isl_range.c

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#include <isl_ctx_private.h>
#include <isl/val.h>
#include <isl_constraint_private.h>
#include <isl/set.h>
#include <isl_polynomial_private.h>
#include <isl_morph.h>
#include <isl_range.h>
 
struct range_data {
  struct isl_bound  *bound;
  int           *signs;
  int     sign;
  int     test_monotonicity;
  int         monotonicity;
  int     tight;
  isl_qpolynomial       *poly;
  isl_pw_qpolynomial_fold *pwf;
  isl_pw_qpolynomial_fold *pwf_tight;
};
 
static isl_stat propagate_on_domain(__isl_take isl_basic_set *bset,
  __isl_take isl_qpolynomial *poly, struct range_data *data);
 
/* Check whether the polynomial "poly" has sign "sign" over "bset",
 * i.e., if sign == 1, check that the lower bound on the polynomial
 * is non-negative and if sign == -1, check that the upper bound on
 * the polynomial is non-positive.
 */
static isl_bool has_sign(__isl_keep isl_basic_set *bset,
  __isl_keep isl_qpolynomial *poly, int sign, int *signs)
{
  struct range_data data_m;
  isl_size nparam;
  isl_space *space;
  isl_val *opt;
  isl_bool r;
  enum isl_fold type;
 
  nparam = isl_basic_set_dim(bset, isl_dim_param);
  if (nparam < 0)
    return isl_bool_error;
 
  bset = isl_basic_set_copy(bset);
  poly = isl_qpolynomial_copy(poly);
 
  bset = isl_basic_set_move_dims(bset, isl_dim_set, 0,
          isl_dim_param, 0, nparam);
  poly = isl_qpolynomial_move_dims(poly, isl_dim_in, 0,
          isl_dim_param, 0, nparam);
 
  space = isl_qpolynomial_get_space(poly);
  space = isl_space_params(space);
  space = isl_space_from_domain(space);
  space = isl_space_add_dims(space, isl_dim_out, 1);
 
  data_m.test_monotonicity = 0;
  data_m.signs = signs;
  data_m.sign = -sign;
  type = data_m.sign < 0 ? isl_fold_min : isl_fold_max;
  data_m.pwf = isl_pw_qpolynomial_fold_zero(space, type);
  data_m.tight = 0;
  data_m.pwf_tight = NULL;
 
  if (propagate_on_domain(bset, poly, &data_m) < 0)
    goto error;
 
  if (sign > 0)
    opt = isl_pw_qpolynomial_fold_min(data_m.pwf);
  else
    opt = isl_pw_qpolynomial_fold_max(data_m.pwf);
 
  if (!opt)
    r = isl_bool_error;
  else if (isl_val_is_nan(opt) ||
     isl_val_is_infty(opt) ||
     isl_val_is_neginfty(opt))
    r = isl_bool_false;
  else
    r = isl_bool_ok(sign * isl_val_sgn(opt) >= 0);
 
  isl_val_free(opt);
 
  return r;
error:
  isl_pw_qpolynomial_fold_free(data_m.pwf);
  return isl_bool_error;
}
 
/* Return  1 if poly is monotonically increasing in the last set variable,
 *        -1 if poly is monotonically decreasing in the last set variable,
 *     0 if no conclusion,
 *    -2 on error.
 *
 * We simply check the sign of p(x+1)-p(x)
 */
static int monotonicity(__isl_keep isl_basic_set *bset,
  __isl_keep isl_qpolynomial *poly, struct range_data *data)
{
  isl_ctx *ctx;
  isl_space *space;
  isl_qpolynomial *sub = NULL;
  isl_qpolynomial *diff = NULL;
  int result = 0;
  isl_bool s;
  isl_size nvar;
 
  nvar = isl_basic_set_dim(bset, isl_dim_set);
  if (nvar < 0)
    return -2;
 
  ctx = isl_qpolynomial_get_ctx(poly);
  space = isl_qpolynomial_get_domain_space(poly);
 
  sub = isl_qpolynomial_var_on_domain(isl_space_copy(space),
            isl_dim_set, nvar - 1);
  sub = isl_qpolynomial_add(sub,
    isl_qpolynomial_rat_cst_on_domain(space, ctx->one, ctx->one));
 
  diff = isl_qpolynomial_substitute(isl_qpolynomial_copy(poly),
      isl_dim_in, nvar - 1, 1, &sub);
  diff = isl_qpolynomial_sub(diff, isl_qpolynomial_copy(poly));
 
  s = has_sign(bset, diff, 1, data->signs);
  if (s < 0)
    goto error;
  if (s)
    result = 1;
  else {
    s = has_sign(bset, diff, -1, data->signs);
    if (s < 0)
      goto error;
    if (s)
      result = -1;
  }
 
  isl_qpolynomial_free(diff);
  isl_qpolynomial_free(sub);
 
  return result;
error:
  isl_qpolynomial_free(diff);
  isl_qpolynomial_free(sub);
  return -2;
}
 
/* Return a positive ("sign" > 0) or negative ("sign" < 0) infinite polynomial
 * with domain space "space".
 */
static __isl_give isl_qpolynomial *signed_infty(__isl_take isl_space *space,
  int sign)
{
  if (sign > 0)
    return isl_qpolynomial_infty_on_domain(space);
  else
    return isl_qpolynomial_neginfty_on_domain(space);
}
 
static __isl_give isl_qpolynomial *bound2poly(__isl_take isl_constraint *bound,
  __isl_take isl_space *space, unsigned pos, int sign)
{
  if (!bound)
    return signed_infty(space, sign);
  isl_space_free(space);
  return isl_qpolynomial_from_constraint(bound, isl_dim_set, pos);
}
 
static int bound_is_integer(__isl_keep isl_constraint *bound, unsigned pos)
{
  isl_int c;
  int is_int;
 
  if (!bound)
    return 1;
 
  isl_int_init(c);
  isl_constraint_get_coefficient(bound, isl_dim_set, pos, &c);
  is_int = isl_int_is_one(c) || isl_int_is_negone(c);
  isl_int_clear(c);
 
  return is_int;
}
 
struct isl_fixed_sign_data {
  int   *signs;
  int   sign;
  isl_qpolynomial *poly;
};
 
/* Add term "term" to data->poly if it has sign data->sign.
 * The sign is determined based on the signs of the parameters
 * and variables in data->signs.  The integer divisions, if
 * any, are assumed to be non-negative.
 */
static isl_stat collect_fixed_sign_terms(__isl_take isl_term *term, void *user)
{
  struct isl_fixed_sign_data *data = (struct isl_fixed_sign_data *)user;
  isl_int n;
  int i;
  int sign;
  isl_size nparam;
  isl_size nvar;
  isl_size exp;
 
  nparam = isl_term_dim(term, isl_dim_param);
  nvar = isl_term_dim(term, isl_dim_set);
  if (nparam < 0 || nvar < 0)
    return isl_stat_error;
 
  isl_int_init(n);
  isl_term_get_num(term, &n);
  sign = isl_int_sgn(n);
  isl_int_clear(n);
 
  for (i = 0; i < nparam; ++i) {
    if (data->signs[i] > 0)
      continue;
    exp = isl_term_get_exp(term, isl_dim_param, i);
    if (exp < 0)
      return isl_stat_error;
    if (exp % 2)
      sign = -sign;
  }
  for (i = 0; i < nvar; ++i) {
    if (data->signs[nparam + i] > 0)
      continue;
    exp = isl_term_get_exp(term, isl_dim_set, i);
    if (exp < 0)
      return isl_stat_error;
    if (exp % 2)
      sign = -sign;
  }
 
  if (sign == data->sign) {
    isl_qpolynomial *t = isl_qpolynomial_from_term(term);
 
    data->poly = isl_qpolynomial_add(data->poly, t);
  } else
    isl_term_free(term);
 
  return isl_stat_ok;
}
 
/* Construct and return a polynomial that consists of the terms
 * in "poly" that have sign "sign".  The integer divisions, if
 * any, are assumed to be non-negative.
 */
__isl_give isl_qpolynomial *isl_qpolynomial_terms_of_sign(
  __isl_keep isl_qpolynomial *poly, int *signs, int sign)
{
  isl_space *space;
  struct isl_fixed_sign_data data = { signs, sign };
 
  space = isl_qpolynomial_get_domain_space(poly);
  data.poly = isl_qpolynomial_zero_on_domain(space);
 
  if (isl_qpolynomial_foreach_term(poly, collect_fixed_sign_terms, &data) < 0)
    goto error;
 
  return data.poly;
error:
  isl_qpolynomial_free(data.poly);
  return NULL;
}
 
/* Helper function to add a guarded polynomial to either pwf_tight or pwf,
 * depending on whether the result has been determined to be tight.
 */
static isl_stat add_guarded_poly(__isl_take isl_basic_set *bset,
  __isl_take isl_qpolynomial *poly, struct range_data *data)
{
  enum isl_fold type = data->sign < 0 ? isl_fold_min : isl_fold_max;
  isl_set *set;
  isl_qpolynomial_fold *fold;
  isl_pw_qpolynomial_fold *pwf;
 
  bset = isl_basic_set_params(bset);
  poly = isl_qpolynomial_project_domain_on_params(poly);
 
  fold = isl_qpolynomial_fold_alloc(type, poly);
  set = isl_set_from_basic_set(bset);
  pwf = isl_pw_qpolynomial_fold_alloc(type, set, fold);
  if (data->tight)
    data->pwf_tight = isl_pw_qpolynomial_fold_fold(
            data->pwf_tight, pwf);
  else
    data->pwf = isl_pw_qpolynomial_fold_fold(data->pwf, pwf);
 
  return isl_stat_ok;
}
 
/* Plug in "sub" for the variable at position "pos" in "poly".
 *
 * If "sub" is an infinite polynomial and if the variable actually
 * appears in "poly", then calling isl_qpolynomial_substitute
 * to perform the substitution may result in a NaN result.
 * In such cases, return positive or negative infinity instead,
 * depending on whether an upper bound or a lower bound is being computed,
 * and mark the result as not being tight.
 */
static __isl_give isl_qpolynomial *plug_in_at_pos(
  __isl_take isl_qpolynomial *poly, int pos,
  __isl_take isl_qpolynomial *sub, struct range_data *data)
{
  isl_bool involves, infty;
 
  involves = isl_qpolynomial_involves_dims(poly, isl_dim_in, pos, 1);
  if (involves < 0)
    goto error;
  if (!involves) {
    isl_qpolynomial_free(sub);
    return poly;
  }
 
  infty = isl_qpolynomial_is_infty(sub);
  if (infty >= 0 && !infty)
    infty = isl_qpolynomial_is_neginfty(sub);
  if (infty < 0)
    goto error;
  if (infty) {
    isl_space *space = isl_qpolynomial_get_domain_space(poly);
    data->tight = 0;
    isl_qpolynomial_free(poly);
    isl_qpolynomial_free(sub);
    return signed_infty(space, data->sign);
  }
 
  poly = isl_qpolynomial_substitute(poly, isl_dim_in, pos, 1, &sub);
  isl_qpolynomial_free(sub);
 
  return poly;
error:
  isl_qpolynomial_free(poly);
  isl_qpolynomial_free(sub);
  return NULL;
}
 
/* Given a lower and upper bound on the final variable and constraints
 * on the remaining variables where these bounds are active,
 * eliminate the variable from data->poly based on these bounds.
 * If the polynomial has been determined to be monotonic
 * in the variable, then simply plug in the appropriate bound.
 * If the current polynomial is tight and if this bound is integer,
 * then the result is still tight.  In all other cases, the results
 * may not be tight.
 * Otherwise, plug in the largest bound (in absolute value) in
 * the positive terms (if an upper bound is wanted) or the negative terms
 * (if a lower bounded is wanted) and the other bound in the other terms.
 *
 * If all variables have been eliminated, then record the result.
 * Ohterwise, recurse on the next variable.
 */
static isl_stat propagate_on_bound_pair(__isl_take isl_constraint *lower,
  __isl_take isl_constraint *upper, __isl_take isl_basic_set *bset,
  void *user)
{
  struct range_data *data = (struct range_data *)user;
  int save_tight = data->tight;
  isl_qpolynomial *poly;
  isl_stat r;
  isl_size nvar, nparam;
 
  nvar = isl_basic_set_dim(bset, isl_dim_set);
  nparam = isl_basic_set_dim(bset, isl_dim_param);
  if (nvar < 0 || nparam < 0)
    goto error;
 
  if (data->monotonicity) {
    isl_qpolynomial *sub;
    isl_space *space = isl_qpolynomial_get_domain_space(data->poly);
    if (data->monotonicity * data->sign > 0) {
      if (data->tight)
        data->tight = bound_is_integer(upper, nvar);
      sub = bound2poly(upper, space, nvar, 1);
      isl_constraint_free(lower);
    } else {
      if (data->tight)
        data->tight = bound_is_integer(lower, nvar);
      sub = bound2poly(lower, space, nvar, -1);
      isl_constraint_free(upper);
    }
    poly = isl_qpolynomial_copy(data->poly);
    poly = plug_in_at_pos(poly, nvar, sub, data);
    poly = isl_qpolynomial_drop_dims(poly, isl_dim_in, nvar, 1);
  } else {
    isl_qpolynomial *l, *u;
    isl_qpolynomial *pos, *neg;
    isl_space *space = isl_qpolynomial_get_domain_space(data->poly);
    int sign = data->sign * data->signs[nparam + nvar];
 
    data->tight = 0;
 
    u = bound2poly(upper, isl_space_copy(space), nvar, 1);
    l = bound2poly(lower, space, nvar, -1);
 
    pos = isl_qpolynomial_terms_of_sign(data->poly, data->signs, sign);
    neg = isl_qpolynomial_terms_of_sign(data->poly, data->signs, -sign);
 
    pos = plug_in_at_pos(pos, nvar, u, data);
    neg = plug_in_at_pos(neg, nvar, l, data);
 
    poly = isl_qpolynomial_add(pos, neg);
    poly = isl_qpolynomial_drop_dims(poly, isl_dim_in, nvar, 1);
  }
 
  if (nvar == 0)
    r = add_guarded_poly(bset, poly, data);
  else
    r = propagate_on_domain(bset, poly, data);
 
  data->tight = save_tight;
 
  return r;
error:
  isl_constraint_free(lower);
  isl_constraint_free(upper);
  isl_basic_set_free(bset);
  return isl_stat_error;
}
 
/* Recursively perform range propagation on the polynomial "poly"
 * defined over the basic set "bset" and collect the results in "data".
 */
static isl_stat propagate_on_domain(__isl_take isl_basic_set *bset,
  __isl_take isl_qpolynomial *poly, struct range_data *data)
{
  isl_bool is_cst;
  isl_ctx *ctx;
  isl_qpolynomial *save_poly = data->poly;
  int save_monotonicity = data->monotonicity;
  isl_size d;
 
  d = isl_basic_set_dim(bset, isl_dim_set);
  is_cst = isl_qpolynomial_is_cst(poly, NULL, NULL);
  if (d < 0 || is_cst < 0)
    goto error;
 
  ctx = isl_basic_set_get_ctx(bset);
  isl_assert(ctx, d >= 1, goto error);
 
  if (is_cst) {
    bset = isl_basic_set_project_out(bset, isl_dim_set, 0, d);
    poly = isl_qpolynomial_drop_dims(poly, isl_dim_in, 0, d);
    return add_guarded_poly(bset, poly, data);
  }
 
  if (data->test_monotonicity)
    data->monotonicity = monotonicity(bset, poly, data);
  else
    data->monotonicity = 0;
  if (data->monotonicity < -1)
    goto error;
 
  data->poly = poly;
  if (isl_basic_set_foreach_bound_pair(bset, isl_dim_set, d - 1,
              &propagate_on_bound_pair, data) < 0)
    goto error;
 
  isl_basic_set_free(bset);
  isl_qpolynomial_free(poly);
  data->monotonicity = save_monotonicity;
  data->poly = save_poly;
 
  return isl_stat_ok;
error:
  isl_basic_set_free(bset);
  isl_qpolynomial_free(poly);
  data->monotonicity = save_monotonicity;
  data->poly = save_poly;
  return isl_stat_error;
}
 
static isl_stat basic_guarded_poly_bound(__isl_take isl_basic_set *bset,
  void *user)
{
  struct range_data *data = (struct range_data *)user;
  isl_ctx *ctx;
  isl_size nparam = isl_basic_set_dim(bset, isl_dim_param);
  isl_size dim = isl_basic_set_dim(bset, isl_dim_set);
  isl_size total = isl_basic_set_dim(bset, isl_dim_all);
  isl_stat r;
 
  data->signs = NULL;
 
  if (nparam < 0 || dim < 0 || total < 0)
    goto error;
 
  ctx = isl_basic_set_get_ctx(bset);
  data->signs = isl_alloc_array(ctx, int, total);
 
  if (isl_basic_set_dims_get_sign(bset, isl_dim_set, 0, dim,
          data->signs + nparam) < 0)
    goto error;
  if (isl_basic_set_dims_get_sign(bset, isl_dim_param, 0, nparam,
          data->signs) < 0)
    goto error;
 
  r = propagate_on_domain(bset, isl_qpolynomial_copy(data->poly), data);
 
  free(data->signs);
 
  return r;
error:
  free(data->signs);
  isl_basic_set_free(bset);
  return isl_stat_error;
}
 
static isl_stat qpolynomial_bound_on_domain_range(
  __isl_take isl_basic_set *bset, __isl_take isl_qpolynomial *poly,
  struct range_data *data)
{
  isl_size nparam = isl_basic_set_dim(bset, isl_dim_param);
  isl_size nvar = isl_basic_set_dim(bset, isl_dim_set);
  isl_set *set = NULL;
 
  if (nparam < 0 || nvar < 0)
    goto error;
 
  if (nvar == 0)
    return add_guarded_poly(bset, poly, data);
 
  set = isl_set_from_basic_set(bset);
  set = isl_set_split_dims(set, isl_dim_param, 0, nparam);
  set = isl_set_split_dims(set, isl_dim_set, 0, nvar);
 
  data->poly = poly;
 
  data->test_monotonicity = 1;
  if (isl_set_foreach_basic_set(set, &basic_guarded_poly_bound, data) < 0)
    goto error;
 
  isl_set_free(set);
  isl_qpolynomial_free(poly);
 
  return isl_stat_ok;
error:
  isl_set_free(set);
  isl_qpolynomial_free(poly);
  return isl_stat_error;
}
 
isl_stat isl_qpolynomial_bound_on_domain_range(__isl_take isl_basic_set *bset,
  __isl_take isl_qpolynomial *poly, struct isl_bound *bound)
{
  struct range_data data;
  isl_stat r;
 
  data.pwf = bound->pwf;
  data.pwf_tight = bound->pwf_tight;
  data.tight = bound->check_tight;
  if (bound->type == isl_fold_min)
    data.sign = -1;
  else
    data.sign = 1;
 
  r = qpolynomial_bound_on_domain_range(bset, poly, &data);
 
  bound->pwf = data.pwf;
  bound->pwf_tight = data.pwf_tight;
 
  return r;
}