pip.c

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/*
 * Copyright 2008-2009 Katholieke Universiteit Leuven
 *
 * Use of this software is governed by the MIT license
 *
 * Written by Sven Verdoolaege, K.U.Leuven, Departement
 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
 */
 
#include <assert.h>
#include <string.h>
#include <isl_map_private.h>
#include <isl/aff.h>
#include <isl/set.h>
#include "isl_sample.h"
#include "isl_scan.h"
#include <isl_seq.h>
#include <isl_ilp_private.h>
#include <isl/printer.h>
#include <isl_point_private.h>
#include <isl_vec_private.h>
#include <isl/options.h>
#include <isl_config.h>
 
/* The input of this program is the same as that of the "example" program
 * from the PipLib distribution, except that the "big parameter column"
 * should always be -1.
 *
 * Context constraints in PolyLib format
 * -1
 * Problem constraints in PolyLib format
 * Optional list of options
 *
 * The options are
 *  Maximize  compute maximum instead of minimum
 *  Rational  compute rational optimum instead of integer optimum
 *  Urs_parms don't assume parameters are non-negative
 *  Urs_unknowns  don't assume unknowns are non-negative
 */
 
struct options {
  struct isl_options  *isl;
  unsigned     verify;
  unsigned     format;
};
 
#define FORMAT_SET  0
#define FORMAT_AFF  1
 
struct isl_arg_choice pip_format[] = {
  {"set",   FORMAT_SET},
  {"affine",  FORMAT_AFF},
  {0}
};
 
ISL_ARGS_START(struct options, options_args)
ISL_ARG_CHILD(struct options, isl, "isl", &isl_options_args, "isl options")
ISL_ARG_BOOL(struct options, verify, 'T', "verify", 0, NULL)
ISL_ARG_CHOICE(struct options, format, 0, "format",
  pip_format, FORMAT_SET, "output format")
ISL_ARGS_END
 
ISL_ARG_DEF(options, struct options, options_args)
 
static __isl_give isl_basic_set *set_bounds(__isl_take isl_basic_set *bset)
{
  isl_size nparam;
  int i, r;
  isl_point *pt, *pt2;
  isl_basic_set *box;
 
  nparam = isl_basic_set_dim(bset, isl_dim_param);
  if (nparam < 0)
    return isl_basic_set_free(bset);
  r = nparam >= 8 ? 4 : nparam >= 5 ? 6 : 30;
 
  pt = isl_basic_set_sample_point(isl_basic_set_copy(bset));
  pt2 = isl_point_copy(pt);
 
  for (i = 0; i < nparam; ++i) {
    pt = isl_point_add_ui(pt, isl_dim_param, i, r);
    pt2 = isl_point_sub_ui(pt2, isl_dim_param, i, r);
  }
 
  box = isl_basic_set_box_from_points(pt, pt2);
 
  return isl_basic_set_intersect(bset, box);
}
 
static __isl_give isl_basic_set *to_parameter_domain(
  __isl_take isl_basic_set *context)
{
  isl_size dim;
 
  dim = isl_basic_set_dim(context, isl_dim_set);
  if (dim < 0)
    return isl_basic_set_free(context);
  context = isl_basic_set_move_dims(context, isl_dim_param, 0,
        isl_dim_set, 0, dim);
  context = isl_basic_set_params(context);
  return context;
}
 
/* If "context" has more parameters than "bset", then reinterpret
 * the last dimensions of "bset" as parameters.
 */
static __isl_give isl_basic_set *move_parameters(__isl_take isl_basic_set *bset,
  __isl_keep isl_basic_set *context)
{
  isl_size nparam, nparam_bset, dim;
 
  nparam = isl_basic_set_dim(context, isl_dim_param);
  nparam_bset = isl_basic_set_dim(bset, isl_dim_param);
  if (nparam < 0 || nparam_bset < 0)
    return isl_basic_set_free(bset);
  if (nparam == nparam_bset)
    return bset;
  dim = isl_basic_set_dim(bset, isl_dim_set);
  if (dim < 0)
    return isl_basic_set_free(bset);
  bset = isl_basic_set_move_dims(bset, isl_dim_param, 0,
              isl_dim_set, dim - nparam, nparam);
  return bset;
}
 
/* Plug in the initial values of "params" for the parameters in "bset" and
 * return the result.  The remaining entries in "params", if any,
 * correspond to the existentially quantified variables in the description
 * of the original context and can be ignored.
 */
static __isl_give isl_basic_set *plug_in_parameters(
  __isl_take isl_basic_set *bset, __isl_take isl_vec *params)
{
  int i;
  isl_size n;
 
  n = isl_basic_set_dim(bset, isl_dim_param);
  if (n < 0)
    bset = isl_basic_set_free(bset);
  for (i = 0; i < n; ++i)
    bset = isl_basic_set_fix(bset,
           isl_dim_param, i, params->el[1 + i]);
 
  bset = isl_basic_set_remove_dims(bset, isl_dim_param, 0, n);
 
  isl_vec_free(params);
 
  return bset;
}
 
/* Plug in the initial values of "params" for the parameters in "set" and
 * return the result.  The remaining entries in "params", if any,
 * correspond to the existentially quantified variables in the description
 * of the original context and can be ignored.
 */
static __isl_give isl_set *set_plug_in_parameters(__isl_take isl_set *set,
  __isl_take isl_vec *params)
{
  int i;
  isl_size n;
 
  n = isl_set_dim(set, isl_dim_param);
  if (n < 0)
    set = isl_set_free(set);
  for (i = 0; i < n; ++i)
    set = isl_set_fix(set, isl_dim_param, i, params->el[1 + i]);
 
  set = isl_set_remove_dims(set, isl_dim_param, 0, n);
 
  isl_vec_free(params);
 
  return set;
}
 
/* Compute the lexicographically minimal (or maximal if max is set)
 * element of bset for the given values of the parameters, by
 * successively solving an ilp problem in each direction.
 */
static __isl_give isl_vec *opt_at(__isl_take isl_basic_set *bset,
  __isl_take isl_vec *params, int max)
{
  isl_size dim;
  isl_ctx *ctx;
  struct isl_vec *opt;
  struct isl_vec *obj;
  int i;
 
  dim = isl_basic_set_dim(bset, isl_dim_set);
  if (dim < 0)
    goto error;
 
  bset = plug_in_parameters(bset, params);
 
  ctx = isl_basic_set_get_ctx(bset);
  if (isl_basic_set_plain_is_empty(bset)) {
    opt = isl_vec_alloc(ctx, 0);
    isl_basic_set_free(bset);
    return opt;
  }
 
  opt = isl_vec_alloc(ctx, 1 + dim);
  assert(opt);
 
  obj = isl_vec_alloc(ctx, 1 + dim);
  assert(obj);
 
  isl_int_set_si(opt->el[0], 1);
  isl_int_set_si(obj->el[0], 0);
 
  for (i = 0; i < dim; ++i) {
    enum isl_lp_result res;
 
    isl_seq_clr(obj->el + 1, dim);
    isl_int_set_si(obj->el[1 + i], 1);
    res = isl_basic_set_solve_ilp(bset, max, obj->el,
            &opt->el[1 + i], NULL);
    if (res == isl_lp_empty)
      goto empty;
    assert(res == isl_lp_ok);
    bset = isl_basic_set_fix(bset, isl_dim_set, i, opt->el[1 + i]);
  }
 
  isl_basic_set_free(bset);
  isl_vec_free(obj);
 
  return opt;
error:
  isl_basic_set_free(bset);
  isl_vec_free(params);
  return NULL;
empty:
  isl_vec_free(opt);
  opt = isl_vec_alloc(ctx, 0);
  isl_basic_set_free(bset);
  isl_vec_free(obj);
 
  return opt;
}
 
struct isl_scan_pip {
  struct isl_scan_callback callback;
  isl_basic_set *bset;
  isl_set *sol;
  isl_set *empty;
  int stride;
  int n;
  int max;
};
 
/* Check if the "manually" computed optimum of bset at the "sample"
 * values of the parameters agrees with the solution of pilp problem
 * represented by the pair (sol, empty).
 * In particular, if there is no solution for this value of the parameters,
 * then it should be an element of the parameter domain "empty".
 * Otherwise, the optimal solution, should be equal to the result of
 * plugging in the value of the parameters in "sol".
 */
static isl_stat scan_one(struct isl_scan_callback *callback,
  __isl_take isl_vec *sample)
{
  struct isl_scan_pip *sp = (struct isl_scan_pip *)callback;
  struct isl_vec *opt;
 
  sp->n--;
 
  opt = opt_at(isl_basic_set_copy(sp->bset), isl_vec_copy(sample), sp->max);
  assert(opt);
 
  if (opt->size == 0) {
    isl_point *sample_pnt;
    sample_pnt = isl_point_alloc(isl_set_get_space(sp->empty), sample);
    assert(isl_set_contains_point(sp->empty, sample_pnt));
    isl_point_free(sample_pnt);
    isl_vec_free(opt);
  } else {
    isl_set *sol;
    isl_set *opt_set;
    opt_set = isl_set_from_basic_set(isl_basic_set_from_vec(opt));
    sol = set_plug_in_parameters(isl_set_copy(sp->sol), sample);
    assert(isl_set_is_equal(opt_set, sol));
    isl_set_free(sol);
    isl_set_free(opt_set);
  }
 
  if (!(sp->n % sp->stride)) {
    printf("o");
    fflush(stdout);
  }
 
  return sp->n >= 1 ? isl_stat_ok : isl_stat_error;
}
 
static void check_solution(isl_basic_set *bset, isl_basic_set *context,
  isl_set *sol, isl_set *empty, int max)
{
  struct isl_scan_pip sp;
  isl_int count, count_max;
  int i, n;
  int r;
 
  context = set_bounds(context);
  context = isl_basic_set_underlying_set(context);
 
  isl_int_init(count);
  isl_int_init(count_max);
 
  isl_int_set_si(count_max, 2000);
  r = isl_basic_set_count_upto(context, count_max, &count);
  assert(r >= 0);
  n = isl_int_get_si(count);
 
  isl_int_clear(count_max);
  isl_int_clear(count);
 
  sp.callback.add = scan_one;
  sp.bset = bset;
  sp.sol = sol;
  sp.empty = empty;
  sp.n = n;
  sp.stride = n > 70 ? 1 + (n + 1)/70 : 1;
  sp.max = max;
 
  for (i = 0; i < n; i += sp.stride)
    printf(".");
  printf("\r");
  fflush(stdout);
 
  isl_basic_set_scan(context, &sp.callback);
 
  printf("\n");
 
  isl_basic_set_free(bset);
}
 
int main(int argc, char **argv)
{
  struct isl_ctx *ctx;
  struct isl_basic_set *context, *bset, *copy, *context_copy;
  struct isl_set *set = NULL;
  struct isl_set *empty;
  isl_pw_multi_aff *pma = NULL;
  int neg_one;
  char s[1024];
  int urs_parms = 0;
  int urs_unknowns = 0;
  int max = 0;
  int rational = 0;
  int n;
  struct options *options;
 
  options = options_new_with_defaults();
  assert(options);
  argc = options_parse(options, argc, argv, ISL_ARG_ALL);
 
  ctx = isl_ctx_alloc_with_options(&options_args, options);
 
  context = isl_basic_set_read_from_file(ctx, stdin);
  assert(context);
  n = fscanf(stdin, "%d", &neg_one);
  assert(n == 1);
  assert(neg_one == -1);
  bset = isl_basic_set_read_from_file(ctx, stdin);
 
  while (fgets(s, sizeof(s), stdin)) {
    if (strncasecmp(s, "Maximize", 8) == 0)
      max = 1;
    if (strncasecmp(s, "Rational", 8) == 0) {
      rational = 1;
      bset = isl_basic_set_set_rational(bset);
    }
    if (strncasecmp(s, "Urs_parms", 9) == 0)
      urs_parms = 1;
    if (strncasecmp(s, "Urs_unknowns", 12) == 0)
      urs_unknowns = 1;
  }
  if (!urs_parms)
    context = isl_basic_set_intersect(context,
    isl_basic_set_positive_orthant(isl_basic_set_get_space(context)));
  context = to_parameter_domain(context);
  bset = move_parameters(bset, context);
  if (!urs_unknowns)
    bset = isl_basic_set_intersect(bset,
    isl_basic_set_positive_orthant(isl_basic_set_get_space(bset)));
 
  if (options->verify) {
    copy = isl_basic_set_copy(bset);
    context_copy = isl_basic_set_copy(context);
  }
 
  if (options->format == FORMAT_AFF) {
    if (max)
      pma = isl_basic_set_partial_lexmax_pw_multi_aff(bset,
                context, &empty);
    else
      pma = isl_basic_set_partial_lexmin_pw_multi_aff(bset,
                context, &empty);
  } else {
    if (max)
      set = isl_basic_set_partial_lexmax(bset,
                context, &empty);
    else
      set = isl_basic_set_partial_lexmin(bset,
                context, &empty);
  }
 
  if (options->verify) {
    assert(!rational);
    if (options->format == FORMAT_AFF)
      set = isl_set_from_pw_multi_aff(pma);
    check_solution(copy, context_copy, set, empty, max);
    isl_set_free(set);
  } else {
    isl_printer *p;
    p = isl_printer_to_file(ctx, stdout);
    if (options->format == FORMAT_AFF)
      p = isl_printer_print_pw_multi_aff(p, pma);
    else
      p = isl_printer_print_set(p, set);
    p = isl_printer_end_line(p);
    p = isl_printer_print_str(p, "no solution: ");
    p = isl_printer_print_set(p, empty);
    p = isl_printer_end_line(p);
    isl_printer_free(p);
    isl_set_free(set);
    isl_pw_multi_aff_free(pma);
  }
 
  isl_set_free(empty);
  isl_ctx_free(ctx);
 
  return 0;
}