isl_box.c

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/*
 * Copyright 2010-2011 INRIA Saclay
 * Copyright 2012-2013 Ecole Normale Superieure
 *
 * Use of this software is governed by the MIT license
 *
 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
 * 91893 Orsay, France
 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
 */
 
#include <isl/val.h>
#include <isl/space.h>
#include <isl_map_private.h>
#include <isl_aff_private.h>
#include <isl/constraint.h>
#include <isl/ilp.h>
#include <isl/fixed_box.h>
 
/* Representation of a box of fixed size containing the elements
 * [offset, offset + size).
 * "size" lives in the target space of "offset".
 *
 * If any of the "offsets" is NaN, then the object represents
 * the failure of finding a fixed-size box.
 */
struct isl_fixed_box {
  isl_multi_aff *offset;
  isl_multi_val *size;
};
 
/* Free "box" and return NULL.
 */
__isl_null isl_fixed_box *isl_fixed_box_free(__isl_take isl_fixed_box *box)
{
  if (!box)
    return NULL;
  isl_multi_aff_free(box->offset);
  isl_multi_val_free(box->size);
  free(box);
  return NULL;
}
 
/* Construct an isl_fixed_box with the given offset and size.
 */
static __isl_give isl_fixed_box *isl_fixed_box_alloc(
  __isl_take isl_multi_aff *offset, __isl_take isl_multi_val *size)
{
  isl_ctx *ctx;
  isl_fixed_box *box;
 
  if (!offset || !size)
    goto error;
  ctx = isl_multi_aff_get_ctx(offset);
  box = isl_alloc_type(ctx, struct isl_fixed_box);
  if (!box)
    goto error;
  box->offset = offset;
  box->size = size;
 
  return box;
error:
  isl_multi_aff_free(offset);
  isl_multi_val_free(size);
  return NULL;
}
 
/* Construct an initial isl_fixed_box with zero offsets
 * in the given space and zero corresponding sizes.
 */
static __isl_give isl_fixed_box *isl_fixed_box_init(
  __isl_take isl_space *space)
{
  isl_multi_aff *offset;
  isl_multi_val *size;
 
  offset = isl_multi_aff_zero(isl_space_copy(space));
  space = isl_space_drop_all_params(isl_space_range(space));
  size = isl_multi_val_zero(space);
  return isl_fixed_box_alloc(offset, size);
}
 
/* Return a copy of "box".
 */
__isl_give isl_fixed_box *isl_fixed_box_copy(__isl_keep isl_fixed_box *box)
{
  isl_multi_aff *offset;
  isl_multi_val *size;
 
  offset = isl_fixed_box_get_offset(box);
  size = isl_fixed_box_get_size(box);
  return isl_fixed_box_alloc(offset, size);
}
 
/* Replace the offset and size in direction "pos" by "offset" and "size"
 * (without checking whether "box" is a valid box).
 */
static __isl_give isl_fixed_box *isl_fixed_box_set_extent(
  __isl_take isl_fixed_box *box, int pos, __isl_keep isl_aff *offset,
  __isl_keep isl_val *size)
{
  if (!box)
    return NULL;
  box->offset = isl_multi_aff_set_aff(box->offset, pos,
              isl_aff_copy(offset));
  box->size = isl_multi_val_set_val(box->size, pos, isl_val_copy(size));
  if (!box->offset || !box->size)
    return isl_fixed_box_free(box);
  return box;
}
 
/* Replace the offset and size in direction "pos" by "offset" and "size",
 * if "box" is a valid box.
 */
static __isl_give isl_fixed_box *isl_fixed_box_set_valid_extent(
  __isl_take isl_fixed_box *box, int pos, __isl_keep isl_aff *offset,
  __isl_keep isl_val *size)
{
  isl_bool valid;
 
  valid = isl_fixed_box_is_valid(box);
  if (valid < 0 || !valid)
    return box;
  return isl_fixed_box_set_extent(box, pos, offset, size);
}
 
/* Replace "box" by an invalid box, by setting all offsets to NaN
 * (and all sizes to infinity).
 */
static __isl_give isl_fixed_box *isl_fixed_box_invalidate(
  __isl_take isl_fixed_box *box)
{
  int i;
  isl_size n;
  isl_space *space;
  isl_val *infty;
  isl_aff *nan;
 
  if (!box)
    return NULL;
  n = isl_multi_val_dim(box->size, isl_dim_set);
  if (n < 0)
    return isl_fixed_box_free(box);
 
  infty = isl_val_infty(isl_fixed_box_get_ctx(box));
  space = isl_space_domain(isl_fixed_box_get_space(box));
  nan = isl_aff_nan_on_domain(isl_local_space_from_space(space));
  for (i = 0; i < n; ++i)
    box = isl_fixed_box_set_extent(box, i, nan, infty);
  isl_aff_free(nan);
  isl_val_free(infty);
 
  if (!box->offset || !box->size)
    return isl_fixed_box_free(box);
  return box;
}
 
/* Project the domain of the fixed box onto its parameter space.
 * In particular, project out the domain of the offset.
 */
static __isl_give isl_fixed_box *isl_fixed_box_project_domain_on_params(
  __isl_take isl_fixed_box *box)
{
  isl_bool valid;
 
  valid = isl_fixed_box_is_valid(box);
  if (valid < 0)
    return isl_fixed_box_free(box);
  if (!valid)
    return box;
 
  box->offset = isl_multi_aff_project_domain_on_params(box->offset);
  if (!box->offset)
    return isl_fixed_box_free(box);
 
  return box;
}
 
/* Return the isl_ctx to which "box" belongs.
 */
isl_ctx *isl_fixed_box_get_ctx(__isl_keep isl_fixed_box *box)
{
  if (!box)
    return NULL;
  return isl_multi_aff_get_ctx(box->offset);
}
 
/* Return the space in which "box" lives.
 */
__isl_give isl_space *isl_fixed_box_get_space(__isl_keep isl_fixed_box *box)
{
  if (!box)
    return NULL;
  return isl_multi_aff_get_space(box->offset);
}
 
/* Does "box" contain valid information?
 */
isl_bool isl_fixed_box_is_valid(__isl_keep isl_fixed_box *box)
{
  if (!box)
    return isl_bool_error;
  return isl_bool_not(isl_multi_aff_involves_nan(box->offset));
}
 
/* Return the offsets of the box "box".
 */
__isl_give isl_multi_aff *isl_fixed_box_get_offset(
  __isl_keep isl_fixed_box *box)
{
  if (!box)
    return NULL;
  return isl_multi_aff_copy(box->offset);
}
 
/* Return the sizes of the box "box".
 */
__isl_give isl_multi_val *isl_fixed_box_get_size(__isl_keep isl_fixed_box *box)
{
  if (!box)
    return NULL;
  return isl_multi_val_copy(box->size);
}
 
/* Data used in set_dim_extent and compute_size_in_direction.
 *
 * "bset" is a wrapped copy of the basic map that has the selected
 * output dimension as range.
 * "pos" is the position of the variable representing the output dimension,
 * i.e., the variable for which the size should be computed.  This variable
 * is also the last variable in "bset".
 * "size" is the best size found so far
 * (infinity if no offset was found so far).
 * "offset" is the offset corresponding to the best size
 * (NULL if no offset was found so far).
 */
struct isl_size_info {
  isl_basic_set *bset;
  isl_size pos;
  isl_val *size;
  isl_aff *offset;
};
 
/* Is "c" a suitable bound on dimension "pos" for use as a lower bound
 * of a fixed-size range.
 * In particular, it needs to be a lower bound on "pos".
 * In order for the final offset not to be too complicated,
 * the constraint itself should also not involve any integer divisions.
 */
static isl_bool is_suitable_bound(__isl_keep isl_constraint *c, unsigned pos)
{
  isl_size n_div;
  isl_bool is_bound, any_divs;
 
  is_bound = isl_constraint_is_lower_bound(c, isl_dim_set, pos);
  if (is_bound < 0 || !is_bound)
    return is_bound;
 
  n_div = isl_constraint_dim(c, isl_dim_div);
  if (n_div < 0)
    return isl_bool_error;
  any_divs = isl_constraint_involves_dims(c, isl_dim_div, 0, n_div);
  return isl_bool_not(any_divs);
}
 
/* Given a constraint from the basic set describing the bounds on
 * an array index, check if it is a lower bound, say m i >= b(x), and,
 * if so, check whether the expression "i - ceil(b(x)/m) + 1" has a constant
 * upper bound.  If so, and if this bound is smaller than any bound
 * derived from earlier constraints, set the size to this bound on
 * the expression and the lower bound to ceil(b(x)/m).
 */
static isl_stat compute_size_in_direction(__isl_take isl_constraint *c,
  void *user)
{
  struct isl_size_info *info = user;
  isl_val *v;
  isl_aff *aff;
  isl_aff *lb;
  isl_bool is_bound, better;
 
  is_bound = is_suitable_bound(c, info->pos);
  if (is_bound < 0 || !is_bound) {
    isl_constraint_free(c);
    return is_bound < 0 ? isl_stat_error : isl_stat_ok;
  }
 
  aff = isl_constraint_get_bound(c, isl_dim_set, info->pos);
  aff = isl_aff_ceil(aff);
 
  lb = isl_aff_copy(aff);
 
  aff = isl_aff_neg(aff);
  aff = isl_aff_add_coefficient_si(aff, isl_dim_in, info->pos, 1);
 
  v = isl_basic_set_max_val(info->bset, aff);
  isl_aff_free(aff);
 
  v = isl_val_add_ui(v, 1);
  better = isl_val_lt(v, info->size);
  if (better >= 0 && better) {
    isl_val_free(info->size);
    info->size = isl_val_copy(v);
    lb = isl_aff_domain_factor_domain(lb);
    isl_aff_free(info->offset);
    info->offset = isl_aff_copy(lb);
  }
  isl_val_free(v);
  isl_aff_free(lb);
 
  isl_constraint_free(c);
 
  return better < 0 ? isl_stat_error : isl_stat_ok;
}
 
/* Look for a fixed-size range of values for the output dimension "pos"
 * of "map", by looking for a lower-bound expression in the parameters
 * and input dimensions such that the range of the output dimension
 * is a constant shifted by this expression.
 *
 * In particular, look through the explicit lower bounds on the output dimension
 * for candidate expressions and pick the one that results in the smallest size.
 * Initialize the size with infinity and if no better size is found
 * then invalidate the box.  Otherwise, set the offset and size
 * in the given direction by those that correspond to the smallest size.
 *
 * Note that while evaluating the size corresponding to a lower bound,
 * an affine expression is constructed from the lower bound.
 * This lower bound may therefore not have any unknown local variables.
 * Eliminate any unknown local variables up front.
 * No such restriction needs to be imposed on the set over which
 * the size is computed.
 */
static __isl_give isl_fixed_box *set_dim_extent(__isl_take isl_fixed_box *box,
  __isl_keep isl_map *map, int pos)
{
  struct isl_size_info info;
  isl_bool valid;
  isl_ctx *ctx;
  isl_basic_set *bset;
 
  if (!box || !map)
    return isl_fixed_box_free(box);
 
  ctx = isl_map_get_ctx(map);
  map = isl_map_copy(map);
  map = isl_map_project_onto(map, isl_dim_out, pos, 1);
  info.size = isl_val_infty(ctx);
  info.offset = NULL;
  info.pos = isl_map_dim(map, isl_dim_in);
  info.bset = isl_basic_map_wrap(isl_map_simple_hull(map));
  bset = isl_basic_set_copy(info.bset);
  bset = isl_basic_set_remove_unknown_divs(bset);
  if (info.pos < 0)
    bset = isl_basic_set_free(bset);
  if (isl_basic_set_foreach_constraint(bset,
          &compute_size_in_direction, &info) < 0)
    box = isl_fixed_box_free(box);
  isl_basic_set_free(bset);
  valid = isl_val_is_int(info.size);
  if (valid < 0)
    box = isl_fixed_box_free(box);
  else if (valid)
    box = isl_fixed_box_set_valid_extent(box, pos,
                 info.offset, info.size);
  else
    box = isl_fixed_box_invalidate(box);
  isl_val_free(info.size);
  isl_aff_free(info.offset);
  isl_basic_set_free(info.bset);
 
  return box;
}
 
/* Try and construct a fixed-size rectangular box with an offset
 * in terms of the domain of "map" that contains the range of "map".
 * If no such box can be constructed, then return an invalidated box,
 * i.e., one where isl_fixed_box_is_valid returns false.
 *
 * Iterate over the dimensions in the range
 * setting the corresponding offset and extent.
 */
__isl_give isl_fixed_box *isl_map_get_range_simple_fixed_box_hull(
  __isl_keep isl_map *map)
{
  int i;
  isl_size n;
  isl_space *space;
  isl_fixed_box *box;
 
  n = isl_map_dim(map, isl_dim_out);
  if (n < 0)
    return NULL;
  space = isl_map_get_space(map);
  box = isl_fixed_box_init(space);
 
  map = isl_map_detect_equalities(isl_map_copy(map));
  for (i = 0; i < n; ++i) {
    isl_bool valid;
 
    box = set_dim_extent(box, map, i);
    valid = isl_fixed_box_is_valid(box);
    if (valid < 0 || !valid)
      break;
  }
  isl_map_free(map);
 
  return box;
}
 
/* Compute a fixed box from "set" using "map_box" by treating it as a map
 * with a zero-dimensional domain and
 * project out the domain again from the result.
 */
static __isl_give isl_fixed_box *fixed_box_as_map(__isl_keep isl_set *set,
  __isl_give isl_fixed_box *(*map_box)(__isl_keep isl_map *map))
{
  isl_map *map;
  isl_fixed_box *box;
 
  map = isl_map_from_range(isl_set_copy(set));
  box = map_box(map);
  isl_map_free(map);
  box = isl_fixed_box_project_domain_on_params(box);
 
  return box;
}
 
/* Try and construct a fixed-size rectangular box with an offset
 * in terms of the parameters of "set" that contains "set".
 * If no such box can be constructed, then return an invalidated box,
 * i.e., one where isl_fixed_box_is_valid returns false.
 *
 * Compute the box using isl_map_get_range_simple_fixed_box_hull
 * by constructing a map from the set and
 * project out the domain again from the result.
 */
__isl_give isl_fixed_box *isl_set_get_simple_fixed_box_hull(
  __isl_keep isl_set *set)
{
  return fixed_box_as_map(set, &isl_map_get_range_simple_fixed_box_hull);
}
 
/* Check whether the output elements lie on a rectangular lattice,
 * possibly depending on the parameters and the input dimensions.
 * Return a tile in this lattice.
 * If no stride information can be found, then return a tile of size 1
 * (and offset 0).
 *
 * Obtain stride information in each output dimension separately and
 * combine the results.
 */
__isl_give isl_fixed_box *isl_map_get_range_lattice_tile(
  __isl_keep isl_map *map)
{
  int i;
  isl_size n;
  isl_space *space;
  isl_fixed_box *box;
 
  n = isl_map_dim(map, isl_dim_out);
  if (n < 0)
    return NULL;
  space = isl_map_get_space(map);
  box = isl_fixed_box_init(space);
 
  for (i = 0; i < n; ++i) {
    isl_val *stride;
    isl_aff *offset;
    isl_stride_info *si;
 
    si = isl_map_get_range_stride_info(map, i);
    stride = isl_stride_info_get_stride(si);
    offset = isl_stride_info_get_offset(si);
    isl_stride_info_free(si);
 
    box = isl_fixed_box_set_valid_extent(box, i, offset, stride);
 
    isl_aff_free(offset);
    isl_val_free(stride);
  }
 
  return box;
}
 
/* Check whether the elements lie on a rectangular lattice,
 * possibly depending on the parameters.
 * Return a tile in this lattice.
 * If no stride information can be found, then return a tile of size 1
 * (and offset 0).
 *
 * Consider the set as a map with a zero-dimensional domain and
 * obtain a lattice tile of that map.
 */
__isl_give isl_fixed_box *isl_set_get_lattice_tile(__isl_keep isl_set *set)
{
  return fixed_box_as_map(set, &isl_map_get_range_lattice_tile);
}
 
#undef BASE
#define BASE multi_val
#include "print_yaml_field_templ.c"
 
#undef BASE
#define BASE multi_aff
#include "print_yaml_field_templ.c"
 
/* Print the information contained in "box" to "p".
 * The information is printed as a YAML document.
 */
__isl_give isl_printer *isl_printer_print_fixed_box(
  __isl_take isl_printer *p, __isl_keep isl_fixed_box *box)
{
  if (!box)
    return isl_printer_free(p);
 
  p = isl_printer_yaml_start_mapping(p);
  p = print_yaml_field_multi_aff(p, "offset", box->offset);
  p = print_yaml_field_multi_val(p, "size", box->size);
  p = isl_printer_yaml_end_mapping(p);
 
  return p;
}
 
#undef BASE
#define BASE fixed_box
#include <print_templ_yaml.c>