim_type type, int pos)
{
  isl_ctx *ctx;
  isl_val *v;

  if (!aff)
    return NULL;

  ctx = isl_aff_get_ctx(aff);
  if (type == isl_dim_out)
    isl_die0(ctx, isl_error_invalid,
      "output/set dimension does not have a coefficient",
      return NULL);
  if (type == isl_dim_in)
    type = isl_dim_set;

  if (pos >= isl_local_space_dim(aff->ls, type))
    isl_die0(ctx, isl_error_invalid,
      "position out of bounds", return NULL);

  if (isl_aff_is_nan(aff))
    return isl_val_nan(ctx);
  pos += isl_local_space_offset(aff->ls, type);
  v = isl_val_rat_from_isl_int(ctx, aff->v->el[1 + pos], aff->v->el[0]);
  return isl_val_normalize(v);
}

/* Return the sign of the coefficient of the variable of type "type"
 * at position "pos" of "aff".
 */
int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff, enum isl_dim_type type,
  int pos)
{
  isl_ctx *ctx;

  if (!aff)
    return 0;

  ctx = isl_aff_get_ctx(aff);
  if (type == isl_dim_out)
    isl_die0(ctx, isl_error_invalid,
      "output/set dimension does not have a coefficient",
      return 0);
  if (type == isl_dim_in)
    type = isl_dim_set;

  if (pos >= isl_local_space_dim(aff->ls, type))
    isl_die0(ctx, isl_error_invalid,
      "position out of bounds", return 0);

  pos += isl_local_space_offset(aff->ls, type);
  return isl_int_sgn(aff->v->el[1 + pos]);
}

/* Replace the numerator of the constant term of "aff" by "v".
 *
 * A NaN is unaffected by this operation.
 */
__isl_give isl_aff *isl_aff_set_constant(__isl_take isl_aff *aff, isl_int v)
{
  if (!aff)
    return NULL;
  if (isl_aff_is_nan(aff))
    return aff;
  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;

  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    return isl_aff_free(aff);

  isl_int_set(aff->v->el[1], v);

  return aff;
}

/* Replace the constant term of "aff" by "v".
 *
 * A NaN is unaffected by this operation.
 */
__isl_give isl_aff *isl_aff_set_constant_val(__isl_take isl_aff *aff,
  __isl_take isl_val *v)
{
  if (!aff || !v)
    goto error;

  if (isl_aff_is_nan(aff)) {
    isl_val_free(v);
    return aff;
  }

  if (!isl_val_is_rat(v))
    isl_die0(isl_aff_get_ctx(aff), isl_error_invalid,
      "expecting rational value", goto error);

  if (isl_int_eq(aff->v->el[1], v->n) &&
      isl_int_eq10(aff->v->el[0], v->d)) {
    isl_val_free(v);
    return aff;
  }

  aff = isl_aff_cow(aff);
  if (!aff)
    goto error;
  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    goto error;

  if (isl_int_eq(aff->v->el[0], v->d)) {
    isl_int_set(aff->v->el[1], v->n);
  } else if (0isl_int_is_one0(v->d)) {
    isl_int_mul(aff->v->el[1], aff->v->el[0], v->n);
  } else {
    isl_seq_scale(aff->v->el + 1,
        aff->v->el + 1, v->d, aff->v->size - 1);
    isl_int_mul(aff->v->el[1], aff->v->el[0], v->n);
    isl_int_mul(aff->v->el[0], aff->v->el[0], v->d);
    aff->v = isl_vec_normalize(aff->v);
    if (!aff->v)
      goto error;
  }

  isl_val_free(v);
  return aff;
error:
  isl_aff_free(aff);
  isl_val_free(v);
  return NULL;
}

/* Add "v" to the constant term of "aff".
 *
 * A NaN is unaffected by this operation.
 */
__isl_give isl_aff *isl_aff_add_constant(__isl_take isl_aff *aff, isl_int v)
{
  if (isl_int_is_zero(v))
    return aff4.71k;

  if (!aff)
    return NULL;
  if (isl_aff_is_nan(aff))
    return aff;
  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;

  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    return isl_aff_free(aff);

  isl_int_addmul(aff->v->el[1], aff->v->el[0], v);

  return aff;
}

/* Add "v" to the constant term of "aff".
 *
 * A NaN is unaffected by this operation.
 */
__isl_give isl_aff *isl_aff_add_constant_val(__isl_take isl_aff *aff,
  __isl_take isl_val *v)
{
  if (!aff || !v)
    goto error;

  if (isl_aff_is_nan(aff) || isl_val_is_zero(v)) {
    isl_val_free(v);
    return aff;
  }

  if (!isl_val_is_rat(v))
    isl_die0(isl_aff_get_ctx(aff), isl_error_invalid,
      "expecting rational value", goto error);

  aff = isl_aff_cow(aff);
  if (!aff)
    goto error;

  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    goto error;

  if (isl_int_is_one(v->d)) {
    isl_int_addmul(aff->v->el[1], aff->v->el[0], v->n);
  } else if (0isl_int_eq0(aff->v->el[0], v->d)) {
    isl_int_add(aff->v->el[1], aff->v->el[1], v->n);
    aff->v = isl_vec_normalize(aff->v);
    if (!aff->v)
      goto error;
  } else {
    isl_seq_scale(aff->v->el + 1,
        aff->v->el + 1, v->d, aff->v->size - 1);
    isl_int_addmul(aff->v->el[1], aff->v->el[0], v->n);
    isl_int_mul(aff->v->el[0], aff->v->el[0], v->d);
    aff->v = isl_vec_normalize(aff->v);
    if (!aff->v)
      goto error;
  }

  isl_val_free(v);
  return aff;
error:
  isl_aff_free(aff);
  isl_val_free(v);
  return NULL;
}

__isl_give isl_aff *isl_aff_add_constant_si(__isl_take isl_aff *aff, int v)
{
  isl_int t;

  isl_int_init(t);
  isl_int_set_si(t, v);
  aff = isl_aff_add_constant(aff, t);
  isl_int_clear(t);

  return aff;
}

/* Add "v" to the numerator of the constant term of "aff".
 *
 * A NaN is unaffected by this operation.
 */
__isl_give isl_aff *isl_aff_add_constant_num(__isl_take isl_aff *aff, isl_int v)
{
  if (isl_int_is_zero(v))
    return aff0;

  if (!aff)
    return NULL;
  if (isl_aff_is_nan(aff))
    return aff;
  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;

  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    return isl_aff_free(aff);

  isl_int_add(aff->v->el[1], aff->v->el[1], v);

  return aff;
}

/* Add "v" to the numerator of the constant term of "aff".
 *
 * A NaN is unaffected by this operation.
 */
__isl_give isl_aff *isl_aff_add_constant_num_si(__isl_take isl_aff *aff, int v)
{
  isl_int t;

  if (v == 0)
    return aff;

  isl_int_init(t);
  isl_int_set_si(t, v);
  aff = isl_aff_add_constant_num(aff, t);
  isl_int_clear(t);

  return aff;
}

/* Replace the numerator of the constant term of "aff" by "v".
 *
 * A NaN is unaffected by this operation.
 */
__isl_give isl_aff *isl_aff_set_constant_si(__isl_take isl_aff *aff, int v)
{
  if (!aff)
    return NULL;
  if (isl_aff_is_nan(aff))
    return aff;
  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;

  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    return isl_aff_free(aff);

  isl_int_set_si(aff->v->el[1], v);

  return aff;
}

/* Replace the numerator of the coefficient of the variable of type "type"
 * at position "pos" of "aff" by "v".
 *
 * A NaN is unaffected by this operation.
 */
__isl_give isl_aff *isl_aff_set_coefficient(__isl_take isl_aff *aff,
  enum isl_dim_type type, int pos, isl_int v)
{
  if (!aff)
    return NULL;

  if (type == isl_dim_out)
    isl_die0(aff->v->ctx, isl_error_invalid,
      "output/set dimension does not have a coefficient",
      return isl_aff_free(aff));
  if (type == isl_dim_in)
    type = isl_dim_set;

  if (pos >= isl_local_space_dim(aff->ls, type))
    isl_die0(aff->v->ctx, isl_error_invalid,
      "position out of bounds", return isl_aff_free(aff));

  if (isl_aff_is_nan(aff))
    return aff;
  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;

  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    return isl_aff_free(aff);

  pos += isl_local_space_offset(aff->ls, type);
  isl_int_set(aff->v->el[1 + pos], v);

  return aff;
}

/* Replace the numerator of the coefficient of the variable of type "type"
 * at position "pos" of "aff" by "v".
 *
 * A NaN is unaffected by this operation.
 */
__isl_give isl_aff *isl_aff_set_coefficient_si(__isl_take isl_aff *aff,
  enum isl_dim_type type, int pos, int v)
{
  if (!aff)
    return NULL;

  if (type == isl_dim_out)
    isl_die0(aff->v->ctx, isl_error_invalid,
      "output/set dimension does not have a coefficient",
      return isl_aff_free(aff));
  if (type == isl_dim_in)
    type = isl_dim_set;

  if (pos < 0 || pos >= isl_local_space_dim(aff->ls, type))
    isl_die0(aff->v->ctx, isl_error_invalid,
      "position out of bounds", return isl_aff_free(aff));

  if (isl_aff_is_nan(aff))
    return aff;
  pos += isl_local_space_offset(aff->ls, type);
  if (isl_int_cmp_si(aff->v->el[1 + pos], v) == 0)
    return aff;

  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;

  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    return isl_aff_free(aff);

  isl_int_set_si(aff->v->el[1 + pos], v);

  return aff;
}

/* Replace the coefficient of the variable of type "type" at position "pos"
 * of "aff" by "v".
 *
 * A NaN is unaffected by this operation.
 */
__isl_give isl_aff *isl_aff_set_coefficient_val(__isl_take isl_aff *aff,
  enum isl_dim_type type, int pos, __isl_take isl_val *v)
{
  if (!aff || !v)
    goto error;

  if (type == isl_dim_out)
    isl_die(aff->v->ctx, isl_error_invalid,
      "output/set dimension does not have a coefficient",
      goto error);
  if (type == isl_dim_in)
    type = isl_dim_set;

  if (pos >= isl_local_space_dim(aff->ls, type))
    isl_die(aff->v->ctx, isl_error_invalid,
      "position out of bounds", goto error);

  if (isl_aff_is_nan(aff)) {
    isl_val_free(v);
    return aff;
  }
  if (!isl_val_is_rat(v))
    isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
      "expecting rational value", goto error);

  pos += isl_local_space_offset(aff->ls, type);
  if (isl_int_eq(aff->v->el[1 + pos], v->n) &&
      isl_int_eq(aff->v->el[0], v->d)) {
    isl_val_free(v);
    return aff;
  }

  aff = isl_aff_cow(aff);
  if (!aff)
    goto error;
  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    goto error;

  if (isl_int_eq(aff->v->el[0], v->d)) {
    isl_int_set(aff->v->el[1 + pos], v->n);
  } else if (isl_int_is_one(v->d)) {
    isl_int_mul(aff->v->el[1 + pos], aff->v->el[0], v->n);
  } else {
    isl_seq_scale(aff->v->el + 1,
        aff->v->el + 1, v->d, aff->v->size - 1);
    isl_int_mul(aff->v->el[1 + pos], aff->v->el[0], v->n);
    isl_int_mul(aff->v->el[0], aff->v->el[0], v->d);
    aff->v = isl_vec_normalize(aff->v);
    if (!aff->v)
      goto error;
  }

  isl_val_free(v);
  return aff;
error:
  isl_aff_free(aff);
  isl_val_free(v);
  return NULL;
}

/* Add "v" to the coefficient of the variable of type "type"
 * at position "pos" of "aff".
 *
 * A NaN is unaffected by this operation.
 */
__isl_give isl_aff *isl_aff_add_coefficient(__isl_take isl_aff *aff,
  enum isl_dim_type type, int pos, isl_int v)
{
  if (!aff)
    return NULL;

  if (type == isl_dim_out)
    isl_die0(aff->v->ctx, isl_error_invalid,
      "output/set dimension does not have a coefficient",
      return isl_aff_free(aff));
  if (type == isl_dim_in)
    type = isl_dim_set;

  if (pos >= isl_local_space_dim(aff->ls, type))
    isl_die0(aff->v->ctx, isl_error_invalid,
      "position out of bounds", return isl_aff_free(aff));

  if (isl_aff_is_nan(aff))
    return aff;
  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;

  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    return isl_aff_free(aff);

  pos += isl_local_space_offset(aff->ls, type);
  isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v);

  return aff;
}

/* Add "v" to the coefficient of the variable of type "type"
 * at position "pos" of "aff".
 *
 * A NaN is unaffected by this operation.
 */
__isl_give isl_aff *isl_aff_add_coefficient_val(__isl_take isl_aff *aff,
  enum isl_dim_type type, int pos, __isl_take isl_val *v)
{
  if (!aff || !v)
    goto error;

  if (isl_val_is_zero(v)) {
    isl_val_free(v);
    return aff;
  }

  if (type == isl_dim_out)
    isl_die(aff->v->ctx, isl_error_invalid,
      "output/set dimension does not have a coefficient",
      goto error);
  if (type == isl_dim_in)
    type = isl_dim_set;

  if (pos >= isl_local_space_dim(aff->ls, type))
    isl_die(aff->v->ctx, isl_error_invalid,
      "position out of bounds", goto error);

  if (isl_aff_is_nan(aff)) {
    isl_val_free(v);
    return aff;
  }
  if (!isl_val_is_rat(v))
    isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
      "expecting rational value", goto error);

  aff = isl_aff_cow(aff);
  if (!aff)
    goto error;

  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    goto error;

  pos += isl_local_space_offset(aff->ls, type);
  if (isl_int_is_one(v->d)) {
    isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v->n);
  } else if (isl_int_eq(aff->v->el[0], v->d)) {
    isl_int_add(aff->v->el[1 + pos], aff->v->el[1 + pos], v->n);
    aff->v = isl_vec_normalize(aff->v);
    if (!aff->v)
      goto error;
  } else {
    isl_seq_scale(aff->v->el + 1,
        aff->v->el + 1, v->d, aff->v->size - 1);
    isl_int_addmul(aff->v->el[1 + pos], aff->v->el[0], v->n);
    isl_int_mul(aff->v->el[0], aff->v->el[0], v->d);
    aff->v = isl_vec_normalize(aff->v);
    if (!aff->v)
      goto error;
  }

  isl_val_free(v);
  return aff;
error:
  isl_aff_free(aff);
  isl_val_free(v);
  return NULL;
}

__isl_give isl_aff *isl_aff_add_coefficient_si(__isl_take isl_aff *aff,
  enum isl_dim_type type, int pos, int v)
{
  isl_int t;

  isl_int_init(t);
  isl_int_set_si(t, v);
  aff = isl_aff_add_coefficient(aff, type, pos, t);
  isl_int_clear(t);

  return aff;
}

__isl_give isl_aff *isl_aff_get_div(__isl_keep isl_aff *aff, int pos)
{
  if (!aff)
    return NULL;

  return isl_local_space_get_div(aff->ls, pos);
}

/* Return the negation of "aff".
 *
 * As a special case, -NaN = NaN.
 */
__isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff)
{
  if (!aff)
    return NULL;
  if (isl_aff_is_nan(aff))
    return aff;
  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;
  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    return isl_aff_free(aff);

  isl_seq_neg(aff->v->el + 1, aff->v->el + 1, aff->v->size - 1);

  return aff;
}

/* Remove divs from the local space that do not appear in the affine
 * expression.
 * We currently only remove divs at the end.
 * Some intermediate divs may also not appear directly in the affine
 * expression, but we would also need to check that no other divs are
 * defined in terms of them.
 */
__isl_give isl_aff *isl_aff_remove_unused_divs(__isl_take isl_aff *aff)
{
  int pos;
  int off;
  int n;

  if (!aff)
    return NULL;

  n = isl_local_space_dim(aff->ls, isl_dim_div);
  off = isl_local_space_offset(aff->ls, isl_dim_div);

  pos = isl_seq_last_non_zero(aff->v->el + 1 + off, n) + 1;
  if (pos == n)
    return aff;

  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;

  aff->ls = isl_local_space_drop_dims(aff->ls, isl_dim_div, pos, n - pos);
  aff->v = isl_vec_drop_els(aff->v, 1 + off + pos, n - pos);
  if (!aff->ls || !aff->v)
    return isl_aff_free(aff);

  return aff;
}

/* Look for any divs in the aff->ls with a denominator equal to one
 * and plug them into the affine expression and any subsequent divs
 * that may reference the div.
 */
static __isl_give isl_aff *plug_in_integral_divs(__isl_take isl_aff *aff)
{
  int i, n;
  int len;
  isl_int v;
  isl_vec *vec;
  isl_local_space *ls;
  unsigned pos;

  if (!aff)
    return NULL;

  n = isl_local_space_dim(aff->ls, isl_dim_div);
  len = aff->v->size;
  for (i = 0; i < n; ++i11.4k) {
    if (!isl_int_is_one(aff->ls->div->row[i][0]))
      continue10.7k;
    ls = isl_local_space_copy(aff->ls);
    ls = isl_local_space_substitute_seq(ls, isl_dim_div, i,
        aff->ls->div->row[i], len, i + 1, n - (i + 1));
    vec = isl_vec_copy(aff->v);
    vec = isl_vec_cow(vec);
    if (!ls || !vec)
      goto error;

    isl_int_init(v);

    pos = isl_local_space_offset(aff->ls, isl_dim_div) + i;
    isl_seq_substitute(vec->el, pos, aff->ls->div->row[i],
          len, len, v);

    isl_int_clear(v);

    isl_vec_free(aff->v);
    aff->v = vec;
    isl_local_space_free(aff->ls);
    aff->ls = ls;
  }

  return aff;
error:
  isl_vec_free(vec);
  isl_local_space_free(ls);
  return isl_aff_free(aff);
}

/* Look for any divs j that appear with a unit coefficient inside
 * the definitions of other divs i and plug them into the definitions
 * of the divs i.
 *
 * In particular, an expression of the form
 *
 *  floor((f(..) + floor(g(..)/n))/m)
 *
 * is simplified to
 *
 *  floor((n * f(..) + g(..))/(n * m))
 *
 * This simplification is correct because we can move the expression
 * f(..) into the inner floor in the original expression to obtain
 *
 *  floor(floor((n * f(..) + g(..))/n)/m)
 *
 * from which we can derive the simplified expression.
 */
static __isl_give isl_aff *plug_in_unit_divs(__isl_take isl_aff *aff)
{
  int i, j, n;
  int off;

  if (!aff)
    return NULL;

  n = isl_local_space_dim(aff->ls, isl_dim_div);
  off = isl_local_space_offset(aff->ls, isl_dim_div);
  for (i = 1; i < n; ++i3.67k) {
    for (j = 0; j < i; ++j6.36k) {
      if (!isl_int_is_one(aff->ls->div->row[i][1 + off + j]))
        continue6.16k;
      aff->ls = isl_local_space_substitute_seq(aff->ls,
        isl_dim_div, j, aff->ls->div->row[j],
        aff->v->size, i, 1);
      if (!aff->ls)
        return isl_aff_free(aff);
    }
  }

  return aff;
}

/* Swap divs "a" and "b" in "aff", which is assumed to be non-NULL.
 *
 * Even though this function is only called on isl_affs with a single
 * reference, we are careful to only change aff->v and aff->ls together.
 */
static __isl_give isl_aff *swap_div(__isl_take isl_aff *aff, int a, int b)
{
  unsigned off = isl_local_space_offset(aff->ls, isl_dim_div);
  isl_local_space *ls;
  isl_vec *v;

  ls = isl_local_space_copy(aff->ls);
  ls = isl_local_space_swap_div(ls, a, b);
  v = isl_vec_copy(aff->v);
  v = isl_vec_cow(v);
  if (!ls || !v)
    goto error;

  isl_int_swap(v->el[1 + off + a], v->el[1 + off + b]);
  isl_vec_free(aff->v);
  aff->v = v;
  isl_local_space_free(aff->ls);
  aff->ls = ls;

  return aff;
error:
  isl_vec_free(v);
  isl_local_space_free(ls);
  return isl_aff_free(aff);
}

/* Merge divs "a" and "b" in "aff", which is assumed to be non-NULL.
 *
 * We currently do not actually remove div "b", but simply add its
 * coefficient to that of "a" and then zero it out.
 */
static __isl_give isl_aff *merge_divs(__isl_take isl_aff *aff, int a, int b)
{
  unsigned off = isl_local_space_offset(aff->ls, isl_dim_div);

  if (isl_int_is_zero(aff->v->el[1 + off + b]))
    return aff74;

  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    return isl_aff_free(aff);

  isl_int_add(aff->v->el[1 + off + a],
        aff->v->el[1 + off + a], aff->v->el[1 + off + b]);
  isl_int_set_si(aff->v->el[1 + off + b], 0);

  return aff;
}

/* Sort the divs in the local space of "aff" according to
 * the comparison function "cmp_row" in isl_local_space.c,
 * combining the coefficients of identical divs.
 *
 * Reordering divs does not change the semantics of "aff",
 * so there is no need to call isl_aff_cow.
 * Moreover, this function is currently only called on isl_affs
 * with a single reference.
 */
static __isl_give isl_aff *sort_divs(__isl_take isl_aff *aff)
{
  int i, j, n;

  if (!aff)
    return NULL;

  n = isl_aff_dim(aff, isl_dim_div);
  for (i = 1; i < n; ++i3.67k) {
    for (j = i - 1; j >= 0; --j2.07k) {
      int cmp = isl_mat_cmp_div(aff->ls->div, j, j + 1);
      if (cmp < 0)
        break;
      if (cmp == 0)
        aff = merge_divs(aff, j, j + 1);
      else
        aff = swap_div(aff, j, j + 1);
      if (!aff)
        return NULL;
    }
  }

  return aff;
}

/* Normalize the representation of "aff".
 *
 * This function should only be called of "new" isl_affs, i.e.,
 * with only a single reference.  We therefore do not need to
 * worry about affecting other instances.
 */
__isl_give isl_aff *isl_aff_normalize(__isl_take isl_aff *aff)
{
  if (!aff)
    return NULL;
  aff->v = isl_vec_normalize(aff->v);
  if (!aff->v)
    return isl_aff_free(aff);
  aff = plug_in_integral_divs(aff);
  aff = plug_in_unit_divs(aff);
  aff = sort_divs(aff);
  aff = isl_aff_remove_unused_divs(aff);
  return aff;
}

/* Given f, return floor(f).
 * If f is an integer expression, then just return f.
 * If f is a constant, then return the constant floor(f).
 * Otherwise, if f = g/m, write g = q m + r,
 * create a new div d = [r/m] and return the expression q + d.
 * The coefficients in r are taken to lie between -m/2 and m/2.
 *
 * reduce_div_coefficients performs the same normalization.
 *
 * As a special case, floor(NaN) = NaN.
 */
__isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff)
{
  int i;
  int size;
  isl_ctx *ctx;
  isl_vec *div;

  if (!aff)
    return NULL;

  if (isl_aff_is_nan(aff))
    return aff;
  if (isl_int_is_one(aff->v->el[0]))
    return aff15.6k;

  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;

  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    return isl_aff_free(aff);

  if (isl_aff_is_cst(aff)) {
    isl_int_fdiv_q(aff->v->el[1], aff->v->el[1], aff->v->el[0]);
    isl_int_set_si(aff->v->el[0], 1);
    return aff;
  }

  div = isl_vec_copy(aff->v);
  div = isl_vec_cow(div);
  if (!div)
    return isl_aff_free(aff);

  ctx = isl_aff_get_ctx(aff);
  isl_int_fdiv_q(aff->v->el[0], aff->v->el[0], ctx->two);
  for (i = 1; i < aff->v->size; ++i15.4k) {
    isl_int_fdiv_r(div->el[i], div->el[i], div->el[0]);
    isl_int_fdiv_q(aff->v->el[i], aff->v->el[i], div->el[0]);
    if (isl_int_gt(div->el[i], aff->v->el[0])) {
      isl_int_sub(div->el[i], div->el[i], div->el[0]);
      isl_int_add_ui(aff->v->el[i], aff->v->el[i], 1);
    }
  }

  aff->ls = isl_local_space_add_div(aff->ls, div);
  if (!aff->ls)
    return isl_aff_free(aff);

  size = aff->v->size;
  aff->v = isl_vec_extend(aff->v, size + 1);
  if (!aff->v)
    return isl_aff_free(aff);
  isl_int_set_si(aff->v->el[0], 1);
  isl_int_set_si(aff->v->el[size], 1);

  aff = isl_aff_normalize(aff);

  return aff;
}

/* Compute
 *
 *  aff mod m = aff - m * floor(aff/m)
 *
 * with m an integer value.
 */
__isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
  __isl_take isl_val *m)
{
  isl_aff *res;

  if (!aff || !m)
    goto error;

  if (!isl_val_is_int(m))
    isl_die0(isl_val_get_ctx(m), isl_error_invalid,
      "expecting integer modulo", goto error);

  res = isl_aff_copy(aff);
  aff = isl_aff_scale_down_val(aff, isl_val_copy(m));
  aff = isl_aff_floor(aff);
  aff = isl_aff_scale_val(aff, m);
  res = isl_aff_sub(res, aff);

  return res;
error:
  isl_aff_free(aff);
  isl_val_free(m);
  return NULL;
}

/* Compute
 *
 *  pwaff mod m = pwaff - m * floor(pwaff/m)
 */
__isl_give isl_pw_aff *isl_pw_aff_mod(__isl_take isl_pw_aff *pwaff, isl_int m)
{
  isl_pw_aff *res;

  res = isl_pw_aff_copy(pwaff);
  pwaff = isl_pw_aff_scale_down(pwaff, m);
  pwaff = isl_pw_aff_floor(pwaff);
  pwaff = isl_pw_aff_scale(pwaff, m);
  res = isl_pw_aff_sub(res, pwaff);

  return res;
}

/* Compute
 *
 *  pa mod m = pa - m * floor(pa/m)
 *
 * with m an integer value.
 */
__isl_give isl_pw_aff *isl_pw_aff_mod_val(__isl_take isl_pw_aff *pa,
  __isl_take isl_val *m)
{
  if (!pa || !m)
    goto error;
  if (!isl_val_is_int(m))
    isl_die0(isl_pw_aff_get_ctx(pa), isl_error_invalid,
      "expecting integer modulo", goto error);
  pa = isl_pw_aff_mod(pa, m->n);
  isl_val_free(m);
  return pa;
error:
  isl_pw_aff_free(pa);
  isl_val_free(m);
  return NULL;
}

/* Given f, return ceil(f).
 * If f is an integer expression, then just return f.
 * Otherwise, let f be the expression
 *
 *  e/m
 *
 * then return
 *
 *  floor((e + m - 1)/m)
 *
 * As a special case, ceil(NaN) = NaN.
 */
__isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff)
{
  if (!aff)
    return NULL;

  if (isl_aff_is_nan(aff))
    return aff;
  if (isl_int_is_one(aff->v->el[0]))
    return aff3.15k;

  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;
  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    return isl_aff_free(aff);

  isl_int_add(aff->v->el[1], aff->v->el[1], aff->v->el[0]);
  isl_int_sub_ui(aff->v->el[1], aff->v->el[1], 1);
  aff = isl_aff_floor(aff);

  return aff;
}

/* Apply the expansion computed by isl_merge_divs.
 * The expansion itself is given by "exp" while the resulting
 * list of divs is given by "div".
 */
__isl_give isl_aff *isl_aff_expand_divs(__isl_take isl_aff *aff,
  __isl_take isl_mat *div, int *exp)
{
  int old_n_div;
  int new_n_div;
  int offset;

  aff = isl_aff_cow(aff);
  if (!aff || !div)
    goto error;

  old_n_div = isl_local_space_dim(aff->ls, isl_dim_div);
  new_n_div = isl_mat_rows(div);
  offset = 1 + isl_local_space_offset(aff->ls, isl_dim_div);

  aff->v = isl_vec_expand(aff->v, offset, old_n_div, exp, new_n_div);
  aff->ls = isl_local_space_replace_divs(aff->ls, div);
  if (!aff->v || !aff->ls)
    return isl_aff_free(aff);
  return aff;
error:
  isl_aff_free(aff);
  isl_mat_free(div);
  return NULL;
}

/* Add two affine expressions that live in the same local space.
 */
static __isl_give isl_aff *add_expanded(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  isl_int gcd, f;

  aff1 = isl_aff_cow(aff1);
  if (!aff1 || !aff2)
    goto error;

  aff1->v = isl_vec_cow(aff1->v);
  if (!aff1->v)
    goto error;

  isl_int_init(gcd);
  isl_int_init(f);
  isl_int_gcd(gcd, aff1->v->el[0], aff2->v->el[0]);
  isl_int_divexact(f, aff2->v->el[0], gcd);
  isl_seq_scale(aff1->v->el + 1, aff1->v->el + 1, f, aff1->v->size - 1);
  isl_int_divexact(f, aff1->v->el[0], gcd);
  isl_seq_addmul(aff1->v->el + 1, f, aff2->v->el + 1, aff1->v->size - 1);
  isl_int_divexact(f, aff2->v->el[0], gcd);
  isl_int_mul(aff1->v->el[0], aff1->v->el[0], f);
  isl_int_clear(f);
  isl_int_clear(gcd);

  isl_aff_free(aff2);
  return aff1;
error:
  isl_aff_free(aff1);
  isl_aff_free(aff2);
  return NULL;
}

/* Return the sum of "aff1" and "aff2".
 *
 * If either of the two is NaN, then the result is NaN.
 */
__isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  isl_ctx *ctx;
  int *exp1 = NULL;
  int *exp2 = NULL;
  isl_mat *div;
  int n_div1, n_div2;

  if (!aff1 || !aff2)
    goto error;

  ctx = isl_aff_get_ctx(aff1);
  if (!isl_space_is_equal(aff1->ls->dim, aff2->ls->dim))
    isl_die0(ctx, isl_error_invalid,
      "spaces don't match", goto error);

  if (isl_aff_is_nan(aff1)) {
    isl_aff_free(aff2);
    return aff1;
  }
  if (isl_aff_is_nan(aff2)) {
    isl_aff_free(aff1);
    return aff2;
  }

  n_div1 = isl_aff_dim(aff1, isl_dim_div);
  n_div2 = isl_aff_dim(aff2, isl_dim_div);
  if (n_div1 == 0 && n_div2 == 052.7k)
    return add_expanded(aff1, aff2);

  exp1 = isl_alloc_array(ctx, int, n_div1);
  exp2 = isl_alloc_array(ctx, int, n_div2);
  if ((n_div1 && !exp113.2k) || (n_div2 && !exp27.51k))
    goto error;

  div = isl_merge_divs(aff1->ls->div, aff2->ls->div, exp1, exp2);
  aff1 = isl_aff_expand_divs(aff1, isl_mat_copy(div), exp1);
  aff2 = isl_aff_expand_divs(aff2, div, exp2);
  free(exp1);
  free(exp2);

  return add_expanded(aff1, aff2);
error:
  free(exp1);
  free(exp2);
  isl_aff_free(aff1);
  isl_aff_free(aff2);
  return NULL;
}

__isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  return isl_aff_add(aff1, isl_aff_neg(aff2));
}

/* Return the result of scaling "aff" by a factor of "f".
 *
 * As a special case, f * NaN = NaN.
 */
__isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff, isl_int f)
{
  isl_int gcd;

  if (!aff)
    return NULL;
  if (isl_aff_is_nan(aff))
    return aff;

  if (isl_int_is_one(f))
    return aff12.1k;

  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;
  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    return isl_aff_free(aff);

  if (isl_int_is_pos(f) && isl_int_is_divisible_by8.57k(aff->v->el[0], f)) {
    isl_int_divexact(aff->v->el[0], aff->v->el[0], f);
    return aff;
  }

  isl_int_init(gcd);
  isl_int_gcd(gcd, aff->v->el[0], f);
  isl_int_divexact(aff->v->el[0], aff->v->el[0], gcd);
  isl_int_divexact(gcd, f, gcd);
  isl_seq_scale(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
  isl_int_clear(gcd);

  return aff;
}

/* Multiple "aff" by "v".
 */
__isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
  __isl_take isl_val *v)
{
  if (!aff || !v)
    goto error;

  if (isl_val_is_one(v)) {
    isl_val_free(v);
    return aff;
  }

  if (!isl_val_is_rat(v))
    isl_die0(isl_aff_get_ctx(aff), isl_error_invalid,
      "expecting rational factor", goto error);

  aff = isl_aff_scale(aff, v->n);
  aff = isl_aff_scale_down(aff, v->d);

  isl_val_free(v);
  return aff;
error:
  isl_aff_free(aff);
  isl_val_free(v);
  return NULL;
}

/* Return the result of scaling "aff" down by a factor of "f".
 *
 * As a special case, NaN/f = NaN.
 */
__isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff, isl_int f)
{
  isl_int gcd;

  if (!aff)
    return NULL;
  if (isl_aff_is_nan(aff))
    return aff;

  if (isl_int_is_one(f))
    return aff16.8k;

  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;

  if (isl_int_is_zero(f))
    isl_die0(isl_aff_get_ctx(aff), isl_error_invalid,
      "cannot scale down by zero", return isl_aff_free(aff));

  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    return isl_aff_free(aff);

  isl_int_init(gcd);
  isl_seq_gcd(aff->v->el + 1, aff->v->size - 1, &gcd);
  isl_int_gcd(gcd, gcd, f);
  isl_seq_scale_down(aff->v->el + 1, aff->v->el + 1, gcd, aff->v->size - 1);
  isl_int_divexact(gcd, f, gcd);
  isl_int_mul(aff->v->el[0], aff->v->el[0], gcd);
  isl_int_clear(gcd);

  return aff;
}

/* Divide "aff" by "v".
 */
__isl_give isl_aff *isl_aff_scale_down_val(__isl_take isl_aff *aff,
  __isl_take isl_val *v)
{
  if (!aff || !v)
    goto error;

  if (isl_val_is_one(v)) {
    isl_val_free(v);
    return aff;
  }

  if (!isl_val_is_rat(v))
    isl_die0(isl_aff_get_ctx(aff), isl_error_invalid,
      "expecting rational factor", goto error);
  if (!isl_val_is_pos(v))
    isl_die0(isl_aff_get_ctx(aff), isl_error_invalid,
      "factor needs to be positive", goto error);

  aff = isl_aff_scale(aff, v->d);
  aff = isl_aff_scale_down(aff, v->n);

  isl_val_free(v);
  return aff;
error:
  isl_aff_free(aff);
  isl_val_free(v);
  return NULL;
}

__isl_give isl_aff *isl_aff_scale_down_ui(__isl_take isl_aff *aff, unsigned f)
{
  isl_int v;

  if (f == 1)
    return aff;

  isl_int_init(v);
  isl_int_set_ui(v, f);
  aff = isl_aff_scale_down(aff, v);
  isl_int_clear(v);

  return aff;
}

__isl_give isl_aff *isl_aff_set_dim_name(__isl_take isl_aff *aff,
  enum isl_dim_type type, unsigned pos, const char *s)
{
  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;
  if (type == isl_dim_out)
    isl_die(aff->v->ctx, isl_error_invalid,
      "cannot set name of output/set dimension",
      return isl_aff_free(aff));
  if (type == isl_dim_in)
    type = isl_dim_set;
  aff->ls = isl_local_space_set_dim_name(aff->ls, type, pos, s);
  if (!aff->ls)
    return isl_aff_free(aff);

  return aff;
}

__isl_give isl_aff *isl_aff_set_dim_id(__isl_take isl_aff *aff,
  enum isl_dim_type type, unsigned pos, __isl_take isl_id *id)
{
  aff = isl_aff_cow(aff);
  if (!aff)
    goto error;
  if (type == isl_dim_out)
    isl_die(aff->v->ctx, isl_error_invalid,
      "cannot set name of output/set dimension",
      goto error);
  if (type == isl_dim_in)
    type = isl_dim_set;
  aff->ls = isl_local_space_set_dim_id(aff->ls, type, pos, id);
  if (!aff->ls)
    return isl_aff_free(aff);

  return aff;
error:
  isl_id_free(id);
  isl_aff_free(aff);
  return NULL;
}

/* Replace the identifier of the input tuple of "aff" by "id".
 * type is currently required to be equal to isl_dim_in
 */
__isl_give isl_aff *isl_aff_set_tuple_id(__isl_take isl_aff *aff,
  enum isl_dim_type type, __isl_take isl_id *id)
{
  aff = isl_aff_cow(aff);
  if (!aff)
    goto error;
  if (type != isl_dim_in)
    isl_die0(aff->v->ctx, isl_error_invalid,
      "cannot only set id of input tuple", goto error);
  aff->ls = isl_local_space_set_tuple_id(aff->ls, isl_dim_set, id);
  if (!aff->ls)
    return isl_aff_free(aff);

  return aff;
error:
  isl_id_free(id);
  isl_aff_free(aff);
  return NULL;
}

/* Exploit the equalities in "eq" to simplify the affine expression
 * and the expressions of the integer divisions in the local space.
 * The integer divisions in this local space are assumed to appear
 * as regular dimensions in "eq".
 */
static __isl_give isl_aff *isl_aff_substitute_equalities_lifted(
  __isl_take isl_aff *aff, __isl_take isl_basic_set *eq)
{
  int i, j;
  unsigned total;
  unsigned n_div;

  if (!eq)
    goto error;
  if (eq->n_eq == 0) {
    isl_basic_set_free(eq);
    return aff;
  }

  aff = isl_aff_cow(aff);
  if (!aff)
    goto error;

  aff->ls = isl_local_space_substitute_equalities(aff->ls,
              isl_basic_set_copy(eq));
  aff->v = isl_vec_cow(aff->v);
  if (!aff->ls || !aff->v)
    goto error;

  total = 1 + isl_space_dim(eq->dim, isl_dim_all);
  n_div = eq->n_div;
  for (i = 0; i < eq->n_eq; ++i6.60k) {
    j = isl_seq_last_non_zero(eq->eq[i], total + n_div);
    if (j < 0 || j == 0 || j >= total)
      continue;

    isl_seq_elim(aff->v->el + 1, eq->eq[i], j, total,
        &aff->v->el[0]);
  }

  isl_basic_set_free(eq);
  aff = isl_aff_normalize(aff);
  return aff;
error:
  isl_basic_set_free(eq);
  isl_aff_free(aff);
  return NULL;
}

/* Exploit the equalities in "eq" to simplify the affine expression
 * and the expressions of the integer divisions in the local space.
 */
__isl_give isl_aff *isl_aff_substitute_equalities(__isl_take isl_aff *aff,
  __isl_take isl_basic_set *eq)
{
  int n_div;

  if (!aff || !eq)
    goto error;
  n_div = isl_local_space_dim(aff->ls, isl_dim_div);
  if (n_div > 0)
    eq = isl_basic_set_add_dims(eq, isl_dim_set, n_div);
  return isl_aff_substitute_equalities_lifted(aff, eq);
error:
  isl_basic_set_free(eq);
  isl_aff_free(aff);
  return NULL;
}

/* Look for equalities among the variables shared by context and aff
 * and the integer divisions of aff, if any.
 * The equalities are then used to eliminate coefficients and/or integer
 * divisions from aff.
 */
__isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
  __isl_take isl_set *context)
{
  isl_basic_set *hull;
  int n_div;

  if (!aff)
    goto error;
  n_div = isl_local_space_dim(aff->ls, isl_dim_div);
  if (n_div > 0) {
    isl_basic_set *bset;
    isl_local_space *ls;
    context = isl_set_add_dims(context, isl_dim_set, n_div);
    ls = isl_aff_get_domain_local_space(aff);
    bset = isl_basic_set_from_local_space(ls);
    bset = isl_basic_set_lift(bset);
    bset = isl_basic_set_flatten(bset);
    context = isl_set_intersect(context,
              isl_set_from_basic_set(bset));
  }

  hull = isl_set_affine_hull(context);
  return isl_aff_substitute_equalities_lifted(aff, hull);
error:
  isl_aff_free(aff);
  isl_set_free(context);
  return NULL;
}

__isl_give isl_aff *isl_aff_gist_params(__isl_take isl_aff *aff,
  __isl_take isl_set *context)
{
  isl_set *dom_context = isl_set_universe(isl_aff_get_domain_space(aff));
  dom_context = isl_set_intersect_params(dom_context, context);
  return isl_aff_gist(aff, dom_context);
}

/* Return a basic set containing those elements in the space
 * of aff where it is positive.  "rational" should not be set.
 *
 * If "aff" is NaN, then it is not positive.
 */
static __isl_give isl_basic_set *aff_pos_basic_set(__isl_take isl_aff *aff,
  int rational)
{
  isl_constraint *ineq;
  isl_basic_set *bset;
  isl_val *c;

  if (!aff)
    return NULL;
  if (isl_aff_is_nan(aff)) {
    isl_space *space = isl_aff_get_domain_space(aff);
    isl_aff_free(aff);
    return isl_basic_set_empty(space);
  }
  if (rational)
    isl_die0(isl_aff_get_ctx(aff), isl_error_unsupported,
      "rational sets not supported", goto error);

  ineq = isl_inequality_from_aff(aff);
  c = isl_constraint_get_constant_val(ineq);
  c = isl_val_sub_ui(c, 1);
  ineq = isl_constraint_set_constant_val(ineq, c);

  bset = isl_basic_set_from_constraint(ineq);
  bset = isl_basic_set_simplify(bset);
  return bset;
error:
  isl_aff_free(aff);
  return NULL;
}

/* Return a basic set containing those elements in the space
 * of aff where it is non-negative.
 * If "rational" is set, then return a rational basic set.
 *
 * If "aff" is NaN, then it is not non-negative (it's not negative either).
 */
static __isl_give isl_basic_set *aff_nonneg_basic_set(
  __isl_take isl_aff *aff, int rational)
{
  isl_constraint *ineq;
  isl_basic_set *bset;

  if (!aff)
    return NULL;
  if (isl_aff_is_nan(aff)) {
    isl_space *space = isl_aff_get_domain_space(aff);
    isl_aff_free(aff);
    return isl_basic_set_empty(space);
  }

  ineq = isl_inequality_from_aff(aff);

  bset = isl_basic_set_from_constraint(ineq);
  if (rational)
    bset = isl_basic_set_set_rational(bset);
  bset = isl_basic_set_simplify(bset);
  return bset;
}

/* Return a basic set containing those elements in the space
 * of aff where it is non-negative.
 */
__isl_give isl_basic_set *isl_aff_nonneg_basic_set(__isl_take isl_aff *aff)
{
  return aff_nonneg_basic_set(aff, 0);
}

/* Return a basic set containing those elements in the domain space
 * of "aff" where it is positive.
 */
__isl_give isl_basic_set *isl_aff_pos_basic_set(__isl_take isl_aff *aff)
{
  aff = isl_aff_add_constant_num_si(aff, -1);
  return isl_aff_nonneg_basic_set(aff);
}

/* Return a basic set containing those elements in the domain space
 * of aff where it is negative.
 */
__isl_give isl_basic_set *isl_aff_neg_basic_set(__isl_take isl_aff *aff)
{
  aff = isl_aff_neg(aff);
  return isl_aff_pos_basic_set(aff);
}

/* Return a basic set containing those elements in the space
 * of aff where it is zero.
 * If "rational" is set, then return a rational basic set.
 *
 * If "aff" is NaN, then it is not zero.
 */
static __isl_give isl_basic_set *aff_zero_basic_set(__isl_take isl_aff *aff,
  int rational)
{
  isl_constraint *ineq;
  isl_basic_set *bset;

  if (!aff)
    return NULL;
  if (isl_aff_is_nan(aff)) {
    isl_space *space = isl_aff_get_domain_space(aff);
    isl_aff_free(aff);
    return isl_basic_set_empty(space);
  }

  ineq = isl_equality_from_aff(aff);

  bset = isl_basic_set_from_constraint(ineq);
  if (rational)
    bset = isl_basic_set_set_rational(bset);
  bset = isl_basic_set_simplify(bset);
  return bset;
}

/* Return a basic set containing those elements in the space
 * of aff where it is zero.
 */
__isl_give isl_basic_set *isl_aff_zero_basic_set(__isl_take isl_aff *aff)
{
  return aff_zero_basic_set(aff, 0);
}

/* Return a basic set containing those elements in the shared space
 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
 */
__isl_give isl_basic_set *isl_aff_ge_basic_set(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  aff1 = isl_aff_sub(aff1, aff2);

  return isl_aff_nonneg_basic_set(aff1);
}

/* Return a basic set containing those elements in the shared domain space
 * of "aff1" and "aff2" where "aff1" is greater than "aff2".
 */
__isl_give isl_basic_set *isl_aff_gt_basic_set(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  aff1 = isl_aff_sub(aff1, aff2);

  return isl_aff_pos_basic_set(aff1);
}

/* Return a set containing those elements in the shared space
 * of aff1 and aff2 where aff1 is greater than or equal to aff2.
 */
__isl_give isl_set *isl_aff_ge_set(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  return isl_set_from_basic_set(isl_aff_ge_basic_set(aff1, aff2));
}

/* Return a set containing those elements in the shared domain space
 * of aff1 and aff2 where aff1 is greater than aff2.
 *
 * If either of the two inputs is NaN, then the result is empty,
 * as comparisons with NaN always return false.
 */
__isl_give isl_set *isl_aff_gt_set(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  return isl_set_from_basic_set(isl_aff_gt_basic_set(aff1, aff2));
}

/* Return a basic set containing those elements in the shared space
 * of aff1 and aff2 where aff1 is smaller than or equal to aff2.
 */
__isl_give isl_basic_set *isl_aff_le_basic_set(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  return isl_aff_ge_basic_set(aff2, aff1);
}

/* Return a basic set containing those elements in the shared domain space
 * of "aff1" and "aff2" where "aff1" is smaller than "aff2".
 */
__isl_give isl_basic_set *isl_aff_lt_basic_set(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  return isl_aff_gt_basic_set(aff2, aff1);
}

/* Return a set containing those elements in the shared space
 * of aff1 and aff2 where aff1 is smaller than or equal to aff2.
 */
__isl_give isl_set *isl_aff_le_set(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  return isl_aff_ge_set(aff2, aff1);
}

/* Return a set containing those elements in the shared domain space
 * of "aff1" and "aff2" where "aff1" is smaller than "aff2".
 */
__isl_give isl_set *isl_aff_lt_set(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  return isl_set_from_basic_set(isl_aff_lt_basic_set(aff1, aff2));
}

/* Return a basic set containing those elements in the shared space
 * of aff1 and aff2 where aff1 and aff2 are equal.
 */
__isl_give isl_basic_set *isl_aff_eq_basic_set(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  aff1 = isl_aff_sub(aff1, aff2);

  return isl_aff_zero_basic_set(aff1);
}

/* Return a set containing those elements in the shared space
 * of aff1 and aff2 where aff1 and aff2 are equal.
 */
__isl_give isl_set *isl_aff_eq_set(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  return isl_set_from_basic_set(isl_aff_eq_basic_set(aff1, aff2));
}

/* Return a set containing those elements in the shared domain space
 * of aff1 and aff2 where aff1 and aff2 are not equal.
 *
 * If either of the two inputs is NaN, then the result is empty,
 * as comparisons with NaN always return false.
 */
__isl_give isl_set *isl_aff_ne_set(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  isl_set *set_lt, *set_gt;

  set_lt = isl_aff_lt_set(isl_aff_copy(aff1),
        isl_aff_copy(aff2));
  set_gt = isl_aff_gt_set(aff1, aff2);
  return isl_set_union_disjoint(set_lt, set_gt);
}

__isl_give isl_aff *isl_aff_add_on_domain(__isl_keep isl_set *dom,
  __isl_take isl_aff *aff1, __isl_take isl_aff *aff2)
{
  aff1 = isl_aff_add(aff1, aff2);
  aff1 = isl_aff_gist(aff1, isl_set_copy(dom));
  return aff1;
}

int isl_aff_is_empty(__isl_keep isl_aff *aff)
{
  if (!aff)
    return -1;

  return 0;
}

/* Check whether the given affine expression has non-zero coefficient
 * for any dimension in the given range or if any of these dimensions
 * appear with non-zero coefficients in any of the integer divisions
 * involved in the affine expression.
 */
isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
  enum isl_dim_type type, unsigned first, unsigned n)
{
  int i;
  isl_ctx *ctx;
  int *active = NULL;
  isl_bool involves = isl_bool_false;

  if (!aff)
    return isl_bool_error;
  if (n == 0)
    return isl_bool_false;

  ctx = isl_aff_get_ctx(aff);
  if (first + n > isl_aff_dim(aff, type))
    isl_die0(ctx, isl_error_invalid,
      "range out of bounds", return isl_bool_error);

  active = isl_local_space_get_active(aff->ls, aff->v->el + 2);
  if (!active)
    goto error;

  first += isl_local_space_offset(aff->ls, type) - 1;
  for (i = 0; i < n; ++i24.5k)
    if (active[first + i]) {
      involves = isl_bool_true;
      break;
    }

  free(active);

  return involves;
error:
  free(active);
  return isl_bool_error;
}

__isl_give isl_aff *isl_aff_drop_dims(__isl_take isl_aff *aff,
  enum isl_dim_type type, unsigned first, unsigned n)
{
  isl_ctx *ctx;

  if (!aff)
    return NULL;
  if (type == isl_dim_out)
    isl_die0(aff->v->ctx, isl_error_invalid,
      "cannot drop output/set dimension",
      return isl_aff_free(aff));
  if (type == isl_dim_in)
    type = isl_dim_set;
  if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type)61)
    return aff;

  ctx = isl_aff_get_ctx(aff);
  if (first + n > isl_local_space_dim(aff->ls, type))
    isl_die0(ctx, isl_error_invalid, "range out of bounds",
      return isl_aff_free(aff));

  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;

  aff->ls = isl_local_space_drop_dims(aff->ls, type, first, n);
  if (!aff->ls)
    return isl_aff_free(aff);

  first += 1 + isl_local_space_offset(aff->ls, type);
  aff->v = isl_vec_drop_els(aff->v, first, n);
  if (!aff->v)
    return isl_aff_free(aff);

  return aff;
}

/* Drop the "n" domain dimensions starting at "first" from "aff",
 * after checking that they do not appear in the affine expression.
 */
static __isl_give isl_aff *drop_domain(__isl_take isl_aff *aff, unsigned first,
  unsigned n)
{
  isl_bool involves;

  involves = isl_aff_involves_dims(aff, isl_dim_in, first, n);
  if (involves < 0)
    return isl_aff_free(aff);
  if (involves)
    isl_die0(isl_aff_get_ctx(aff), isl_error_invalid,
        "affine expression involves some of the domain dimensions",
        return isl_aff_free(aff));
  return isl_aff_drop_dims(aff, isl_dim_in, first, n);
}

/* Project the domain of the affine expression onto its parameter space.
 * The affine expression may not involve any of the domain dimensions.
 */
__isl_give isl_aff *isl_aff_project_domain_on_params(__isl_take isl_aff *aff)
{
  isl_space *space;
  unsigned n;

  n = isl_aff_dim(aff, isl_dim_in);
  aff = drop_domain(aff, 0, n);
  space = isl_aff_get_domain_space(aff);
  space = isl_space_params(space);
  aff = isl_aff_reset_domain_space(aff, space);
  return aff;
}

/* Check that the domain of "aff" is a product.
 */
static isl_stat check_domain_product(__isl_keep isl_aff *aff)
{
  isl_bool is_product;

  is_product = isl_space_is_product(isl_aff_peek_domain_space(aff));
  if (is_product < 0)
    return isl_stat_error;
  if (!is_product)
    isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
      "domain is not a product", return isl_stat_error);
  return isl_stat_ok;
}

/* Given an affine function with a domain of the form [A -> B] that
 * does not depend on B, return the same function on domain A.
 */
__isl_give isl_aff *isl_aff_domain_factor_domain(__isl_take isl_aff *aff)
{
  isl_space *space;
  int n, n_in;

  if (check_domain_product(aff) < 0)
    return isl_aff_free(aff);
  space = isl_aff_get_domain_space(aff);
  n = isl_space_dim(space, isl_dim_set);
  space = isl_space_factor_domain(space);
  n_in = isl_space_dim(space, isl_dim_set);
  aff = drop_domain(aff, n_in, n - n_in);
  aff = isl_aff_reset_domain_space(aff, space);
  return aff;
}

/* Convert an affine expression defined over a parameter domain
 * into one that is defined over a zero-dimensional set.
 */
__isl_give isl_aff *isl_aff_from_range(__isl_take isl_aff *aff)
{
  isl_local_space *ls;

  ls = isl_aff_take_domain_local_space(aff);
  ls = isl_local_space_set_from_params(ls);
  aff = isl_aff_restore_domain_local_space(aff, ls);

  return aff;
}

__isl_give isl_aff *isl_aff_insert_dims(__isl_take isl_aff *aff,
  enum isl_dim_type type, unsigned first, unsigned n)
{
  isl_ctx *ctx;

  if (!aff)
    return NULL;
  if (type == isl_dim_out)
    isl_die0(aff->v->ctx, isl_error_invalid,
      "cannot insert output/set dimensions",
      return isl_aff_free(aff));
  if (type == isl_dim_in)
    type = isl_dim_set;
  if (n == 0 && !isl_local_space_is_named_or_nested(aff->ls, type)1.72k)
    return aff;

  ctx = isl_aff_get_ctx(aff);
  if (first > isl_local_space_dim(aff->ls, type))
    isl_die0(ctx, isl_error_invalid, "position out of bounds",
      return isl_aff_free(aff));

  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;

  aff->ls = isl_local_space_insert_dims(aff->ls, type, first, n);
  if (!aff->ls)
    return isl_aff_free(aff);

  first += 1 + isl_local_space_offset(aff->ls, type);
  aff->v = isl_vec_insert_zero_els(aff->v, first, n);
  if (!aff->v)
    return isl_aff_free(aff);

  return aff;
}

__isl_give isl_aff *isl_aff_add_dims(__isl_take isl_aff *aff,
  enum isl_dim_type type, unsigned n)
{
  unsigned pos;

  pos = isl_aff_dim(aff, type);

  return isl_aff_insert_dims(aff, type, pos, n);
}

__isl_give isl_pw_aff *isl_pw_aff_add_dims(__isl_take isl_pw_aff *pwaff,
  enum isl_dim_type type, unsigned n)
{
  unsigned pos;

  pos = isl_pw_aff_dim(pwaff, type);

  return isl_pw_aff_insert_dims(pwaff, type, pos, n);
}

/* Move the "n" dimensions of "src_type" starting at "src_pos" of "aff"
 * to dimensions of "dst_type" at "dst_pos".
 *
 * We only support moving input dimensions to parameters and vice versa.
 */
__isl_give isl_aff *isl_aff_move_dims(__isl_take isl_aff *aff,
  enum isl_dim_type dst_type, unsigned dst_pos,
  enum isl_dim_type src_type, unsigned src_pos, unsigned n)
{
  unsigned g_dst_pos;
  unsigned g_src_pos;

  if (!aff)
    return NULL;
  if (n == 0 &&
      !isl_local_space_is_named_or_nested(aff->ls, src_type) &&
      !isl_local_space_is_named_or_nested(aff->ls, dst_type))
    return aff;

  if (dst_type == isl_dim_out || src_type == isl_dim_out)
    isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
      "cannot move output/set dimension",
      return isl_aff_free(aff));
  if (dst_type == isl_dim_div || src_type == isl_dim_div)
    isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
      "cannot move divs", return isl_aff_free(aff));
  if (dst_type == isl_dim_in)
    dst_type = isl_dim_set;
  if (src_type == isl_dim_in)
    src_type = isl_dim_set;

  if (src_pos + n > isl_local_space_dim(aff->ls, src_type))
    isl_die(isl_aff_get_ctx(aff), isl_error_invalid,
      "range out of bounds", return isl_aff_free(aff));
  if (dst_type == src_type)
    isl_die(isl_aff_get_ctx(aff), isl_error_unsupported,
      "moving dims within the same type not supported",
      return isl_aff_free(aff));

  aff = isl_aff_cow(aff);
  if (!aff)
    return NULL;

  g_src_pos = 1 + isl_local_space_offset(aff->ls, src_type) + src_pos;
  g_dst_pos = 1 + isl_local_space_offset(aff->ls, dst_type) + dst_pos;
  if (dst_type > src_type)
    g_dst_pos -= n;

  aff->v = isl_vec_move_els(aff->v, g_dst_pos, g_src_pos, n);
  aff->ls = isl_local_space_move_dims(aff->ls, dst_type, dst_pos,
            src_type, src_pos, n);
  if (!aff->v || !aff->ls)
    return isl_aff_free(aff);

  aff = sort_divs(aff);

  return aff;
}

__isl_give isl_pw_aff *isl_pw_aff_from_aff(__isl_take isl_aff *aff)
{
  isl_set *dom = isl_set_universe(isl_aff_get_domain_space(aff));
  return isl_pw_aff_alloc(dom, aff);
}

#define isl_aff_involves_nan isl_aff_is_nan

#undef PW
#define PW isl_pw_aff
#undef EL
#define EL isl_aff
#undef EL_IS_ZERO
#define EL_IS_ZERO is_empty
#undef ZERO
#define ZERO empty
#undef IS_ZERO
#define IS_ZERO is_empty
#undef FIELD
#define FIELD aff
#undef DEFAULT_IS_ZERO
#define DEFAULT_IS_ZERO 0

#define NO_OPT
#define NO_LIFT
#define NO_MORPH

#include <isl_pw_templ.c>
#include <isl_pw_eval.c>
#include <isl_pw_hash.c>
#include <isl_pw_union_opt.c>

#undef BASE
#define BASE pw_aff

#include <isl_union_single.c>
#include <isl_union_neg.c>

static __isl_give isl_set *align_params_pw_pw_set_and(
  __isl_take isl_pw_aff *pwaff1, __isl_take isl_pw_aff *pwaff2,
  __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
            __isl_take isl_pw_aff *pwaff2))
{
  isl_bool equal_params;

  if (!pwaff1 || !pwaff2)
    goto error;
  equal_params = isl_space_has_equal_params(pwaff1->dim, pwaff2->dim);
  if (equal_params < 0)
    goto error;
  if (equal_params)
    return fn(pwaff1, pwaff2);
  if (isl_pw_aff_check_named_params(pwaff1) < 0 ||
      isl_pw_aff_check_named_params(pwaff2) < 0)
    goto error;
  pwaff1 = isl_pw_aff_align_params(pwaff1, isl_pw_aff_get_space(pwaff2));
  pwaff2 = isl_pw_aff_align_params(pwaff2, isl_pw_aff_get_space(pwaff1));
  return fn(pwaff1, pwaff2);
error:
  isl_pw_aff_free(pwaff1);
  isl_pw_aff_free(pwaff2);
  return NULL;
}

/* Align the parameters of the to isl_pw_aff arguments and
 * then apply a function "fn" on them that returns an isl_map.
 */
static __isl_give isl_map *align_params_pw_pw_map_and(
  __isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2,
  __isl_give isl_map *(*fn)(__isl_take isl_pw_aff *pa1,
            __isl_take isl_pw_aff *pa2))
{
  isl_bool equal_params;

  if (!pa1 || !pa2)
    goto error;
  equal_params = isl_space_has_equal_params(pa1->dim, pa2->dim);
  if (equal_params < 0)
    goto error;
  if (equal_params)
    return fn(pa1, pa2);
  if (isl_pw_aff_check_named_params(pa1) < 0 ||
      isl_pw_aff_check_named_params(pa2) < 0)
    goto error;
  pa1 = isl_pw_aff_align_params(pa1, isl_pw_aff_get_space(pa2));
  pa2 = isl_pw_aff_align_params(pa2, isl_pw_aff_get_space(pa1));
  return fn(pa1, pa2);
error:
  isl_pw_aff_free(pa1);
  isl_pw_aff_free(pa2);
  return NULL;
}

/* Compute a piecewise quasi-affine expression with a domain that
 * is the union of those of pwaff1 and pwaff2 and such that on each
 * cell, the quasi-affine expression is the maximum of those of pwaff1
 * and pwaff2.  If only one of pwaff1 or pwaff2 is defined on a given
 * cell, then the associated expression is the defined one.
 */
static __isl_give isl_pw_aff *pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return isl_pw_aff_union_opt_cmp(pwaff1, pwaff2, &isl_aff_ge_set);
}

__isl_give isl_pw_aff *isl_pw_aff_union_max(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
              &pw_aff_union_max);
}

/* Compute a piecewise quasi-affine expression with a domain that
 * is the union of those of pwaff1 and pwaff2 and such that on each
 * cell, the quasi-affine expression is the minimum of those of pwaff1
 * and pwaff2.  If only one of pwaff1 or pwaff2 is defined on a given
 * cell, then the associated expression is the defined one.
 */
static __isl_give isl_pw_aff *pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return isl_pw_aff_union_opt_cmp(pwaff1, pwaff2, &isl_aff_le_set);
}

__isl_give isl_pw_aff *isl_pw_aff_union_min(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2,
              &pw_aff_union_min);
}

__isl_give isl_pw_aff *isl_pw_aff_union_opt(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2, int max)
{
  if (max)
    return isl_pw_aff_union_max(pwaff1, pwaff2);
  else
    return isl_pw_aff_union_min(pwaff1, pwaff2);
}

/* Return a set containing those elements in the domain
 * of "pwaff" where it satisfies "fn" (if complement is 0) or
 * does not satisfy "fn" (if complement is 1).
 *
 * The pieces with a NaN never belong to the result since
 * NaN does not satisfy any property.
 */
static __isl_give isl_set *pw_aff_locus(__isl_take isl_pw_aff *pwaff,
  __isl_give isl_basic_set *(*fn)(__isl_take isl_aff *aff, int rational),
  int complement)
{
  int i;
  isl_set *set;

  if (!pwaff)
    return NULL;

  set = isl_set_empty(isl_pw_aff_get_domain_space(pwaff));

  for (i = 0; i < pwaff->n; ++i26.2k) {
    isl_basic_set *bset;
    isl_set *set_i, *locus;
    isl_bool rational;

    if (isl_aff_is_nan(pwaff->p[i].aff))
      continue;

    rational = isl_set_has_rational(pwaff->p[i].set);
    bset = fn(isl_aff_copy(pwaff->p[i].aff), rational);
    locus = isl_set_from_basic_set(bset);
    set_i = isl_set_copy(pwaff->p[i].set);
    if (complement)
      set_i = isl_set_subtract(set_i, locus);
    else
      set_i = isl_set_intersect(set_i, locus);
    set = isl_set_union_disjoint(set, set_i);
  }

  isl_pw_aff_free(pwaff);

  return set;
}

/* Return a set containing those elements in the domain
 * of "pa" where it is positive.
 */
__isl_give isl_set *isl_pw_aff_pos_set(__isl_take isl_pw_aff *pa)
{
  return pw_aff_locus(pa, &aff_pos_basic_set, 0);
}

/* Return a set containing those elements in the domain
 * of pwaff where it is non-negative.
 */
__isl_give isl_set *isl_pw_aff_nonneg_set(__isl_take isl_pw_aff *pwaff)
{
  return pw_aff_locus(pwaff, &aff_nonneg_basic_set, 0);
}

/* Return a set containing those elements in the domain
 * of pwaff where it is zero.
 */
__isl_give isl_set *isl_pw_aff_zero_set(__isl_take isl_pw_aff *pwaff)
{
  return pw_aff_locus(pwaff, &aff_zero_basic_set, 0);
}

/* Return a set containing those elements in the domain
 * of pwaff where it is not zero.
 */
__isl_give isl_set *isl_pw_aff_non_zero_set(__isl_take isl_pw_aff *pwaff)
{
  return pw_aff_locus(pwaff, &aff_zero_basic_set, 1);
}

/* Return a set containing those elements in the shared domain
 * of pwaff1 and pwaff2 where pwaff1 is greater than (or equal) to pwaff2.
 *
 * We compute the difference on the shared domain and then construct
 * the set of values where this difference is non-negative.
 * If strict is set, we first subtract 1 from the difference.
 * If equal is set, we only return the elements where pwaff1 and pwaff2
 * are equal.
 */
static __isl_give isl_set *pw_aff_gte_set(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2, int strict, int equal)
{
  isl_set *set1, *set2;

  set1 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff1));
  set2 = isl_pw_aff_domain(isl_pw_aff_copy(pwaff2));
  set1 = isl_set_intersect(set1, set2);
  pwaff1 = isl_pw_aff_intersect_domain(pwaff1, isl_set_copy(set1));
  pwaff2 = isl_pw_aff_intersect_domain(pwaff2, isl_set_copy(set1));
  pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_neg(pwaff2));

  if (strict) {
    isl_space *dim = isl_set_get_space(set1);
    isl_aff *aff;
    aff = isl_aff_zero_on_domain(isl_local_space_from_space(dim));
    aff = isl_aff_add_constant_si(aff, -1);
    pwaff1 = isl_pw_aff_add(pwaff1, isl_pw_aff_alloc(set1, aff));
  } else
    isl_set_free(set1);

  if (equal)
    return isl_pw_aff_zero_set(pwaff1);
  return isl_pw_aff_nonneg_set(pwaff1);
}

/* Return a set containing those elements in the shared domain
 * of pwaff1 and pwaff2 where pwaff1 is equal to pwaff2.
 */
static __isl_give isl_set *pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return pw_aff_gte_set(pwaff1, pwaff2, 0, 1);
}

__isl_give isl_set *isl_pw_aff_eq_set(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_eq_set);
}

/* Return a set containing those elements in the shared domain
 * of pwaff1 and pwaff2 where pwaff1 is greater than or equal to pwaff2.
 */
static __isl_give isl_set *pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return pw_aff_gte_set(pwaff1, pwaff2, 0, 0);
}

__isl_give isl_set *isl_pw_aff_ge_set(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ge_set);
}

/* Return a set containing those elements in the shared domain
 * of pwaff1 and pwaff2 where pwaff1 is strictly greater than pwaff2.
 */
static __isl_give isl_set *pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return pw_aff_gte_set(pwaff1, pwaff2, 1, 0);
}

__isl_give isl_set *isl_pw_aff_gt_set(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_gt_set);
}

__isl_give isl_set *isl_pw_aff_le_set(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return isl_pw_aff_ge_set(pwaff2, pwaff1);
}

__isl_give isl_set *isl_pw_aff_lt_set(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return isl_pw_aff_gt_set(pwaff2, pwaff1);
}

/* Return a map containing pairs of elements in the domains of "pa1" and "pa2"
 * where the function values are ordered in the same way as "order",
 * which returns a set in the shared domain of its two arguments.
 * The parameters of "pa1" and "pa2" are assumed to have been aligned.
 *
 * Let "pa1" and "pa2" be defined on domains A and B respectively.
 * We first pull back the two functions such that they are defined on
 * the domain [A -> B].  Then we apply "order", resulting in a set
 * in the space [A -> B].  Finally, we unwrap this set to obtain
 * a map in the space A -> B.
 */
static __isl_give isl_map *isl_pw_aff_order_map_aligned(
  __isl_take isl_pw_aff *pa1, __isl_take isl_pw_aff *pa2,
  __isl_give isl_set *(*order)(__isl_take isl_pw_aff *pa1,
    __isl_take isl_pw_aff *pa2))
{
  isl_space *space1, *space2;
  isl_multi_aff *ma;
  isl_set *set;

  space1 = isl_space_domain(isl_pw_aff_get_space(pa1));
  space2 = isl_space_domain(isl_pw_aff_get_space(pa2));
  space1 = isl_space_map_from_domain_and_range(space1, space2);
  ma = isl_multi_aff_domain_map(isl_space_copy(space1));
  pa1 = isl_pw_aff_pullback_multi_aff(pa1, ma);
  ma = isl_multi_aff_range_map(space1);
  pa2 = isl_pw_aff_pullback_multi_aff(pa2, ma);
  set = order(pa1, pa2);

  return isl_set_unwrap(set);
}

/* Return a map containing pairs of elements in the domains of "pa1" and "pa2"
 * where the function values are equal.
 * The parameters of "pa1" and "pa2" are assumed to have been aligned.
 */
static __isl_give isl_map *isl_pw_aff_eq_map_aligned(__isl_take isl_pw_aff *pa1,
  __isl_take isl_pw_aff *pa2)
{
  return isl_pw_aff_order_map_aligned(pa1, pa2, &isl_pw_aff_eq_set);
}

/* Return a map containing pairs of elements in the domains of "pa1" and "pa2"
 * where the function values are equal.
 */
__isl_give isl_map *isl_pw_aff_eq_map(__isl_take isl_pw_aff *pa1,
  __isl_take isl_pw_aff *pa2)
{
  return align_params_pw_pw_map_and(pa1, pa2, &isl_pw_aff_eq_map_aligned);
}

/* Return a map containing pairs of elements in the domains of "pa1" and "pa2"
 * where the function value of "pa1" is less than the function value of "pa2".
 * The parameters of "pa1" and "pa2" are assumed to have been aligned.
 */
static __isl_give isl_map *isl_pw_aff_lt_map_aligned(__isl_take isl_pw_aff *pa1,
  __isl_take isl_pw_aff *pa2)
{
  return isl_pw_aff_order_map_aligned(pa1, pa2, &isl_pw_aff_lt_set);
}

/* Return a map containing pairs of elements in the domains of "pa1" and "pa2"
 * where the function value of "pa1" is less than the function value of "pa2".
 */
__isl_give isl_map *isl_pw_aff_lt_map(__isl_take isl_pw_aff *pa1,
  __isl_take isl_pw_aff *pa2)
{
  return align_params_pw_pw_map_and(pa1, pa2, &isl_pw_aff_lt_map_aligned);
}

/* Return a map containing pairs of elements in the domains of "pa1" and "pa2"
 * where the function value of "pa1" is greater than the function value
 * of "pa2".
 * The parameters of "pa1" and "pa2" are assumed to have been aligned.
 */
static __isl_give isl_map *isl_pw_aff_gt_map_aligned(__isl_take isl_pw_aff *pa1,
  __isl_take isl_pw_aff *pa2)
{
  return isl_pw_aff_order_map_aligned(pa1, pa2, &isl_pw_aff_gt_set);
}

/* Return a map containing pairs of elements in the domains of "pa1" and "pa2"
 * where the function value of "pa1" is greater than the function value
 * of "pa2".
 */
__isl_give isl_map *isl_pw_aff_gt_map(__isl_take isl_pw_aff *pa1,
  __isl_take isl_pw_aff *pa2)
{
  return align_params_pw_pw_map_and(pa1, pa2, &isl_pw_aff_gt_map_aligned);
}

/* Return a set containing those elements in the shared domain
 * of the elements of list1 and list2 where each element in list1
 * has the relation specified by "fn" with each element in list2.
 */
static __isl_give isl_set *pw_aff_list_set(__isl_take isl_pw_aff_list *list1,
  __isl_take isl_pw_aff_list *list2,
  __isl_give isl_set *(*fn)(__isl_take isl_pw_aff *pwaff1,
            __isl_take isl_pw_aff *pwaff2))
{
  int i, j;
  isl_ctx *ctx;
  isl_set *set;

  if (!list1 || !list2)
    goto error;

  ctx = isl_pw_aff_list_get_ctx(list1);
  if (list1->n < 1 || list2->n < 1)
    isl_die0(ctx, isl_error_invalid,
      "list should contain at least one element", goto error);

  set = isl_set_universe(isl_pw_aff_get_domain_space(list1->p[0]));
  for (i = 0; i < list1->n; ++i5.69k)
    for (j = 0; 5.69kj < list2->n; ++j5.89k) {
      isl_set *set_ij;

      set_ij = fn(isl_pw_aff_copy(list1->p[i]),
            isl_pw_aff_copy(list2->p[j]));
      set = isl_set_intersect(set, set_ij);
    }

  isl_pw_aff_list_free(list1);
  isl_pw_aff_list_free(list2);
  return set;
error:
  isl_pw_aff_list_free(list1);
  isl_pw_aff_list_free(list2);
  return NULL;
}

/* Return a set containing those elements in the shared domain
 * of the elements of list1 and list2 where each element in list1
 * is equal to each element in list2.
 */
__isl_give isl_set *isl_pw_aff_list_eq_set(__isl_take isl_pw_aff_list *list1,
  __isl_take isl_pw_aff_list *list2)
{
  return pw_aff_list_set(list1, list2, &isl_pw_aff_eq_set);
}

__isl_give isl_set *isl_pw_aff_list_ne_set(__isl_take isl_pw_aff_list *list1,
  __isl_take isl_pw_aff_list *list2)
{
  return pw_aff_list_set(list1, list2, &isl_pw_aff_ne_set);
}

/* Return a set containing those elements in the shared domain
 * of the elements of list1 and list2 where each element in list1
 * is less than or equal to each element in list2.
 */
__isl_give isl_set *isl_pw_aff_list_le_set(__isl_take isl_pw_aff_list *list1,
  __isl_take isl_pw_aff_list *list2)
{
  return pw_aff_list_set(list1, list2, &isl_pw_aff_le_set);
}

__isl_give isl_set *isl_pw_aff_list_lt_set(__isl_take isl_pw_aff_list *list1,
  __isl_take isl_pw_aff_list *list2)
{
  return pw_aff_list_set(list1, list2, &isl_pw_aff_lt_set);
}

__isl_give isl_set *isl_pw_aff_list_ge_set(__isl_take isl_pw_aff_list *list1,
  __isl_take isl_pw_aff_list *list2)
{
  return pw_aff_list_set(list1, list2, &isl_pw_aff_ge_set);
}

__isl_give isl_set *isl_pw_aff_list_gt_set(__isl_take isl_pw_aff_list *list1,
  __isl_take isl_pw_aff_list *list2)
{
  return pw_aff_list_set(list1, list2, &isl_pw_aff_gt_set);
}


/* Return a set containing those elements in the shared domain
 * of pwaff1 and pwaff2 where pwaff1 is not equal to pwaff2.
 */
static __isl_give isl_set *pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  isl_set *set_lt, *set_gt;

  set_lt = isl_pw_aff_lt_set(isl_pw_aff_copy(pwaff1),
           isl_pw_aff_copy(pwaff2));
  set_gt = isl_pw_aff_gt_set(pwaff1, pwaff2);
  return isl_set_union_disjoint(set_lt, set_gt);
}

__isl_give isl_set *isl_pw_aff_ne_set(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return align_params_pw_pw_set_and(pwaff1, pwaff2, &pw_aff_ne_set);
}

__isl_give isl_pw_aff *isl_pw_aff_scale_down(__isl_take isl_pw_aff *pwaff,
  isl_int v)
{
  int i;

  if (isl_int_is_one(v))
    return pwaff0;
  if (!isl_int_is_pos(v))
    isl_die0(isl_pw_aff_get_ctx(pwaff), isl_error_invalid,
      "factor needs to be positive",
      return isl_pw_aff_free(pwaff));
  pwaff = isl_pw_aff_cow(pwaff);
  if (!pwaff)
    return NULL;
  if (pwaff->n == 0)
    return pwaff;

  for (i = 0; 3.41ki < pwaff->n; ++i3.65k) {
    pwaff->p[i].aff = isl_aff_scale_down(pwaff->p[i].aff, v);
    if (!pwaff->p[i].aff)
      return isl_pw_aff_free(pwaff);
  }

  return pwaff;
}

__isl_give isl_pw_aff *isl_pw_aff_floor(__isl_take isl_pw_aff *pwaff)
{
  int i;

  pwaff = isl_pw_aff_cow(pwaff);
  if (!pwaff)
    return NULL;
  if (pwaff->n == 0)
    return pwaff;

  for (i = 0; 7.61ki < pwaff->n; ++i8.06k) {
    pwaff->p[i].aff = isl_aff_floor(pwaff->p[i].aff);
    if (!pwaff->p[i].aff)
      return isl_pw_aff_free(pwaff);
  }

  return pwaff;
}

__isl_give isl_pw_aff *isl_pw_aff_ceil(__isl_take isl_pw_aff *pwaff)
{
  int i;

  pwaff = isl_pw_aff_cow(pwaff);
  if (!pwaff)
    return NULL;
  if (pwaff->n == 0)
    return pwaff;

  for (i = 0; 110i < pwaff->n; ++i112) {
    pwaff->p[i].aff = isl_aff_ceil(pwaff->p[i].aff);
    if (!pwaff->p[i].aff)
      return isl_pw_aff_free(pwaff);
  }

  return pwaff;
}

/* Assuming that "cond1" and "cond2" are disjoint,
 * return an affine expression that is equal to pwaff1 on cond1
 * and to pwaff2 on cond2.
 */
static __isl_give isl_pw_aff *isl_pw_aff_select(
  __isl_take isl_set *cond1, __isl_take isl_pw_aff *pwaff1,
  __isl_take isl_set *cond2, __isl_take isl_pw_aff *pwaff2)
{
  pwaff1 = isl_pw_aff_intersect_domain(pwaff1, cond1);
  pwaff2 = isl_pw_aff_intersect_domain(pwaff2, cond2);

  return isl_pw_aff_add_disjoint(pwaff1, pwaff2);
}

/* Return an affine expression that is equal to pwaff_true for elements
 * where "cond" is non-zero and to pwaff_false for elements where "cond"
 * is zero.
 * That is, return cond ? pwaff_true : pwaff_false;
 *
 * If "cond" involves and NaN, then we conservatively return a NaN
 * on its entire domain.  In principle, we could consider the pieces
 * where it is NaN separately from those where it is not.
 *
 * If "pwaff_true" and "pwaff_false" are obviously equal to each other,
 * then only use the domain of "cond" to restrict the domain.
 */
__isl_give isl_pw_aff *isl_pw_aff_cond(__isl_take isl_pw_aff *cond,
  __isl_take isl_pw_aff *pwaff_true, __isl_take isl_pw_aff *pwaff_false)
{
  isl_set *cond_true, *cond_false;
  isl_bool equal;

  if (!cond)
    goto error;
  if (isl_pw_aff_involves_nan(cond)) {
    isl_space *space = isl_pw_aff_get_domain_space(cond);
    isl_local_space *ls = isl_local_space_from_space(space);
    isl_pw_aff_free(cond);
    isl_pw_aff_free(pwaff_true);
    isl_pw_aff_free(pwaff_false);
    return isl_pw_aff_nan_on_domain(ls);
  }

  pwaff_true = isl_pw_aff_align_params(pwaff_true,
              isl_pw_aff_get_space(pwaff_false));
  pwaff_false = isl_pw_aff_align_params(pwaff_false,
              isl_pw_aff_get_space(pwaff_true));
  equal = isl_pw_aff_plain_is_equal(pwaff_true, pwaff_false);
  if (equal < 0)
    goto error;
  if (equal) {
    isl_set *dom;

    dom = isl_set_coalesce(isl_pw_aff_domain(cond));
    isl_pw_aff_free(pwaff_false);
    return isl_pw_aff_intersect_domain(pwaff_true, dom);
  }

  cond_true = isl_pw_aff_non_zero_set(isl_pw_aff_copy(cond));
  cond_false = isl_pw_aff_zero_set(cond);
  return isl_pw_aff_select(cond_true, pwaff_true,
         cond_false, pwaff_false);
error:
  isl_pw_aff_free(cond);
  isl_pw_aff_free(pwaff_true);
  isl_pw_aff_free(pwaff_false);
  return NULL;
}

isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff)
{
  if (!aff)
    return isl_bool_error;

  return isl_seq_first_non_zero(aff->v->el + 2, aff->v->size - 2) == -1;
}

/* Check whether pwaff is a piecewise constant.
 */
isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff)
{
  int i;

  if (!pwaff)
    return isl_bool_error;

  for (i = 0; 326i < pwaff->n; ++i326) {
    isl_bool is_cst = isl_aff_is_cst(pwaff->p[i].aff);
    if (is_cst < 0 || !is_cst)
      return is_cst;
  }

  return isl_bool_true;
}

/* Are all elements of "mpa" piecewise constants?
 */
isl_bool isl_multi_pw_aff_is_cst(__isl_keep isl_multi_pw_aff *mpa)
{
  int i;

  if (!mpa)
    return isl_bool_error;

  for (i = 0; i < mpa->n; ++i) {
    isl_bool is_cst = isl_pw_aff_is_cst(mpa->u.p[i]);
    if (is_cst < 0 || !is_cst)
      return is_cst;
  }

  return isl_bool_true;
}

/* Return the product of "aff1" and "aff2".
 *
 * If either of the two is NaN, then the result is NaN.
 *
 * Otherwise, at least one of "aff1" or "aff2" needs to be a constant.
 */
__isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  if (!aff1 || !aff2)
    goto error;

  if (isl_aff_is_nan(aff1)) {
    isl_aff_free(aff2);
    return aff1;
  }
  if (isl_aff_is_nan(aff2)) {
    isl_aff_free(aff1);
    return aff2;
  }

  if (!isl_aff_is_cst(aff2) && isl_aff_is_cst(aff1)3.18k)
    return isl_aff_mul(aff2, aff1);

  if (!isl_aff_is_cst(aff2))
    isl_die0(isl_aff_get_ctx(aff1), isl_error_invalid,
      "at least one affine expression should be constant",
      goto error);

  aff1 = isl_aff_cow(aff1);
  if (!aff1 || !aff2)
    goto error;

  aff1 = isl_aff_scale(aff1, aff2->v->el[1]);
  aff1 = isl_aff_scale_down(aff1, aff2->v->el[0]);

  isl_aff_free(aff2);
  return aff1;
error:
  isl_aff_free(aff1);
  isl_aff_free(aff2);
  return NULL;
}

/* Divide "aff1" by "aff2", assuming "aff2" is a constant.
 *
 * If either of the two is NaN, then the result is NaN.
 */
__isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
  __isl_take isl_aff *aff2)
{
  int is_cst;
  int neg;

  if (!aff1 || !aff2)
    goto error;

  if (isl_aff_is_nan(aff1)) {
    isl_aff_free(aff2);
    return aff1;
  }
  if (isl_aff_is_nan(aff2)) {
    isl_aff_free(aff1);
    return aff2;
  }

  is_cst = isl_aff_is_cst(aff2);
  if (is_cst < 0)
    goto error;
  if (!is_cst)
    isl_die0(isl_aff_get_ctx(aff2), isl_error_invalid,
      "second argument should be a constant", goto error);

  if (!aff2)
    goto error;

  neg = isl_int_is_neg(aff2->v->el[1]);
  if (neg) {
    isl_int_neg(aff2->v->el[0], aff2->v->el[0]);
    isl_int_neg(aff2->v->el[1], aff2->v->el[1]);
  }

  aff1 = isl_aff_scale(aff1, aff2->v->el[0]);
  aff1 = isl_aff_scale_down(aff1, aff2->v->el[1]);

  if (neg) {
    isl_int_neg(aff2->v->el[0], aff2->v->el[0]);
    isl_int_neg(aff2->v->el[1], aff2->v->el[1]);
  }

  isl_aff_free(aff2);
  return aff1;
error:
  isl_aff_free(aff1);
  isl_aff_free(aff2);
  return NULL;
}

static __isl_give isl_pw_aff *pw_aff_add(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_add);
}

__isl_give isl_pw_aff *isl_pw_aff_add(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_add);
}

__isl_give isl_pw_aff *isl_pw_aff_union_add(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return isl_pw_aff_union_add_(pwaff1, pwaff2);
}

static __isl_give isl_pw_aff *pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return isl_pw_aff_on_shared_domain(pwaff1, pwaff2, &isl_aff_mul);
}

__isl_give isl_pw_aff *isl_pw_aff_mul(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return isl_pw_aff_align_params_pw_pw_and(pwaff1, pwaff2, &pw_aff_mul);
}

static __isl_give isl_pw_aff *pw_aff_div(__isl_take isl_pw_aff *pa1,
  __isl_take isl_pw_aff *pa2)
{
  return isl_pw_aff_on_shared_domain(pa1, pa2, &isl_aff_div);
}

/* Divide "pa1" by "pa2", assuming "pa2" is a piecewise constant.
 */
__isl_give isl_pw_aff *isl_pw_aff_div(__isl_take isl_pw_aff *pa1,
  __isl_take isl_pw_aff *pa2)
{
  int is_cst;

  is_cst = isl_pw_aff_is_cst(pa2);
  if (is_cst < 0)
    goto error;
  if (!is_cst)
    isl_die0(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
      "second argument should be a piecewise constant",
      goto error);
  return isl_pw_aff_align_params_pw_pw_and(pa1, pa2, &pw_aff_div);
error:
  isl_pw_aff_free(pa1);
  isl_pw_aff_free(pa2);
  return NULL;
}

/* Compute the quotient of the integer division of "pa1" by "pa2"
 * with rounding towards zero.
 * "pa2" is assumed to be a piecewise constant.
 *
 * In particular, return
 *
 *  pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2)
 *
 */
__isl_give isl_pw_aff *isl_pw_aff_tdiv_q(__isl_take isl_pw_aff *pa1,
  __isl_take isl_pw_aff *pa2)
{
  int is_cst;
  isl_set *cond;
  isl_pw_aff *f, *c;

  is_cst = isl_pw_aff_is_cst(pa2);
  if (is_cst < 0)
    goto error;
  if (!is_cst)
    isl_die0(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
      "second argument should be a piecewise constant",
      goto error);

  pa1 = isl_pw_aff_div(pa1, pa2);

  cond = isl_pw_aff_nonneg_set(isl_pw_aff_copy(pa1));
  f = isl_pw_aff_floor(isl_pw_aff_copy(pa1));
  c = isl_pw_aff_ceil(pa1);
  return isl_pw_aff_cond(isl_set_indicator_function(cond), f, c);
error:
  isl_pw_aff_free(pa1);
  isl_pw_aff_free(pa2);
  return NULL;
}

/* Compute the remainder of the integer division of "pa1" by "pa2"
 * with rounding towards zero.
 * "pa2" is assumed to be a piecewise constant.
 *
 * In particular, return
 *
 *  pa1 - pa2 * (pa1 >= 0 ? floor(pa1/pa2) : ceil(pa1/pa2))
 *
 */
__isl_give isl_pw_aff *isl_pw_aff_tdiv_r(__isl_take isl_pw_aff *pa1,
  __isl_take isl_pw_aff *pa2)
{
  int is_cst;
  isl_pw_aff *res;

  is_cst = isl_pw_aff_is_cst(pa2);
  if (is_cst < 0)
    goto error;
  if (!is_cst)
    isl_die0(isl_pw_aff_get_ctx(pa2), isl_error_invalid,
      "second argument should be a piecewise constant",
      goto error);
  res = isl_pw_aff_tdiv_q(isl_pw_aff_copy(pa1), isl_pw_aff_copy(pa2));
  res = isl_pw_aff_mul(pa2, res);
  res = isl_pw_aff_sub(pa1, res);
  return res;
error:
  isl_pw_aff_free(pa1);
  isl_pw_aff_free(pa2);
  return NULL;
}

/* Does either of "pa1" or "pa2" involve any NaN2?
 */
static isl_bool either_involves_nan(__isl_keep isl_pw_aff *pa1,
  __isl_keep isl_pw_aff *pa2)
{
  isl_bool has_nan;

  has_nan = isl_pw_aff_involves_nan(pa1);
  if (has_nan < 0 || has_nan)
    return has_nan;
  return isl_pw_aff_involves_nan(pa2);
}

/* Replace "pa1" and "pa2" (at least one of which involves a NaN)
 * by a NaN on their shared domain.
 *
 * In principle, the result could be refined to only being NaN
 * on the parts of this domain where at least one of "pa1" or "pa2" is NaN.
 */
static __isl_give isl_pw_aff *replace_by_nan(__isl_take isl_pw_aff *pa1,
  __isl_take isl_pw_aff *pa2)
{
  isl_local_space *ls;
  isl_set *dom;
  isl_pw_aff *pa;

  dom = isl_set_intersect(isl_pw_aff_domain(pa1), isl_pw_aff_domain(pa2));
  ls = isl_local_space_from_space(isl_set_get_space(dom));
  pa = isl_pw_aff_nan_on_domain(ls);
  pa = isl_pw_aff_intersect_domain(pa, dom);

  return pa;
}

static __isl_give isl_pw_aff *pw_aff_min(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  isl_set *le;
  isl_set *dom;

  dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
        isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
  le = isl_pw_aff_le_set(isl_pw_aff_copy(pwaff1),
        isl_pw_aff_copy(pwaff2));
  dom = isl_set_subtract(dom, isl_set_copy(le));
  return isl_pw_aff_select(le, pwaff1, dom, pwaff2);
}

static __isl_give isl_pw_aff *pw_aff_max(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  isl_set *ge;
  isl_set *dom;

  dom = isl_set_intersect(isl_pw_aff_domain(isl_pw_aff_copy(pwaff1)),
        isl_pw_aff_domain(isl_pw_aff_copy(pwaff2)));
  ge = isl_pw_aff_ge_set(isl_pw_aff_copy(pwaff1),
        isl_pw_aff_copy(pwaff2));
  dom = isl_set_subtract(dom, isl_set_copy(ge));
  return isl_pw_aff_select(ge, pwaff1, dom, pwaff2);
}

/* Return an expression for the minimum (if "max" is not set) or
 * the maximum (if "max" is set) of "pa1" and "pa2".
 * If either expression involves any NaN, then return a NaN
 * on the shared domain as result.
 */
static __isl_give isl_pw_aff *pw_aff_min_max(__isl_take isl_pw_aff *pa1,
  __isl_take isl_pw_aff *pa2, int max)
{
  isl_bool has_nan;

  has_nan = either_involves_nan(pa1, pa2);
  if (has_nan < 0)
    pa1 = isl_pw_aff_free(pa1);
  else if (has_nan)
    return replace_by_nan(pa1, pa2);

  if (max)
    return isl_pw_aff_align_params_pw_pw_and(pa1, pa2, &pw_aff_max);
  else
    return isl_pw_aff_align_params_pw_pw_and(pa1, pa2, &pw_aff_min);
}

/* Return an expression for the minimum of "pwaff1" and "pwaff2".
 */
__isl_give isl_pw_aff *isl_pw_aff_min(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return pw_aff_min_max(pwaff1, pwaff2, 0);
}

/* Return an expression for the maximum of "pwaff1" and "pwaff2".
 */
__isl_give isl_pw_aff *isl_pw_aff_max(__isl_take isl_pw_aff *pwaff1,
  __isl_take isl_pw_aff *pwaff2)
{
  return pw_aff_min_max(pwaff1, pwaff2, 1);
}

static __isl_give isl_pw_aff *pw_aff_list_reduce(
  __isl_take isl_pw_aff_list *list,
  __isl_give isl_pw_aff *(*fn)(__isl_take isl_pw_aff *pwaff1,
          __isl_take isl_pw_aff *pwaff2))
{
  int i;
  isl_ctx *ctx;
  isl_pw_aff *res;

  if (!list)
    return NULL;

  ctx = isl_pw_aff_list_get_ctx(list);
  if (list->n < 1)
    isl_die0(ctx, isl_error_invalid,
      "list should contain at least one element", goto error);

  res = isl_pw_aff_copy(list->p[0]);
  for (i = 1; i < list->n; ++i6)
    res = fn(res, isl_pw_aff_copy(list->p[i]));

  isl_pw_aff_list_free(list);
  return res;
error:
  isl_pw_aff_list_free(list);
  return NULL;
}

/* Return an isl_pw_aff that maps each element in the intersection of the
 * domains of the elements of list to the minimal corresponding affine
 * expression.
 */
__isl_give isl_pw_aff *isl_pw_aff_list_min(__isl_take isl_pw_aff_list *list)
{
  return pw_aff_list_reduce(list, &isl_pw_aff_min);
}

/* Return an isl_pw_aff that maps each element in the intersection of the
 * domains of the elements of list to the maximal corresponding affine
 * expression.
 */
__isl_give isl_pw_aff *isl_pw_aff_list_max(__isl_take isl_pw_aff_list *list)
{
  return pw_aff_list_reduce(list, &isl_pw_aff_max);
}

/* Mark the domains of "pwaff" as rational.
 */
__isl_give isl_pw_aff *isl_pw_aff_set_rational(__isl_take isl_pw_aff *pwaff)
{
  int i;

  pwaff = isl_pw_aff_cow(pwaff);
  if (!pwaff)
    return NULL;
  if (pwaff->n == 0)
    return pwaff;

  for (i = 0; 307i < pwaff->n; ++i307) {
    pwaff->p[i].set = isl_set_set_rational(pwaff->p[i].set);
    if (!pwaff->p[i].set)
      return isl_pw_aff_free(pwaff);
  }

  return pwaff;
}

/* Mark the domains of the elements of "list" as rational.
 */
__isl_give isl_pw_aff_list *isl_pw_aff_list_set_rational(
  __isl_take isl_pw_aff_list *list)
{
  int i, n;

  if (!list)
    return NULL;
  if (list->n == 0)
    return list;

  n = list->n;
  for (i = 0; i < n; ++i50) {
    isl_pw_aff *pa;

    pa = isl_pw_aff_list_get_pw_aff(list, i);
    pa = isl_pw_aff_set_rational(pa);
    list = isl_pw_aff_list_set_pw_aff(list, i, pa);
  }

  return list;
}

/* Do the parameters of "aff" match those of "space"?
 */
isl_bool isl_aff_matching_params(__isl_keep isl_aff *aff,
  __isl_keep isl_space *space)
{
  isl_space *aff_space;
  isl_bool match;

  if (!aff || !space)
    return isl_bool_error;

  aff_space = isl_aff_get_domain_space(aff);

  match = isl_space_has_equal_params(space, aff_space);

  isl_space_free(aff_space);
  return match;
}

/* Check that the domain space of "aff" matches "space".
 */
isl_stat isl_aff_check_match_domain_space(__isl_keep isl_aff *aff,
  __isl_keep isl_space *space)
{
  isl_space *aff_space;
  isl_bool match;

  if (!aff || !space)
    return isl_stat_error;

  aff_space = isl_aff_get_domain_space(aff);

  match = isl_space_has_equal_params(space, aff_space);
  if (match < 0)
    goto error;
  if (!match)
    isl_die0(isl_aff_get_ctx(aff), isl_error_invalid,
      "parameters don't match", goto error);
  match = isl_space_tuple_is_equal(space, isl_dim_in,
          aff_space, isl_dim_set);
  if (match < 0)
    goto error;
  if (!match)
    isl_die0(isl_aff_get_ctx(aff), isl_error_invalid,
      "domains don't match", goto error);
  isl_space_free(aff_space);
  return isl_stat_ok;
error:
  isl_space_free(aff_space);
  return isl_stat_error;
}

#undef BASE
#define BASE aff
#undef DOMBASE
#define DOMBASE set
#define NO_DOMAIN

#include <isl_multi_no_explicit_domain.c>
#include <isl_multi_templ.c>
#include <isl_multi_apply_set.c>
#include <isl_multi_cmp.c>
#include <isl_multi_dims.c>
#include <isl_multi_floor.c>
#include <isl_multi_gist.c>

#undef NO_DOMAIN

/* Construct an isl_multi_aff living in "space" that corresponds
 * to the affine transformation matrix "mat".
 */
__isl_give isl_multi_aff *isl_multi_aff_from_aff_mat(
  __isl_take isl_space *space, __isl_take isl_mat *mat)
{
  isl_ctx *ctx;
  isl_local_space *ls = NULL;
  isl_multi_aff *ma = NULL;
  int n_row, n_col, n_out, total;
  int i;

  if (!space || !mat)
    goto error;

  ctx = isl_mat_get_ctx(mat);

  n_row = isl_mat_rows(mat);
  n_col = isl_mat_cols(mat);
  if (n_row < 1)
    isl_die0(ctx, isl_error_invalid,
      "insufficient number of rows", goto error);
  if (n_col < 1)
    isl_die0(ctx, isl_error_invalid,
      "insufficient number of columns", goto error);
  n_out = isl_space_dim(space, isl_dim_out);
  total = isl_space_dim(space, isl_dim_all);
  if (1 + n_out != n_row || 2 + total != n_row + n_col)
    isl_die0(ctx, isl_error_invalid,
      "dimension mismatch", goto error);

  ma = isl_multi_aff_zero(isl_space_copy(space));
  ls = isl_local_space_from_space(isl_space_domain(space));

  for (i = 0; i < n_row - 1; ++i2) {
    isl_vec *v;
    isl_aff *aff;

    v = isl_vec_alloc(ctx, 1 + n_col);
    if (!v)
      goto error;
    isl_int_set(v->el[0], mat->row[0][0]);
    isl_seq_cpy(v->el + 1, mat->row[1 + i], n_col);
    v = isl_vec_normalize(v);
    aff = isl_aff_alloc_vec(isl_local_space_copy(ls), v);
    ma = isl_multi_aff_set_aff(ma, i, aff);
  }

  isl_local_space_free(ls);
  isl_mat_free(mat);
  return ma;
error:
  isl_local_space_free(ls);
  isl_mat_free(mat);
  isl_multi_aff_free(ma);
  return NULL;
}

/* Remove any internal structure of the domain of "ma".
 * If there is any such internal structure in the input,
 * then the name of the corresponding space is also removed.
 */
__isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
  __isl_take isl_multi_aff *ma)
{
  isl_space *space;

  if (!ma)
    return NULL;

  if (!ma->space->nested[0])
    return ma;

  space = isl_multi_aff_get_space(ma);
  space = isl_space_flatten_domain(space);
  ma = isl_multi_aff_reset_space(ma, space);

  return ma;
}

/* Given a map space, return an isl_multi_aff that maps a wrapped copy
 * of the space to its domain.
 */
__isl_give isl_multi_aff *isl_multi_aff_domain_map(__isl_take isl_space *space)
{
  int i, n_in;
  isl_local_space *ls;
  isl_multi_aff *ma;

  if (!space)
    return NULL;
  if (!isl_space_is_map(space))
    isl_die0(isl_space_get_ctx(space), isl_error_invalid,
      "not a map space", goto error);

  n_in = isl_space_dim(space, isl_dim_in);
  space = isl_space_domain_map(space);

  ma = isl_multi_aff_alloc(isl_space_copy(space));
  if (n_in == 0) {
    isl_space_free(space);
    return ma;
  }

  space = isl_space_domain(space);
  ls = isl_local_space_from_space(space);
  for (i = 0; i < n_in; ++i1.13k) {
    isl_aff *aff;

    aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
            isl_dim_set, i);
    ma = isl_multi_aff_set_aff(ma, i, aff);
  }
  isl_local_space_free(ls);
  return ma;
error:
  isl_space_free(space);
  return NULL;
}

/* Given a map space, return an isl_multi_aff that maps a wrapped copy
 * of the space to its range.
 */
__isl_give isl_multi_aff *isl_multi_aff_range_map(__isl_take isl_space *space)
{
  int i, n_in, n_out;
  isl_local_space *ls;
  isl_multi_aff *ma;

  if (!space)
    return NULL;
  if (!isl_space_is_map(space))
    isl_die0(isl_space_get_ctx(space), isl_error_invalid,
      "not a map space", goto error);

  n_in = isl_space_dim(space, isl_dim_in);
  n_out = isl_space_dim(space, isl_dim_out);
  space = isl_space_range_map(space);

  ma = isl_multi_aff_alloc(isl_space_copy(space));
  if (n_out == 0) {
    isl_space_free(space);
    return ma;
  }

  space = isl_space_domain(space);
  ls = isl_local_space_from_space(space);
  for (i = 0; i < n_out; ++i32) {
    isl_aff *aff;

    aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
            isl_dim_set, n_in + i);
    ma = isl_multi_aff_set_aff(ma, i, aff);
  }
  isl_local_space_free(ls);
  return ma;
error:
  isl_space_free(space);
  return NULL;
}

/* Given a map space, return an isl_pw_multi_aff that maps a wrapped copy
 * of the space to its range.
 */
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
  __isl_take isl_space *space)
{
  return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_range_map(space));
}

/* Given the space of a set and a range of set dimensions,
 * construct an isl_multi_aff that projects out those dimensions.
 */
__isl_give isl_multi_aff *isl_multi_aff_project_out_map(
  __isl_take isl_space *space, enum isl_dim_type type,
  unsigned first, unsigned n)
{
  int i, dim;
  isl_local_space *ls;
  isl_multi_aff *ma;

  if (!space)
    return NULL;
  if (!isl_space_is_set(space))
    isl_die0(isl_space_get_ctx(space), isl_error_unsupported,
      "expecting set space", goto error);
  if (type != isl_dim_set)
    isl_die0(isl_space_get_ctx(space), isl_error_invalid,
      "only set dimensions can be projected out", goto error);

  dim = isl_space_dim(space, isl_dim_set);
  if (first + n > dim)
    isl_die0(isl_space_get_ctx(space), isl_error_invalid,
      "range out of bounds", goto error);

  space = isl_space_from_domain(space);
  space = isl_space_add_dims(space, isl_dim_out, dim - n);

  if (dim == n)
    return isl_multi_aff_alloc(space);

  ma = isl_multi_aff_alloc(isl_space_copy(space));
  space = isl_space_domain(space);
  ls = isl_local_space_from_space(space);

  for (i = 0; i < first; ++i3.35k) {
    isl_aff *aff;

    aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
            isl_dim_set, i);
    ma = isl_multi_aff_set_aff(ma, i, aff);
  }

  for (i = 0; i < dim - (first + n); ++i43) {
    isl_aff *aff;

    aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
            isl_dim_set, first + n + i);
    ma = isl_multi_aff_set_aff(ma, first + i, aff);
  }

  isl_local_space_free(ls);
  return ma;
error:
  isl_space_free(space);
  return NULL;
}

/* Given the space of a set and a range of set dimensions,
 * construct an isl_pw_multi_aff that projects out those dimensions.
 */
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_project_out_map(
  __isl_take isl_space *space, enum isl_dim_type type,
  unsigned first, unsigned n)
{
  isl_multi_aff *ma;

  ma = isl_multi_aff_project_out_map(space, type, first, n);
  return isl_pw_multi_aff_from_multi_aff(ma);
}

/* Create an isl_pw_multi_aff with the given isl_multi_aff on a universe
 * domain.
 */
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_multi_aff(
  __isl_take isl_multi_aff *ma)
{
  isl_set *dom = isl_set_universe(isl_multi_aff_get_domain_space(ma));
  return isl_pw_multi_aff_alloc(dom, ma);
}

/* Create a piecewise multi-affine expression in the given space that maps each
 * input dimension to the corresponding output dimension.
 */
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
  __isl_take isl_space *space)
{
  return isl_pw_multi_aff_from_multi_aff(isl_multi_aff_identity(space));
}

/* Exploit the equalities in "eq" to simplify the affine expressions.
 */
static __isl_give isl_multi_aff *isl_multi_aff_substitute_equalities(
  __isl_take isl_multi_aff *maff, __isl_take isl_basic_set *eq)
{
  int i;

  maff = isl_multi_aff_cow(maff);
  if (!maff || !eq)
    goto error;

  for (i = 0; 3.15ki < maff->n; ++i6.77k) {
    maff->u.p[i] = isl_aff_substitute_equalities(maff->u.p[i],
                isl_basic_set_copy(eq));
    if (!maff->u.p[i])
      goto error;
  }

  isl_basic_set_free(eq);
  return maff;
error:
  isl_basic_set_free(eq);
  isl_multi_aff_free(maff);
  return NULL;
}

__isl_give isl_multi_aff *isl_multi_aff_scale(__isl_take isl_multi_aff *maff,
  isl_int f)
{
  int i;

  maff = isl_multi_aff_cow(maff);
  if (!maff)
    return NULL;

  for (i = 0; i < maff->n; ++i) {
    maff->u.p[i] = isl_aff_scale(maff->u.p[i], f);
    if (!maff->u.p[i])
      return isl_multi_aff_free(maff);
  }

  return maff;
}

__isl_give isl_multi_aff *isl_multi_aff_add_on_domain(__isl_keep isl_set *dom,
  __isl_take isl_multi_aff *maff1, __isl_take isl_multi_aff *maff2)
{
  maff1 = isl_multi_aff_add(maff1, maff2);
  maff1 = isl_multi_aff_gist(maff1, isl_set_copy(dom));
  return maff1;
}

int isl_multi_aff_is_empty(__isl_keep isl_multi_aff *maff)
{
  if (!maff)
    return -1;

  return 0;
}

/* Return the set of domain elements where "ma1" is lexicographically
 * smaller than or equal to "ma2".
 */
__isl_give isl_set *isl_multi_aff_lex_le_set(__isl_take isl_multi_aff *ma1,
  __isl_take isl_multi_aff *ma2)
{
  return isl_multi_aff_lex_ge_set(ma2, ma1);
}

/* Return the set of domain elements where "ma1" is lexicographically
 * smaller than "ma2".
 */
__isl_give isl_set *isl_multi_aff_lex_lt_set(__isl_take isl_multi_aff *ma1,
  __isl_take isl_multi_aff *ma2)
{
  return isl_multi_aff_lex_gt_set(ma2, ma1);
}

/* Return the set of domain elements where "ma1" and "ma2"
 * satisfy "order".
 */
static __isl_give isl_set *isl_multi_aff_order_set(
  __isl_take isl_multi_aff *ma1, __isl_take isl_multi_aff *ma2,
  __isl_give isl_map *order(__isl_take isl_space *set_space))
{
  isl_space *space;
  isl_map *map1, *map2;
  isl_map *map, *ge;

  map1 = isl_map_from_multi_aff_internal(ma1);
  map2 = isl_map_from_multi_aff_internal(ma2);
  map = isl_map_range_product(map1, map2);
  space = isl_space_range(isl_map_get_space(map));
  space = isl_space_domain(isl_space_unwrap(space));
  ge = order(space);
  map = isl_map_intersect_range(map, isl_map_wrap(ge));

  return isl_map_domain(map);
}

/* Return the set of domain elements where "ma1" is lexicographically
 * greater than or equal to "ma2".
 */
__isl_give isl_set *isl_multi_aff_lex_ge_set(__isl_take isl_multi_aff *ma1,
  __isl_take isl_multi_aff *ma2)
{
  return isl_multi_aff_order_set(ma1, ma2, &isl_map_lex_ge);
}

/* Return the set of domain elements where "ma1" is lexicographically
 * greater than "ma2".
 */
__isl_give isl_set *isl_multi_aff_lex_gt_set(__isl_take isl_multi_aff *ma1,
  __isl_take isl_multi_aff *ma2)
{
  return isl_multi_aff_order_set(ma1, ma2, &isl_map_lex_gt);
}

#undef PW
#define PW isl_pw_multi_aff
#undef EL
#define EL isl_multi_aff
#undef EL_IS_ZERO
#define EL_IS_ZERO is_empty
#undef ZERO
#define ZERO empty
#undef IS_ZERO
#define IS_ZERO is_empty
#undef FIELD
#define FIELD maff
#undef DEFAULT_IS_ZERO
#define DEFAULT_IS_ZERO 0

#define NO_SUB
#define NO_OPT
#define NO_INSERT_DIMS
#define NO_LIFT
#define NO_MORPH

#include <isl_pw_templ.c>
#include <isl_pw_union_opt.c>

#undef NO_SUB

#undef BASE
#define BASE pw_multi_aff

#include <isl_union_multi.c>
#include <isl_union_neg.c>

static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmax(
  __isl_take isl_pw_multi_aff *pma1,
  __isl_take isl_pw_multi_aff *pma2)
{
  return isl_pw_multi_aff_union_opt_cmp(pma1, pma2,
              &isl_multi_aff_lex_ge_set);
}

/* Given two piecewise multi affine expressions, return a piecewise
 * multi-affine expression defined on the union of the definition domains
 * of the inputs that is equal to the lexicographic maximum of the two
 * inputs on each cell.  If only one of the two inputs is defined on
 * a given cell, then it is considered to be the maximum.
 */
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
  __isl_take isl_pw_multi_aff *pma1,
  __isl_take isl_pw_multi_aff *pma2)
{
  return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
                &pw_multi_aff_union_lexmax);
}

static __isl_give isl_pw_multi_aff *pw_multi_aff_union_lexmin(
  __isl_take isl_pw_multi_aff *pma1,
  __isl_take isl_pw_multi_aff *pma2)
{
  return isl_pw_multi_aff_union_opt_cmp(pma1, pma2,
              &isl_multi_aff_lex_le_set);
}

/* Given two piecewise multi affine expressions, return a piecewise
 * multi-affine expression defined on the union of the definition domains
 * of the inputs that is equal to the lexicographic minimum of the two
 * inputs on each cell.  If only one of the two inputs is defined on
 * a given cell, then it is considered to be the minimum.
 */
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
  __isl_take isl_pw_multi_aff *pma1,
  __isl_take isl_pw_multi_aff *pma2)
{
  return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
                &pw_multi_aff_union_lexmin);
}

static __isl_give isl_pw_multi_aff *pw_multi_aff_add(
  __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
{
  return isl_pw_multi_aff_on_shared_domain(pma1, pma2,
            &isl_multi_aff_add);
}

__isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
  __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
{
  return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
            &pw_multi_aff_add);
}

static __isl_give isl_pw_multi_aff *pw_multi_aff_sub(
  __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
{
  return isl_pw_multi_aff_on_shared_domain(pma1, pma2,
            &isl_multi_aff_sub);
}

/* Subtract "pma2" from "pma1" and return the result.
 */
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
  __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
{
  return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
            &pw_multi_aff_sub);
}

__isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
  __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
{
  return isl_pw_multi_aff_union_add_(pma1, pma2);
}

/* Compute the sum of "upa1" and "upa2" 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.
 */
__isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
  __isl_take isl_union_pw_aff *upa1, __isl_take isl_union_pw_aff *upa2)
{
  return isl_union_pw_aff_union_add_(upa1, upa2);
}

/* Compute the sum of "upma1" and "upma2" 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.
 */
__isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_union_add(
  __isl_take isl_union_pw_multi_aff *upma1,
  __isl_take isl_union_pw_multi_aff *upma2)
{
  return isl_union_pw_multi_aff_union_add_(upma1, upma2);
}

/* Given two piecewise multi-affine expressions A -> B and C -> D,
 * construct a piecewise multi-affine expression [A -> C] -> [B -> D].
 */
static __isl_give isl_pw_multi_aff *pw_multi_aff_product(
  __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
{
  int i, j, n;
  isl_space *space;
  isl_pw_multi_aff *res;

  if (!pma1 || !pma2)
    goto error;

  n = pma1->n * pma2->n;
  space = isl_space_product(isl_space_copy(pma1->dim),
          isl_space_copy(pma2->dim));
  res = isl_pw_multi_aff_alloc_size(space, n);

  for (i = 0; i < pma1->n; ++i2) {
    for (j = 0; j < pma2->n; ++j2) {
      isl_set *domain;
      isl_multi_aff *ma;

      domain = isl_set_product(isl_set_copy(pma1->p[i].set),
             isl_set_copy(pma2->p[j].set));
      ma = isl_multi_aff_product(
          isl_multi_aff_copy(pma1->p[i].maff),
          isl_multi_aff_copy(pma2->p[j].maff));
      res = isl_pw_multi_aff_add_piece(res, domain, ma);
    }
  }

  isl_pw_multi_aff_free(pma1);
  isl_pw_multi_aff_free(pma2);
  return res;
error:
  isl_pw_multi_aff_free(pma1);
  isl_pw_multi_aff_free(pma2);
  return NULL;
}

__isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
  __isl_take isl_pw_multi_aff *pma1, __isl_take isl_pw_multi_aff *pma2)
{
  return isl_pw_multi_aff_align_params_pw_pw_and(pma1, pma2,
            &pw_multi_aff_product);
}

/* Subtract the initial "n" elements in "ma" with coefficients in "c" and
 * denominator "denom".
 * "denom" is allowed to be negative, in which case the actual denominator
 * is -denom and the expressions are added instead.
 */
static __isl_give isl_aff *subtract_initial(__isl_take isl_aff *aff,
  __isl_keep isl_multi_aff *ma, int n, isl_int *c, isl_int denom)
{
  int i, first;
  int sign;
  isl_int d;

  first = isl_seq_first_non_zero(c, n);
  if (first == -1)
    return aff;

  sign = isl_int_sgn(denom);
  isl_int_init(d);
  isl_int_abs(d, denom);
  for (i = first; i < n; ++i3) {
    isl_aff *aff_i;

    if (isl_int_is_zero(c[i]))
      continue0;
    aff_i = isl_multi_aff_get_aff(ma, i);
    aff_i = isl_aff_scale(aff_i, c[i]);
    aff_i = isl_aff_scale_down(aff_i, d);
    if (sign >= 0)
      aff = isl_aff_sub(aff, aff_i);
    else
      aff = isl_aff_add(aff, aff_i);
  }
  isl_int_clear(d);

  return aff;
}

/* Extract an affine expression that expresses the output dimension "pos"
 * of "bmap" in terms of the parameters and input dimensions from
 * equality "eq".
 * Note that this expression may involve integer divisions defined
 * in terms of parameters and input dimensions.
 * The equality may also involve references to earlier (but not later)
 * output dimensions.  These are replaced by the corresponding elements
 * in "ma".
 *
 * If the equality is of the form
 *
 *  f(i) + h(j) + a x + g(i) = 0,
 *
 * with f(i) a linear combinations of the parameters and input dimensions,
 * g(i) a linear combination of integer divisions defined in terms of the same
 * and h(j) a linear combinations of earlier output dimensions,
 * then the affine expression is
 *
 *  (-f(i) - g(i))/a - h(j)/a
 *
 * If the equality is of the form
 *
 *  f(i) + h(j) - a x + g(i) = 0,
 *
 * then the affine expression is
 *
 *  (f(i) + g(i))/a - h(j)/(-a)
 *
 *
 * If "div" refers to an integer division (i.e., it is smaller than
 * the number of integer divisions), then the equality constraint
 * does involve an integer division (the one at position "div") that
 * is defined in terms of output dimensions.  However, this integer
 * division can be eliminated by exploiting a pair of constraints
 * x >= l and x <= l + n, with n smaller than the coefficient of "div"
 * in the equality constraint.  "ineq" refers to inequality x >= l, i.e.,
 * -l + x >= 0.
 * In particular, let
 *
 *  x = e(i) + m floor(...)
 *
 * with e(i) the expression derived above and floor(...) the integer
 * division involving output dimensions.
 * From
 *
 *  l <= x <= l + n,
 *
 * we have
 *
 *  0 <= x - l <= n
 *
 * This means
 *
 *  e(i) + m floor(...) - l = (e(i) + m floor(...) - l) mod m
 *                          = (e(i) - l) mod m
 *
 * Therefore,
 *
 *  x - l = (e(i) - l) mod m
 *
 * or
 *
 *  x = ((e(i) - l) mod m) + l
 *
 * The variable "shift" below contains the expression -l, which may
 * also involve a linear combination of earlier output dimensions.
 */
static __isl_give isl_aff *extract_aff_from_equality(
  __isl_keep isl_basic_map *bmap, int pos, int eq, int div, int ineq,
  __isl_keep isl_multi_aff *ma)
{
  unsigned o_out;
  unsigned n_div, n_out;
  isl_ctx *ctx;
  isl_local_space *ls;
  isl_aff *aff, *shift;
  isl_val *mod;

  ctx = isl_basic_map_get_ctx(bmap);
  ls = isl_basic_map_get_local_space(bmap);
  ls = isl_local_space_domain(ls);
  aff = isl_aff_alloc(isl_local_space_copy(ls));
  if (!aff)
    goto error;
  o_out = isl_basic_map_offset(bmap, isl_dim_out);
  n_out = isl_basic_map_dim(bmap, isl_dim_out);
  n_div = isl_basic_map_dim(bmap, isl_dim_div);
  if (isl_int_is_neg(bmap->eq[eq][o_out + pos])) {
    isl_seq_cpy(aff->v->el + 1, bmap->eq[eq], o_out);
    isl_seq_cpy(aff->v->el + 1 + o_out,
          bmap->eq[eq] + o_out + n_out, n_div);
  } else {
    isl_seq_neg(aff->v->el + 1, bmap->eq[eq], o_out);
    isl_seq_neg(aff->v->el + 1 + o_out,
          bmap->eq[eq] + o_out + n_out, n_div);
  }
  if (div < n_div)
    isl_int_set_si101(aff->v->el[1 + o_out + div], 0);
  isl_int_abs(aff->v->el[0], bmap->eq[eq][o_out + pos]);
  aff = subtract_initial(aff, ma, pos, bmap->eq[eq] + o_out,
          bmap->eq[eq][o_out + pos]);
  if (div < n_div) {
    shift = isl_aff_alloc(isl_local_space_copy(ls));
    if (!shift)
      goto error;
    isl_seq_cpy(shift->v->el + 1, bmap->ineq[ineq], o_out);
    isl_seq_cpy(shift->v->el + 1 + o_out,
          bmap->ineq[ineq] + o_out + n_out, n_div);
    isl_int_set_si(shift->v->el[0], 1);
    shift = subtract_initial(shift, ma, pos,
          bmap->ineq[ineq] + o_out, ctx->negone);
    aff = isl_aff_add(aff, isl_aff_copy(shift));
    mod = isl_val_int_from_isl_int(ctx,
              bmap->eq[eq][o_out + n_out + div]);
    mod = isl_val_abs(mod);
    aff = isl_aff_mod_val(aff, mod);
    aff = isl_aff_sub(aff, shift);
  }

  isl_local_space_free(ls);
  return aff;
error:
  isl_local_space_free(ls);
  isl_aff_free(aff);
  return NULL;
}

/* Given a basic map with output dimensions defined
 * in terms of the parameters input dimensions and earlier
 * output dimensions using an equality (and possibly a pair on inequalities),
 * extract an isl_aff that expresses output dimension "pos" in terms
 * of the parameters and input dimensions.
 * Note that this expression may involve integer divisions defined
 * in terms of parameters and input dimensions.
 * "ma" contains the expressions corresponding to earlier output dimensions.
 *
 * This function shares some similarities with
 * isl_basic_map_has_defining_equality and isl_constraint_get_bound.
 */
static __isl_give isl_aff *extract_isl_aff_from_basic_map(
  __isl_keep isl_basic_map *bmap, int pos, __isl_keep isl_multi_aff *ma)
{
  int eq, div, ineq;
  isl_aff *aff;

  if (!bmap)
    return NULL;
  eq = isl_basic_map_output_defining_equality(bmap, pos, &div, &ineq);
  if (eq >= bmap->n_eq)
    isl_die0(isl_basic_map_get_ctx(bmap), isl_error_invalid,
      "unable to find suitable equality", return NULL);
  aff = extract_aff_from_equality(bmap, pos, eq, div, ineq, ma);

  aff = isl_aff_remove_unused_divs(aff);
  return aff;
}

/* Given a basic map where each output dimension is defined
 * in terms of the parameters and input dimensions using an equality,
 * extract an isl_multi_aff that expresses the output dimensions in terms
 * of the parameters and input dimensions.
 */
static __isl_give isl_multi_aff *extract_isl_multi_aff_from_basic_map(
  __isl_take isl_basic_map *bmap)
{
  int i;
  unsigned n_out;
  isl_multi_aff *ma;

  if (!bmap)
    return NULL;

  ma = isl_multi_aff_alloc(isl_basic_map_get_space(bmap));
  n_out = isl_basic_map_dim(bmap, isl_dim_out);

  for (i = 0; i < n_out; ++i10.5k) {
    isl_aff *aff;

    aff = extract_isl_aff_from_basic_map(bmap, i, ma);
    ma = isl_multi_aff_set_aff(ma, i, aff);
  }

  isl_basic_map_free(bmap);

  return ma;
}

/* Given a basic set where each set dimension is defined
 * in terms of the parameters using an equality,
 * extract an isl_multi_aff that expresses the set dimensions in terms
 * of the parameters.
 */
__isl_give isl_multi_aff *isl_multi_aff_from_basic_set_equalities(
  __isl_take isl_basic_set *bset)
{
  return extract_isl_multi_aff_from_basic_map(bset);
}

/* Create an isl_pw_multi_aff that is equivalent to
 * isl_map_intersect_domain(isl_map_from_basic_map(bmap), domain).
 * The given basic map is such that each output dimension is defined
 * in terms of the parameters and input dimensions using an equality.
 *
 * Since some applications expect the result of isl_pw_multi_aff_from_map
 * to only contain integer affine expressions, we compute the floor
 * of the expression before returning.
 *
 * Remove all constraints involving local variables without
 * an explicit representation (resulting in the removal of those
 * local variables) prior to the actual extraction to ensure
 * that the local spaces in which the resulting affine expressions
 * are created do not contain any unknown local variables.
 * Removing such constraints is safe because constraints involving
 * unknown local variables are not used to determine whether
 * a basic map is obviously single-valued.
 */
static __isl_give isl_pw_multi_aff *plain_pw_multi_aff_from_map(
  __isl_take isl_set *domain, __isl_take isl_basic_map *bmap)
{
  isl_multi_aff *ma;

  bmap = isl_basic_map_drop_constraint_involving_unknown_divs(bmap);
  ma = extract_isl_multi_aff_from_basic_map(bmap);
  ma = isl_multi_aff_floor(ma);
  return isl_pw_multi_aff_alloc(domain, ma);
}

/* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
 * This obviously only works if the input "map" is single-valued.
 * If so, we compute the lexicographic minimum of the image in the form
 * of an isl_pw_multi_aff.  Since the image is unique, it is equal
 * to its lexicographic minimum.
 * If the input is not single-valued, we produce an error.
 */
static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_base(
  __isl_take isl_map *map)
{
  int i;
  int sv;
  isl_pw_multi_aff *pma;

  sv = isl_map_is_single_valued(map);
  if (sv < 0)
    goto error;
  if (!sv)
    isl_die0(isl_map_get_ctx(map), isl_error_invalid,
      "map is not single-valued", goto error);
  map = isl_map_make_disjoint(map);
  if (!map)
    return NULL;

  pma = isl_pw_multi_aff_empty(isl_map_get_space(map));

  for (i = 0; i < map->n; ++i76) {
    isl_pw_multi_aff *pma_i;
    isl_basic_map *bmap;
    bmap = isl_basic_map_copy(map->p[i]);
    pma_i = isl_basic_map_lexmin_pw_multi_aff(bmap);
    pma = isl_pw_multi_aff_add_disjoint(pma, pma_i);
  }

  isl_map_free(map);
  return pma;
error:
  isl_map_free(map);
  return NULL;
}

/* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map,
 * taking into account that the output dimension at position "d"
 * can be represented as
 *
 *  x = floor((e(...) + c1) / m)
 *
 * given that constraint "i" is of the form
 *
 *  e(...) + c1 - m x >= 0
 *
 *
 * Let "map" be of the form
 *
 *  A -> B
 *
 * We construct a mapping
 *
 *  A -> [A -> x = floor(...)]
 *
 * apply that to the map, obtaining
 *
 *  [A -> x = floor(...)] -> B
 *
 * and equate dimension "d" to x.
 * We then compute a isl_pw_multi_aff representation of the resulting map
 * and plug in the mapping above.
 */
static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_div(
  __isl_take isl_map *map, __isl_take isl_basic_map *hull, int d, int i)
{
  isl_ctx *ctx;
  isl_space *space;
  isl_local_space *ls;
  isl_multi_aff *ma;
  isl_aff *aff;
  isl_vec *v;
  isl_map *insert;
  int offset;
  int n;
  int n_in;
  isl_pw_multi_aff *pma;
  isl_bool is_set;

  is_set = isl_map_is_set(map);
  if (is_set < 0)
    goto error;

  offset = isl_basic_map_offset(hull, isl_dim_out);
  ctx = isl_map_get_ctx(map);
  space = isl_space_domain(isl_map_get_space(map));
  n_in = isl_space_dim(space, isl_dim_set);
  n = isl_space_dim(space, isl_dim_all);

  v = isl_vec_alloc(ctx, 1 + 1 + n);
  if (v) {
    isl_int_neg(v->el[0], hull->ineq[i][offset + d]);
    isl_seq_cpy(v->el + 1, hull->ineq[i], 1 + n);
  }
  isl_basic_map_free(hull);

  ls = isl_local_space_from_space(isl_space_copy(space));
  aff = isl_aff_alloc_vec(ls, v);
  aff = isl_aff_floor(aff);
  if (is_set) {
    isl_space_free(space);
    ma = isl_multi_aff_from_aff(aff);
  } else {
    ma = isl_multi_aff_identity(isl_space_map_from_set(space));
    ma = isl_multi_aff_range_product(ma,
            isl_multi_aff_from_aff(aff));
  }

  insert = isl_map_from_multi_aff_internal(isl_multi_aff_copy(ma));
  map = isl_map_apply_domain(map, insert);
  map = isl_map_equate(map, isl_dim_in, n_in, isl_dim_out, d);
  pma = isl_pw_multi_aff_from_map(map);
  pma = isl_pw_multi_aff_pullback_multi_aff(pma, ma);

  return pma;
error:
  isl_map_free(map);
  isl_basic_map_free(hull);
  return NULL;
}

/* Is constraint "c" of the form
 *
 *  e(...) + c1 - m x >= 0
 *
 * or
 *
 *  -e(...) + c2 + m x >= 0
 *
 * where m > 1 and e only depends on parameters and input dimemnsions?
 *
 * "offset" is the offset of the output dimensions
 * "pos" is the position of output dimension x.
 */
static int is_potential_div_constraint(isl_int *c, int offset, int d, int total)
{
  if (isl_int_is_zero(c[offset + d]))
    return 01.05k;
  if (isl_int_is_one(c[offset + d]))
    return 018;
  if (isl_int_is_negone(c[offset + d]))
    return 010;
  if (isl_seq_first_non_zero(c + offset, d) != -1)
    return 0;
  if (isl_seq_first_non_zero(c + offset + d + 1,
            total - (offset + d + 1)) != -1)
    return 0;
  return 1;
}

/* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
 *
 * As a special case, we first check if there is any pair of constraints,
 * shared by all the basic maps in "map" that force a given dimension
 * to be equal to the floor of some affine combination of the input dimensions.
 *
 * In particular, if we can find two constraints
 *
 *  e(...) + c1 - m x >= 0    i.e.,   m x <= e(...) + c1
 *
 * and
 *
 *  -e(...) + c2 + m x >= 0   i.e.,   m x >= e(...) - c2
 *
 * where m > 1 and e only depends on parameters and input dimemnsions,
 * and such that
 *
 *  c1 + c2 < m     i.e.,   -c2 >= c1 - (m - 1)
 *
 * then we know that we can take
 *
 *  x = floor((e(...) + c1) / m)
 *
 * without having to perform any computation.
 *
 * Note that we know that
 *
 *  c1 + c2 >= 1
 *
 * If c1 + c2 were 0, then we would have detected an equality during
 * simplification.  If c1 + c2 were negative, then we would have detected
 * a contradiction.
 */
static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_check_div(
  __isl_take isl_map *map)
{
  int d, dim;
  int i, j, n;
  int offset, total;
  isl_int sum;
  isl_basic_map *hull;

  hull = isl_map_unshifted_simple_hull(isl_map_copy(map));
  if (!hull)
    goto error;

  isl_int_init(sum);
  dim = isl_map_dim(map, isl_dim_out);
  offset = isl_basic_map_offset(hull, isl_dim_out);
  total = 1 + isl_basic_map_total_dim(hull);
  n = hull->n_ineq;
  for (d = 0; d < dim; ++d147) {
    for (i = 0; i < n; ++i1.17k) {
      if (!is_potential_div_constraint(hull->ineq[i],
              offset, d, total))
        continue;
      for (j = i + 1; 104j < n; ++j18) {
        if (!isl_seq_is_neg(hull->ineq[i] + 1,
            hull->ineq[j] + 1, total - 1))
          continue;
        isl_int_add(sum, hull->ineq[i][0],
            hull->ineq[j][0]);
        if (isl_int_abs_lt(sum,
                hull->ineq[i][offset + d]))
          break;

      }
      if (j >= n)
        continue;
      isl_int_clear(sum);
      if (isl_int_is_pos(hull->ineq[j][offset + d]))
        j = i73;
      return pw_multi_aff_from_map_div(map, hull, d, j);
    }
  }
  isl_int_clear31(sum);
  isl_basic_map_free(hull);
  return pw_multi_aff_from_map_base(map);
error:
  isl_map_free(map);
  isl_basic_map_free(hull);
  return NULL;
}

/* Given an affine expression
 *
 *  [A -> B] -> f(A,B)
 *
 * construct an isl_multi_aff
 *
 *  [A -> B] -> B'
 *
 * such that dimension "d" in B' is set to "aff" and the remaining
 * dimensions are set equal to the corresponding dimensions in B.
 * "n_in" is the dimension of the space A.
 * "n_out" is the dimension of the space B.
 *
 * If "is_set" is set, then the affine expression is of the form
 *
 *  [B] -> f(B)
 *
 * and we construct an isl_multi_aff
 *
 *  B -> B'
 */
static __isl_give isl_multi_aff *range_map(__isl_take isl_aff *aff, int d,
  unsigned n_in, unsigned n_out, int is_set)
{
  int i;
  isl_multi_aff *ma;
  isl_space *space, *space2;
  isl_local_space *ls;

  space = isl_aff_get_domain_space(aff);
  ls = isl_local_space_from_space(isl_space_copy(space));
  space2 = isl_space_copy(space);
  if (!is_set)
    space2 = isl_space_range(isl_space_unwrap(space2));
  space = isl_space_map_from_domain_and_range(space, space2);
  ma = isl_multi_aff_alloc(space);
  ma = isl_multi_aff_set_aff(ma, d, aff);

  for (i = 0; i < n_out; ++i60) {
    if (i == d)
      continue;
    aff = isl_aff_var_on_domain(isl_local_space_copy(ls),
            isl_dim_set, n_in + i);
    ma = isl_multi_aff_set_aff(ma, i, aff);
  }

  isl_local_space_free(ls);

  return ma;
}

/* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map,
 * taking into account that the dimension at position "d" can be written as
 *
 *  x = m a + f(..)           (1)
 *
 * where m is equal to "gcd".
 * "i" is the index of the equality in "hull" that defines f(..).
 * In particular, the equality is of the form
 *
 *  f(..) - x + m g(existentials) = 0
 *
 * or
 *
 *  -f(..) + x + m g(existentials) = 0
 *
 * We basically plug (1) into "map", resulting in a map with "a"
 * in the range instead of "x".  The corresponding isl_pw_multi_aff
 * defining "a" is then plugged back into (1) to obtain a definition for "x".
 *
 * Specifically, given the input map
 *
 *  A -> B
 *
 * We first wrap it into a set
 *
 *  [A -> B]
 *
 * and define (1) on top of the corresponding space, resulting in "aff".
 * We use this to create an isl_multi_aff that maps the output position "d"
 * from "a" to "x", leaving all other (intput and output) dimensions unchanged.
 * We plug this into the wrapped map, unwrap the result and compute the
 * corresponding isl_pw_multi_aff.
 * The result is an expression
 *
 *  A -> T(A)
 *
 * We adjust that to
 *
 *  A -> [A -> T(A)]
 *
 * so that we can plug that into "aff", after extending the latter to
 * a mapping
 *
 *  [A -> B] -> B'
 *
 *
 * If "map" is actually a set, then there is no "A" space, meaning
 * that we do not need to perform any wrapping, and that the result
 * of the recursive call is of the form
 *
 *  [T]
 *
 * which is plugged into a mapping of the form
 *
 *  B -> B'
 */
static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_stride(
  __isl_take isl_map *map, __isl_take isl_basic_map *hull, int d, int i,
  isl_int gcd)
{
  isl_set *set;
  isl_space *space;
  isl_local_space *ls;
  isl_aff *aff;
  isl_multi_aff *ma;
  isl_pw_multi_aff *pma, *id;
  unsigned n_in;
  unsigned o_out;
  unsigned n_out;
  isl_bool is_set;

  is_set = isl_map_is_set(map);
  if (is_set < 0)
    goto error;

  n_in = isl_basic_map_dim(hull, isl_dim_in);
  n_out = isl_basic_map_dim(hull, isl_dim_out);
  o_out = isl_basic_map_offset(hull, isl_dim_out);

  if (is_set)
    set = map;
  else
    set = isl_map_wrap(map);
  space = isl_space_map_from_set(isl_set_get_space(set));
  ma = isl_multi_aff_identity(space);
  ls = isl_local_space_from_space(isl_set_get_space(set));
  aff = isl_aff_alloc(ls);
  if (aff) {
    isl_int_set_si(aff->v->el[0], 1);
    if (isl_int_is_one(hull->eq[i][o_out + d]))
      isl_seq_neg(aff->v->el + 1, hull->eq[i],
            aff->v->size - 1);
    else
      isl_seq_cpy(aff->v->el + 1, hull->eq[i],
            aff->v->size - 1);
    isl_int_set(aff->v->el[1 + o_out + d], gcd);
  }
  ma = isl_multi_aff_set_aff(ma, n_in + d, isl_aff_copy(aff));
  set = isl_set_preimage_multi_aff(set, ma);

  ma = range_map(aff, d, n_in, n_out, is_set);

  if (is_set)
    map = set;
  else
    map = isl_set_unwrap(set);
  pma = isl_pw_multi_aff_from_map(map);

  if (!is_set) {
    space = isl_pw_multi_aff_get_domain_space(pma);
    space = isl_space_map_from_set(space);
    id = isl_pw_multi_aff_identity(space);
    pma = isl_pw_multi_aff_range_product(id, pma);
  }
  id = isl_pw_multi_aff_from_multi_aff(ma);
  pma = isl_pw_multi_aff_pullback_pw_multi_aff(id, pma);

  isl_basic_map_free(hull);
  return pma;
error:
  isl_map_free(map);
  isl_basic_map_free(hull);
  return NULL;
}

/* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
 * "hull" contains the equalities valid for "map".
 *
 * Check if any of the output dimensions is "strided".
 * That is, we check if it can be written as
 *
 *  x = m a + f(..)
 *
 * with m greater than 1, a some combination of existentially quantified
 * variables and f an expression in the parameters and input dimensions.
 * If so, we remove the stride in pw_multi_aff_from_map_stride.
 *
 * Otherwise, we continue with pw_multi_aff_from_map_check_div for a further
 * special case.
 */
static __isl_give isl_pw_multi_aff *pw_multi_aff_from_map_check_strides(
  __isl_take isl_map *map, __isl_take isl_basic_map *hull)
{
  int i, j;
  unsigned n_out;
  unsigned o_out;
  unsigned n_div;
  unsigned o_div;
  isl_int gcd;

  n_div = isl_basic_map_dim(hull, isl_dim_div);
  o_div = isl_basic_map_offset(hull, isl_dim_div);

  if (n_div == 0) {
    isl_basic_map_free(hull);
    return pw_multi_aff_from_map_check_div(map);
  }

  isl_int_init(gcd);

  n_out = isl_basic_map_dim(hull, isl_dim_out);
  o_out = isl_basic_map_offset(hull, isl_dim_out);

  for (i = 0; i < n_out; ++i132) {
    for (j = 0; j < hull->n_eq; ++j201) {
      isl_int *eq = hull->eq[j];
      isl_pw_multi_aff *res;

      if (!isl_int_is_one(eq[o_out + i]) &&
          !186isl_int_is_negone186(eq[o_out + i]))
        continue168;
      if (isl_seq_first_non_zero(eq + o_out, i) != -1)
        continue;
      if (isl_seq_first_non_zero(eq + o_out + i + 1,
                n_out - (i + 1)) != -1)
        continue;
      isl_seq_gcd(eq + o_div, n_div, &gcd);
      if (isl_int_is_zero(gcd))
        continue33;
      if (isl_int_is_one(gcd))
        continue0;

      res = pw_multi_aff_from_map_stride(map, hull,
                i, j, gcd);
      isl_int_clear(gcd);
      return res;
    }
  }

  isl_int_clear33(gcd);
  isl_basic_map_free(hull);
  return pw_multi_aff_from_map_check_div(map);
}

/* Try and create an isl_pw_multi_aff that is equivalent to the given isl_map.
 *
 * As a special case, we first check if all output dimensions are uniquely
 * defined in terms of the parameters and input dimensions over the entire
 * domain.  If so, we extract the desired isl_pw_multi_aff directly
 * from the affine hull of "map" and its domain.
 *
 * Otherwise, continue with pw_multi_aff_from_map_check_strides for more
 * special cases.
 */
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(__isl_take isl_map *map)
{
  isl_bool sv;
  isl_basic_map *hull;

  if (!map)
    return NULL;

  if (isl_map_n_basic_map(map) == 1) {
    hull = isl_map_unshifted_simple_hull(isl_map_copy(map));
    hull = isl_basic_map_plain_affine_hull(hull);
    sv = isl_basic_map_plain_is_single_valued(hull);
    if (sv >= 0 && sv)
      return plain_pw_multi_aff_from_map(isl_map_domain(map),
                  hull);
    isl_basic_map_free(hull);
  }
  map = isl_map_detect_equalities(map);
  hull = isl_map_unshifted_simple_hull(isl_map_copy(map));
  sv = isl_basic_map_plain_is_single_valued(hull);
  if (sv >= 0 && sv)
    return plain_pw_multi_aff_from_map(isl_map_domain(map), hull);
  if (sv >= 0)
    return pw_multi_aff_from_map_check_strides(map, hull);
  isl_basic_map_free(hull);
  isl_map_free(map);
  return NULL;
}

__isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(__isl_take isl_set *set)
{
  return isl_pw_multi_aff_from_map(set);
}

/* Convert "map" into an isl_pw_multi_aff (if possible) and
 * add it to *user.
 */
static isl_stat pw_multi_aff_from_map(__isl_take isl_map *map, void *user)
{
  isl_union_pw_multi_aff **upma = user;
  isl_pw_multi_aff *pma;

  pma = isl_pw_multi_aff_from_map(map);
  *upma = isl_union_pw_multi_aff_add_pw_multi_aff(*upma, pma);

  return *upma ? isl_stat_ok : isl_stat_error0;
}

/* Create an isl_union_pw_multi_aff with the given isl_aff on a universe
 * domain.
 */
__isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_aff(
  __isl_take isl_aff *aff)
{
  isl_multi_aff *ma;
  isl_pw_multi_aff *pma;

  ma = isl_multi_aff_from_aff(aff);
  pma = isl_pw_multi_aff_from_multi_aff(ma);
  return isl_union_pw_multi_aff_from_pw_multi_aff(pma);
}

/* Try and create an isl_union_pw_multi_aff that is equivalent
 * to the given isl_union_map.
 * The isl_union_map is required to be single-valued in each space.
 * Otherwise, an error is produced.
 */
__isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_union_map(
  __isl_take isl_union_map *umap)
{
  isl_space *space;
  isl_union_pw_multi_aff *upma;

  space = isl_union_map_get_space(umap);
  upma = isl_union_pw_multi_aff_empty(space);
  if (isl_union_map_foreach_map(umap, &pw_multi_aff_from_map, &upma) < 0)
    upma = isl_union_pw_multi_aff_free(upma);
  isl_union_map_free(umap);

  return upma;
}

/* Try and create an isl_union_pw_multi_aff that is equivalent
 * to the given isl_union_set.
 * The isl_union_set is required to be a singleton in each space.
 * Otherwise, an error is produced.
 */
__isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_from_union_set(
  __isl_take isl_union_set *uset)
{
  return isl_union_pw_multi_aff_from_union_map(uset);
}

/* Return the piecewise affine expression "set ? 1 : 0".
 */
__isl_give isl_pw_aff *isl_set_indicator_function(__isl_take isl_set *set)
{
  isl_pw_aff *pa;
  isl_space *space = isl_set_get_space(set);
  isl_local_space *ls = isl_local_space_from_space(space);
  isl_aff *zero = isl_aff_zero_on_domain(isl_local_space_copy(ls));
  isl_aff *one = isl_aff_zero_on_domain(ls);

  one = isl_aff_add_constant_si(one, 1);
  pa = isl_pw_aff_alloc(isl_set_copy(set), one);
  set = isl_set_complement(set);
  pa = isl_pw_aff_add_disjoint(pa, isl_pw_aff_alloc(set, zero));

  return pa;
}

/* Plug in "subs" for dimension "type", "pos" of "aff".
 *
 * Let i be the dimension to replace and let "subs" be of the form
 *
 *  f/d
 *
 * and "aff" of the form
 *
 *  (a i + g)/m
 *
 * The result is
 *
 *  (a f + d g')/(m d)
 *
 * where g' is the result of plugging in "subs" in each of the integer
 * divisions in g.
 */
__isl_give isl_aff *isl_aff_substitute(__isl_take isl_aff *aff,
  enum isl_dim_type type, unsigned pos, __isl_keep isl_aff *subs)
{
  isl_ctx *ctx;
  isl_int v;

  aff = isl_aff_cow(aff);
  if (!aff || !subs)
    return isl_aff_free(aff);

  ctx = isl_aff_get_ctx(aff);
  if (!isl_space_is_equal(aff->ls->dim, subs->ls->dim))
    isl_die0(ctx, isl_error_invalid,
      "spaces don't match", return isl_aff_free(aff));
  if (isl_local_space_dim(subs->ls, isl_dim_div) != 0)
    isl_die0(ctx, isl_error_unsupported,
      "cannot handle divs yet", return isl_aff_free(aff));

  aff->ls = isl_local_space_substitute(aff->ls, type, pos, subs);
  if (!aff->ls)
    return isl_aff_free(aff);

  aff->v = isl_vec_cow(aff->v);
  if (!aff->v)
    return isl_aff_free(aff);

  pos += isl_local_space_offset(aff->ls, type);

  isl_int_init(v);
  isl_seq_substitute(aff->v->el, pos, subs->v->el,
          aff->v->size, subs->v->size, v);
  isl_int_clear(v);

  return aff;
}

/* Plug in "subs" for dimension "type", "pos" in each of the affine
 * expressions in "maff".
 */
__isl_give isl_multi_aff *isl_multi_aff_substitute(
  __isl_take isl_multi_aff *maff, enum isl_dim_type type, unsigned pos,
  __isl_keep isl_aff *subs)
{
  int i;

  maff = isl_multi_aff_cow(maff);
  if (!maff || !subs)
    return isl_multi_aff_free(maff);

  if (type == isl_dim_in)
    type = isl_dim_set;

  for (i = 0; i < maff->n; ++i1.20k) {
    maff->u.p[i] = isl_aff_substitute(maff->u.p[i],
            type, pos, subs);
    if (!maff->u.p[i])
      return isl_multi_aff_free(maff);
  }

  return maff;
}

/* Plug in "subs" for dimension "type", "pos" of "pma".
 *
 * pma is of the form
 *
 *  A_i(v) -> M_i(v)
 *
 * while subs is of the form
 *
 *  v' = B_j(v) -> S_j
 *
 * Each pair i,j such that C_ij = A_i \cap B_i is non-empty
 * has a contribution in the result, in particular
 *
 *  C_ij(S_j) -> M_i(S_j)
 *
 * Note that plugging in S_j in C_ij may also result in an empty set
 * and this contribution should simply be discarded.
 */
__isl_give isl_pw_multi_aff *isl_pw_multi_aff_substitute(
  __isl_take isl_pw_multi_aff *pma, enum isl_dim_type type, unsigned pos,
  __isl_keep isl_pw_aff *subs)
{
  int i, j, n;
  isl_pw_multi_aff *res;

  if (!pma || !subs)
    return isl_pw_multi_aff_free(pma);

  n = pma->n * subs->n;
  res = isl_pw_multi_aff_alloc_size(isl_space_copy(pma->dim), n);

  for (i = 0; i < pma->n; ++i180) {
    for (j = 0; j < subs->n; ++j360) {
      isl_set *common;
      isl_multi_aff *res_ij;
      int empty;

      common = isl_set_intersect(
          isl_set_copy(pma->p[i].set),
          isl_set_copy(subs->p[j].set));
      common = isl_set_substitute(common,
          type, pos, subs->p[j].aff);
      empty = isl_set_plain_is_empty(common);
      if (empty < 0 || empty) {
        isl_set_free(common);
        if (empty < 0)
          goto error;
        continue;
      }

      res_ij = isl_multi_aff_substitute(
          isl_multi_aff_copy(pma->p[i].maff),
          type, pos, subs->p[j].aff);

      res = isl_pw_multi_aff_add_piece(res, common, res_ij);
    }
  }

  isl_pw_multi_aff_free(pma);
  return res;
5395

Coverage Report

Created: 2019-07-24 05:18